Iterative methods for mixed finite element equations
NASA Technical Reports Server (NTRS)
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
An iterative algorithm for finite element analysis
NASA Astrophysics Data System (ADS)
Laouafa, F.; Royis, P.
2004-03-01
In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the GMRES algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration.
Material nonlinear analysis via mixed-iterative finite element method
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
Elastic-plastic mixed-iterative finite element analysis: Implementation and performance assessment
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1993-01-01
An elastic-plastic algorithm based on Von Mises and associative flow criteria is implemented in MHOST-a mixed iterative finite element analysis computer program developed by NASA Lewis Research Center. The performance of the resulting elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors of 4-node quadrilateral shell finite elements are tested for elastic-plastic performance. Generally, the membrane results are excellent, indicating the implementation of elastic-plastic mixed-iterative analysis is appropriate.
NASA Technical Reports Server (NTRS)
Muller, A.; Hughes, T. J. R.
1984-01-01
A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.
Failure analysis of laminated composites by using iterative three-dimensional finite element method
NASA Astrophysics Data System (ADS)
Hwang, W. C.; Sun, C. T.
1989-05-01
A failure analysis of laminated composites is accomplished by using an iterative three-dimensional finite element method. Based on Tsai-Wu failure theory, three different modes of failure are proposed: fiber breakage, matrix cracking, and delamination. The first ply failure load is then evaluated. As the applied load exceeds the first ply failure load, localized structural failure occurs and the global structural stiffness should change. The global stiffness matrix is modified by taking nonlinearity due to partial failures within a laminate into consideration. The first ply failure load is analyzed by using a iterative mixed field method in solving the linear part of the finite element equations. The progressive failure problem is solved numerically by using Newton-Raphson iterative schemes for the solution of nonlinear finite element equations. Numerical examples include angle-ply symmetric Thornel 300 graphite/934 resin epoxy laminates under uniaxial tension. First ply failure loads as well as the final failure loads are evaluated. Good correlation between analytical results and experimental data are observed. Numerical results also include the investigation of composite specimens with a centered hole, under uniaxial tension. Excellent correlation with the experimental data is observed.
NASA Technical Reports Server (NTRS)
Achar, N. S.; Gaonkar, G. H.
1993-01-01
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
NASA Technical Reports Server (NTRS)
Achar, N. S.; Gaonkar, G. H.
1993-01-01
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
NASA Astrophysics Data System (ADS)
Widdle, Richard D., Jr.; Grimshaw, Matthew T.; Shome, Moushumi
2009-03-01
A method is described for solving an inverse design problem to find the unassembled, stress-free component shapes of a structure thatis integrally actuated with shape memory alloy (SMA) actuators. Morphing and multifunctional structures are of interest in the aerospace industry becasue of the potential for improving structural and aerodynamic performance across multiple operating conditions. The focus of this work is on structures that are morphed with SMA flexural actuators. For the case where the geometry is known for unassembled components, assembly can be simulated to find the assembled shapes of the morphing structure. In the usual design case, however, only the desired shapes as assembled are known in multiple actuation states, and the corresponding unassembled shapes must be determined by an iterative solution process. An iterative finite element analysis approach to this problem is reported here. First an initial guess for the unassembled shapes is made and assembly is simulated with the finite element method. The resulting shapes are found for both SMA phases and compared with the desired shapes. A gradient-based optimization method is employed to update the initial geometry and iteration continues until the desired shapes are achieved. A simplified method of modeling the SMA material behavior is used for computational efficiently. It is found that this approach provides a practical way to solve the inverse design problem for structures that are integrally actuated with SMA material.
NASA Astrophysics Data System (ADS)
Lavery, N.; Taylor, C.
1999-07-01
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright
An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients
NASA Astrophysics Data System (ADS)
Hou, Thomas Y.; Hwang, Feng-Nan; Liu, Pengfei; Yao, Chien-Chou
2017-05-01
We propose an iteratively adaptive Multi-scale Finite Element Method (MsFEM) for elliptic PDEs with rough coefficients. The choice of the local boundary conditions for the multi-sale basis functions determines the accuracy of the MsFEM numerical solution, and one needs to incorporate the global information of the elliptic equation into the local boundary conditions of the multi-scale basis functions to recover the underlying fine-mesh solution of the equation. In our proposed iteratively adaptive method, we achieve this global-to-local information transfer through the combination of coarse-mesh solving using adaptive multi-scale basis functions and fine-mesh smoothing operations. In each iteration step, we first update the multi-scale basis functions based on the approximate numerical solutions of the previous iteration steps, and obtain the coarse-mesh approximate solution using a Galerkin projection. Then we apply several steps of smoothing operations to the coarse-mesh approximate solution on the underlying fine mesh to get the updated approximate numerical solution. The proposed algorithm can be viewed as a nonlinear two-level multi-grid method with the restriction and prolongation operators adapted to the approximate numerical solutions of the previous iteration steps. Convergence analysis of the proposed algorithm is carried out under the framework of two-level multi-grid method, and the harmonic coordinates are employed to establish the approximation property of the adaptive multi-scale basis functions. We demonstrate the efficiency of our proposed multi-scale methods through several numerical examples including a multi-scale coefficient problem, a high-contrast interface problem, and a convection-dominated diffusion problem.
Parallel finite element methods and iterative solution techniques for viscous incompressible flows
NASA Astrophysics Data System (ADS)
Barragy, Edward Joseph
The present work is motivated by a desire to map the solution structure of nonlinear systems of partial differential equations (PDE). Of particular interest are viscous flow problems in 2D, possibly with coupled heat transfer or species transport. Due to the nonlinearity of the governing PDE's, many complicated solution structures may arise. These may include sharp layers, multiple solutions, and the possibility of bifurcation. The existence of spurious solutions, arising from insufficiently refined meshes, underscores the need for highly accurate solution procedures. This, in turn, motivates the use of p type finite element discretizations. Continuation techniques have been developed by several authors for the solution of these types of nonlinear problems. These techniques involve the solution of linear algebraic systems arising from a Newton iteration, for many, possibly hundreds, of discrete parameter values. This large computational burden motivates the use of large scale, parallel supercomputing facilities. A study of the impact of high p finite element discretizations as applied to the continuation solution of viscous incompressible flows in two dimensions is presented. The impact of these methods is considered for a Newton type continuation method coupled with gradient type element-by-element (EBE) iterative solvers. Significant issues considered concern the effect of high p on performance for various supercomputing platforms, implementation issues for EBE schemes in a distributed memory setting, and issues of scalability in a distributed memory multiprocessor setting. These issues are examined in conjunction with the development of preconditioners appropriate for high p methods, and the development of bifurcation detection schemes appropriate for high p methods and gradient type solution schemes.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-01-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-11-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
A comparison of direct and iterative finite element inversion techniques in dynamic elastography.
Honarvar, M; Rohling, R; Salcudean, S E
2016-04-21
As part of tissue elasticity imaging or elastography, an inverse problem needs to be solved to find the elasticity distribution from the measured displacements. The finite element method (FEM) is a common method for solving the inverse problem in dynamic elastography. This problem has been solved with both direct and iterative FEM schemes. Each of these methods has its own advantages and disadvantages which are examined in this paper. Choosing the data resolution and the excitation frequency are critical for achieving the best estimation of the tissue elasticity in FEM methods. In this paper we investigate the performance of both direct and iterative FEMs for different ranges of excitation frequency. A new form of iterative method is suggested here which requires a lower mesh density compared to the original form. Also two forms of the direct method are compared in this paper: one using the exact fit for derivatives calculation and the other using the least squares fit. We also perform a study on the spatial resolution of these methods using simulations. The comparison is also validated using a phantom experiment. The results suggest that the direct method with least squares fit is more robust to noise compared to other methods but has slightly lower resolution results. For example, for the homogenous region with 20 dB noise added to the data, the RMS error for the direct method with least squares fit is approximately half of the iterative method. It was observed that the ratio of voxel size to the wavelength should be within a specific range for the results to be reliable. For example for the direct method with least squares fit, for the case of 20 dB noise level, this ratio should be between 0.1 to 0.2. On balance, considering the much higher computational cost of the iterative method, the dependency of the iterative method on the initial guess, and the greater robustness of the direct method to noise, we suggest using the direct method with least squares fit for
A comparison of direct and iterative finite element inversion techniques in dynamic elastography
NASA Astrophysics Data System (ADS)
Honarvar, M.; Rohling, R.; Salcudean, S. E.
2016-04-01
As part of tissue elasticity imaging or elastography, an inverse problem needs to be solved to find the elasticity distribution from the measured displacements. The finite element method (FEM) is a common method for solving the inverse problem in dynamic elastography. This problem has been solved with both direct and iterative FEM schemes. Each of these methods has its own advantages and disadvantages which are examined in this paper. Choosing the data resolution and the excitation frequency are critical for achieving the best estimation of the tissue elasticity in FEM methods. In this paper we investigate the performance of both direct and iterative FEMs for different ranges of excitation frequency. A new form of iterative method is suggested here which requires a lower mesh density compared to the original form. Also two forms of the direct method are compared in this paper: one using the exact fit for derivatives calculation and the other using the least squares fit. We also perform a study on the spatial resolution of these methods using simulations. The comparison is also validated using a phantom experiment. The results suggest that the direct method with least squares fit is more robust to noise compared to other methods but has slightly lower resolution results. For example, for the homogenous region with 20 dB noise added to the data, the RMS error for the direct method with least squares fit is approximately half of the iterative method. It was observed that the ratio of voxel size to the wavelength should be within a specific range for the results to be reliable. For example for the direct method with least squares fit, for the case of 20 dB noise level, this ratio should be between 0.1 to 0.2. On balance, considering the much higher computational cost of the iterative method, the dependency of the iterative method on the initial guess, and the greater robustness of the direct method to noise, we suggest using the direct method with least squares fit for
Koteras, J.R.
1993-07-01
Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C.
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Cwik, T.; Jamnejad, V.; Zuffada, C.
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
Electrical defibrillation optimization: An automated, iterative parallel finite-element approach
Hutchinson, S.A.; Shadid, J.N.; Ng, K.T.; Nadeem, A.
1997-04-01
To date, optimization of electrode systems for electrical defibrillation has been limited to hand-selected electrode configurations. In this paper we present an automated approach which combines detailed, three-dimensional (3-D) finite element torso models with optimization techniques to provide a flexible analysis and design tool for electrical defibrillation optimization. Specifically, a parallel direct search (PDS) optimization technique is used with a representative objective function to find an electrode configuration which corresponds to the satisfaction of a postulated defibrillation criterion with a minimum amount of power and a low possibility of myocardium damage. For adequate representation of the thoracic inhomogeneities, 3-D finite-element torso models are used in the objective function computations. The CPU-intensive finite-element calculations required for the objective function evaluation have been implemented on a message-passing parallel computer in order to complete the optimization calculations in a timely manner. To illustrate the optimization procedure, it has been applied to a representative electrode configuration for transmyocardial defibrillation, namely the subcutaneous patch-right ventricular catheter (SP-RVC) system. Sensitivity of the optimal solutions to various tissue conductivities has been studied. 39 refs., 9 figs., 2 tabs.
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region.
NASA Astrophysics Data System (ADS)
Cao, Yong; Chu, Yuchuan; He, Xiaoming; Lin, Tao
2015-01-01
Interface problems involving the non-homogeneous flux jump condition are critical for engineering designs in the magnetostatic/electrostatic field. In applications, such as plasma simulation, we often only know the total electric quantity on the surface of the object, not the charge density distribution on the surface which appears as the non-homogeneous flux jump condition in the usual interface problems considered in the literature for the magnetostatic/electrostatic field. Based on structured meshes independent of the interface, this article proposes an iterative method that employs both the immersed finite element (IFE) method with non-homogeneous flux jump conditions and the regular finite element method with ghost nodes introduced in the object to solve the 2D interface problem for the potential field according to the given total electric quantity on the surface of the object. Numerical experiments are provided to illustrate the accuracy and efficiency of the proposed method.
Woiczinski, Matthias; Tollrian, Christopher; Schröder, Christian; Steinbrück, Arnd; Müller, Peter E; Jansson, Volkmar
2013-08-01
With the aging but still active population, research on total joint replacements relies increasingly on numerical methods, such as finite element analysis, to improve wear resistance of components. However, the validity of finite element models largely depends on the accuracy of their material behavior and geometrical representation. In particular, material properties are often based on manufacturer data or literature reports, but can alternatively be estimated by matching experimental measurements and structural predictions through modal analyses and identification of eigenfrequencies. The aim of the present study was to compare the accuracy of common setups used for estimating the eigenfrequencies of typical components often used in prosthetized joints. Eigenfrequencies of cobalt-chrome and ultra-high-molecular weight polyethylene components were therefore measured with four different setups, and used in modal analyses of corresponding finite element models for an iterative adjustment of their material properties. Results show that for the low-damped cobalt chromium endoprosthesis components, all common measuring setups provided accurate measurements. In the case of high-damped structures, measurements were only possible with setups including a continuously excitation system such as electrodynamic shakers. This study demonstrates that the iterative back-calculation of eigenfrequencies can be a reliable method to estimate the elastic properties for finite element models.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
NASA Astrophysics Data System (ADS)
Leibs, Christopher A.
Efforts are currently being directed towards a fully implicit, electromagnetic, JFNK-based solver, motivating the necessity of developing a fluid-based, electromag- netic, preconditioning strategy. The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP model couples both an ion and an electron fluid with Maxwell's equations. The fluid equations consist of the conservation of momentum and number density. A Darwin approximation of Maxwell is used to eliminate light waves from the model in order to facilitate coupling to non-relativistic particle models. We analyze the TFP-Darwin system in the context of a stand-alone solver with consideration of preconditioning a kinetic-JFNK approach. The TFP-Darwin system is addressed numerically by use of nested iteration (NI) and a First-Order Systems Least Squares (FOSLS) discretization. An important goal of NI is to produce an approximation that is within the basis of attraction for Newton's method on a relatively coarse mesh and, thus, on all subsequent meshes. After scaling and modification, the TFP-Darwin model yields a nonlinear, first-order system of equa- tions whose Frechet derivative is shown to be uniformly H1-elliptic in a neighborhood of the exact solution. H1 ellipticity yields optimal finite element performance and lin- ear systems amenable to solution with Algebraic Multigrid (AMG). To efficiently focus computational resources, an adaptive mesh refinement scheme, based on the accuracy per computational cost, is leveraged. Numerical tests demonstrate the efficacy of the approach, yielding an approximate solution within discretization error in a relatively small number of computational work units.
Lew, S.; Wolters, C.H.; Dierkes, T.; Röer, C.; MacLeod, R.S.
2009-01-01
Accuracy and run-time play an important role in medical diagnostics and research as well as in the field of neuroscience. In Electroencephalography (EEG) source reconstruction, a current distribution in the human brain is reconstructed noninvasively from measured potentials at the head surface (the EEG inverse problem). Numerical modeling techniques are used to simulate head surface potentials for dipolar current sources in the human cortex, the so-called EEG forward problem. In this paper, the efficiency of algebraic multigrid (AMG), incomplete Cholesky (IC) and Jacobi preconditioners for the conjugate gradient (CG) method are compared for iteratively solving the finite element (FE) method based EEG forward problem. The interplay of the three solvers with a full subtraction approach and two direct potential approaches, the Venant and the partial integration method for the treatment of the dipole singularity is examined. The examination is performed in a four-compartment sphere model with anisotropic skull layer, where quasi-analytical solutions allow for an exact quantification of computational speed versus numerical error. Specifically-tuned constrained Delaunay tetrahedralization (CDT) FE meshes lead to high accuracies for both the full subtraction and the direct potential approaches. Best accuracies are achieved by the full subtraction approach if the homogeneity condition is fulfilled. It is shown that the AMG-CG achieves an order of magnitude higher computational speed than the CG with the standard preconditioners with an increasing gain factor when decreasing mesh size. Our results should broaden the application of accurate and fast high-resolution FE volume conductor modeling in source analysis routine. PMID:20161462
Finite elements and finite differences for transonic flow calculations
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1993-01-01
A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.
Large Scale Finite Element Modeling Using Scalable Parallel Processing
NASA Technical Reports Server (NTRS)
Cwik, T.; Katz, D.; Zuffada, C.; Jamnejad, V.
1995-01-01
An iterative solver for use with finite element codes was developed for the Cray T3D massively parallel processor at the Jet Propulsion Laboratory. Finite element modeling is useful for simulating scattered or radiated electromagnetic fields from complex three-dimensional objects with geometry variations smaller than an electrical wavelength.
Finite element analysis of wrinkling membranes
NASA Technical Reports Server (NTRS)
Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.
1984-01-01
The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.
NASA Astrophysics Data System (ADS)
Akhir, M. K. M.; Sulaiman, J.
2017-09-01
Weighted iterative methods particularly Accelerated Over Relaxation (AOR) method are used to solve linear system generated from triangle finite element approximation equation in solving 2D Helmholtz equation. The development of the AOR iterative method were also presented. Numerical experiments have been carried out and the results obtained confirm the superiority of the proposed iterative method
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
Toward automatic finite element analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Perucchio, Renato; Voelcker, Herbert
1987-01-01
Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.
Second order tensor finite element
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Finite element shell instability analysis
NASA Technical Reports Server (NTRS)
1975-01-01
Formulation procedures and the associated computer program for finite element thin shell instability analysis are discussed. Data cover: (1) formulation of basic element relationships, (2) construction of solution algorithms on both the conceptual and algorithmic levels, and (3) conduction of numerical analyses to verify the accuracy and efficiency of the theory and related programs therein are described.
Adaptive implicit-explicit and parallel element-by-element iteration schemes
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.
1989-01-01
Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.
Adaptive implicit-explicit and parallel element-by-element iteration schemes
NASA Astrophysics Data System (ADS)
Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.
Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.
Adaptive implicit-explicit and parallel element-by-element iteration schemes
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.
1989-01-01
Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.
Finite element modeling of permanent magnet devices
NASA Astrophysics Data System (ADS)
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
Finite element concepts in computational aerodynamics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.
Geometrical nonlinearity of 14-node brick finite element
NASA Astrophysics Data System (ADS)
Chandan, Swet; Chauhan, Alok P. S.
2017-01-01
The present work depicts the geometrical nonlinearity analysis for the finite element, PN5X1. Here, the general problem of elasticity is numerically solved using iteration method. The proposed element is passed through different tests in order to prove that it works not only for modeling sheet metal forming process but also for other large deformation problems.
Parallel, Implicit, Finite Element Solver
NASA Astrophysics Data System (ADS)
Lowrie, Weston; Shumlak, Uri; Meier, Eric; Marklin, George
2007-11-01
A parallel, implicit, finite element solver is described for solutions to the ideal MHD equations and the Pseudo-1D Euler equations. The solver uses the conservative flux source form of the equations. This helps simplify the discretization of the finite element method by keeping the specification of the physics separate. An implicit time advance is used to allow sufficiently large time steps. The Portable Extensible Toolkit for Scientific Computation (PETSc) is implemented for parallel matrix solvers and parallel data structures. Results for several test cases are described as well as accuracy of the method.
Simple bounds on limit loads by elastic finite element analysis
Mackenzie, D.; Nadarajah, C.; Shi, J.; Boyle, J.T. . Dept. of Mechanical Engineering)
1993-02-01
A method for bounding limit loads by an iterative elastic continuum finite element analysis procedure, referred to as the elastic compensation method, is proposed. A number of sample problems are considered, based on both exact solutions and finite element analysis, and it is concluded that the method may be used to obtain limit-load bounds for pressure vessel design by analysis applications with useful accuracy.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
The Relation of Finite Element and Finite Difference Methods
NASA Technical Reports Server (NTRS)
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Nonlinear, finite deformation, finite element analysis
NASA Astrophysics Data System (ADS)
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
ANSYS duplicate finite-element checker routine
NASA Technical Reports Server (NTRS)
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
Infinite Possibilities for the Finite Element.
ERIC Educational Resources Information Center
Finlayson, Bruce A.
1981-01-01
Describes the uses of finite element methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of finite element methods. (Author/WB)
SUPG Finite Element Simulations of Compressible Flows
NASA Technical Reports Server (NTRS)
Kirk, Brnjamin, S.
2006-01-01
The Streamline-Upwind Petrov-Galerkin (SUPG) finite element simulations of compressible flows is presented. The topics include: 1) Introduction; 2) SUPG Galerkin Finite Element Methods; 3) Applications; and 4) Bibliography.
Peridynamic Multiscale Finite Element Methods
Costa, Timothy; Bond, Stephen D.; Littlewood, David John; Moore, Stan Gerald
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Finite element model and identification procedure
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Blackwood, Gary; Anderson, Eric; Balmes, Etienne
1992-01-01
Viewgraphs on finite element model and identification procedure are presented. Topics covered include: interferometer finite element model; testbed mode shapes; finite element model update; identification procedure; shaker locations; data analysis; modal frequency and damping comparison; computational procedure; fit comparison; residue analysis; typical residues; identification/FEM residual comparison; and pathlength control using isolation mounts.
Finite-element solutions for geothermal systems
NASA Technical Reports Server (NTRS)
Chen, J. C.; Conel, J. E.
1977-01-01
Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.
Finite-element solutions for geothermal systems
NASA Technical Reports Server (NTRS)
Chen, J. C.; Conel, J. E.
1977-01-01
Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.
A finite element model with nonviscous damping
NASA Technical Reports Server (NTRS)
Roussos, L. A.; Hyer, M. W.; Thornton, E. A.
1981-01-01
A constitutive law by which structural damping is modeled as a relationship between stress, strain, and strain rate in a material is used in conjunction with the finite element method to develop general integral expressions for viscous and nonviscous damping matrices. To solve the set of nonlinear equations resulting from the presence of nonviscous damping, a solution technique is developed by modifying the Newmark method to accommodate an iterative solution and treat the nonviscous damping as a pseudo-force. The technique is then checked for accuracy and convergence in single- and multi-degree-of-freedom problems, and is found to be accurate and efficient for initial-condition problems with small nonviscous damping.
Iterative finite element solver on transputer networks
NASA Technical Reports Server (NTRS)
Danial, Albert; Watson, James
1988-01-01
The parallelism inherent in the Conjugate Gradient method is described. The initial results of a parallel implementation on a network of twelve transputers are discussed. The high efficiencies obtained indicate that significant speedup can be obtained with larger transputer arrays if communication overhead can be kept low. To this end, a method of communication that allows large, dynamically reconfigurable transputer arrays to exchange data in log sub 4 N steps for N processors is suggested.
Finite element simulation of microindentation
NASA Astrophysics Data System (ADS)
Zhuk, D. I.; Isaenkova, M. G.; Perlovich, Yu. A.; Krymskaya, O. A.
2017-05-01
Finite element models are created to describe the testing of a material by a Berkovich indenter. The results of calculations by these models are compared to experimental data on indentation of the same material (grade 10 steel). The experimental and calculated data agree well with each other. The developed models for an indenter and the material to be tested are used to find the laws of behavior of a material during indentation. The state of stress in the material under an indenter is studied by various methods. The indentation results are plotted versus the mechanical properties of a material.
Fourier analysis of finite element preconditioned collocation schemes
NASA Technical Reports Server (NTRS)
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
User's Guide for ENSAERO_FE Parallel Finite Element Solver
NASA Technical Reports Server (NTRS)
Eldred, Lloyd B.; Guruswamy, Guru P.
1999-01-01
A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Feng, Xiaobing
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
Finite element coiled cochlea model
NASA Astrophysics Data System (ADS)
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U.
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
A finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.; Nayani, S.
1990-01-01
Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.
Finite-Element Composite-Analysis Program
NASA Technical Reports Server (NTRS)
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
Finite element analysis of helicopter structures
NASA Technical Reports Server (NTRS)
Rich, M. J.
1978-01-01
Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
3-D Finite Element Code Postprocessor
1996-07-15
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
Books and monographs on finite element technology
NASA Technical Reports Server (NTRS)
Noor, A. K.
1985-01-01
The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.
Books and monographs on finite element technology
NASA Technical Reports Server (NTRS)
Noor, A. K.
1985-01-01
The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.
A composite nodal finite element for hexagons
Hennart, J.P.; Mund, E.H. |; Valle, E. Del
1997-10-01
A nodal algorithm for the solution of the multigroup diffusion equations in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quarters onto squares. The resulting boundary value problem on a quadrangular domain is solved in primal weak formulation. Nodal finite element methods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration cannot be performed on the equations in the quadrangular domain as simply as it is usually done on squares because these equations have essentially variable coefficients. However, by considering an auxiliary problem with constant coefficients (on the same quadrangular domain) and by using a preconditioning approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are presented for a simple model problem with a known analytical solution and for k{sub eff} evaluations of some benchmark problems proposed in the literature. For the analytical problem, the results indicate that the theoretical convergence orders of RTk schemes (k = 0,1) are obtained, yielding accurate solutions at the expense of a few preconditioning iterations.
Finite element analysis of arc welding
Friedman, E.
1980-01-01
Analytical models of the gas tungsten-arc welding process into finite element computer programs provides a valuable tool for determining the welding thermal cycle, weld bead shape, and penetration characteristics, as well as for evaluating the stresses and distortions generated as a result of the temperature transients. The analysis procedures are applicable to planar or axisymmetric welds with arbitrary cross-sectional geometries, under quasistationary conditions. The method used for determining temperatures features an iteration procedure to accurately account for the latent heat absorbed during melting and liberated during solidification of the weld. By simulating the heat input from the arc to the workpiece by a normal distribution function, temperature transients, weld bead dimensions, and cooling rates are evaluated as functions of both the magnitude and distribution of heat input, weldment geometry, and weld speed (or duration of heating for stationary arcs). Modeling of the welding thermal cycle is a prerequisite to analytical treatments of metallurgical changes in weld metal and heat-affected zone material, residual stresses and distortions, and weld defects. A quasistationary formulation for moving welds enables temperatures to be calculated using a two-dimensional heat conduction computer program. The present limitation of high welding speed can, however, be relaxed without altering the two-dimensional framework of the procedure.
Assignment Of Finite Elements To Parallel Processors
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.
1990-01-01
Elements assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform finite-element computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of elements to subdomains minimizes cost of computation.
Assignment Of Finite Elements To Parallel Processors
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.
1990-01-01
Elements assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform finite-element computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of elements to subdomains minimizes cost of computation.
Optimizing header strength utilizing finite element analyses
NASA Astrophysics Data System (ADS)
Burchett, S. N.
Finite element techniques have been successfully applied as a design tool in the optimization of high strength headers for pyrotechnic-driven actuators. These techniques have been applied to three aspects of the design process of a high strength header. The design process was a joint effort of experts from several disciplines including design engineers, material scientists, test engineers, manufacturing engineers, and structural analysts. Following material selection, finite element techniques were applied to evaluate the residual stresses due to manufacturing which were developed in the high strength glass ceramic-to-metal seal headers. Results from these finite element analyses were used to identify header designs which were manufacturable and had a minimum residual stress state. Finite element techniques were than applied to obtain the response of the header due to pyrotechnic burn. The results provided realistic upper bounds on the pressure containment ability of various preliminary header designs and provided a quick and inexpensive method of strengthening and refining the designs. Since testing of the headers was difficult and sometimes destructive, results of the analyses were also used to interpret test results and identify failure modes. In this paper, details of the finite element element techniques including the models used, material properties, material failure models, and loading will be presented. Results from the analyses showing the header failure process will also be presented. This paper will show that significant gains in capability and understanding can result when finite element techniques are included as an integral part of the design process of complicated high strength headers.
Visualization of higher order finite elements.
Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay
2004-04-01
Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Finite element schemes for Fermi equation
NASA Astrophysics Data System (ADS)
Asadzadeh, M.; Beilina, L.; Naseer, M.; Standar, C.
2017-07-01
A priori error estimates are derived for the streamline diffusion (SD) finite element methods for the Fermi pencil-beam equation. Two-dimensional numerical examples confirm our theoretical investigations.
Hybrid finite element-finite difference method for thermal analysis of blood vessels.
Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B
2000-01-01
A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems.
Finite element modeling of the human pelvis
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Multigrid waveform relaxation on spatial finite element meshes
Janssen, J.; Vandewalle, S.
1994-12-31
The authors shall discuss the numerical solution of a parabolic partial differential equation {partial_derivative}u/{partial_derivative}t(x,t) = Lu(x,t) + f(x,t), x{element_of}{Omega}, t>0, (1) supplied with a boundary condition and given initial values. The spatial finite element discretization of (1) on a discrete grid {Omega}{sub h} leads to an initial value problem of the form B{dot u} + Au = f, u(0) = u{sub o}, t > 0, (2) with B a non-singular matrix. The waveform relaxation method is a method for solving ordinary differential equations. It differs from most standard iterative techniques in that it is a continuous-time method, iterating with functions in time, and thereby well-suited for parallel computation.
Finite element analysis of flexible, rotating blades
NASA Technical Reports Server (NTRS)
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Stabilized Finite Elements in FUN3D
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
Wave dispersion properties of compound finite elements
NASA Astrophysics Data System (ADS)
Melvin, Thomas; Thuburn, John
2017-06-01
Mixed finite elements use different approximation spaces for different dependent variables. Certain classes of mixed finite elements, called compatible finite elements, have been shown to exhibit a number of desirable properties for a numerical weather prediction model. In two-dimensions the lowest order element of the Raviart-Thomas based mixed element is the finite element equivalent of the widely used C-grid staggering, which is known to possess good wave dispersion properties, at least for quadrilateral grids. It has recently been proposed that building compound elements from a number of triangular Raviart-Thomas sub-elements, such that both the primal and (implied) dual grid are constructed from the same sub-elements, would allow greater flexibility in the use of different advection schemes along with the ability to build arbitrary polygonal elements. Although the wave dispersion properties of the triangular sub-elements are well understood, those of the compound elements are unknown. It would be useful to know how they compare with the non-compound elements and what properties of the triangular sub-grid elements are inherited? Here a numerical dispersion analysis is presented for the linear shallow water equations in two dimensions discretised using the lowest order compound Raviart-Thomas finite elements on regular quadrilateral and hexagonal grids. It is found that, in comparison with the well known C-grid scheme, the compound elements exhibit a more isotropic dispersion relation, with a small over estimation of the frequency for short waves compared with the relatively large underestimation for the C-grid. On a quadrilateral grid the compound elements are found to differ from the non-compound Raviart-Thomas quadrilateral elements even for uniform elements, exhibiting the influence of the underlying sub-elements. This is shown to lead to small improvements in the accuracy of the dispersion relation: the compound quadrilateral element is slightly better for
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Model Reduction of Viscoelastic Finite Element Models
NASA Astrophysics Data System (ADS)
Park, C. H.; Inman, D. J.; Lam, M. J.
1999-01-01
This paper examines a method of adding viscoelastic properties to finite element models by using additional co-ordinates to account for the frequency dependence usually associated with such damping materials. Several such methods exist and all suffer from an increase in order of the final finite model which is undesirable in many applications. Here we propose to combine one of these methods, the GHM (Golla-Hughes-McTavish) method, with model reduction techniques to remove the objection of increased model order. The result of combining several methods is an ability to add the effects of visoelastic components to finite element or other analytical models without increasing the order of the system. The procedure is illustrated by a numerical example. The method proposed here results in a viscoelastic finite element of a structure without increasing the order of the original model.
Finite-Element Analysis of Multiphase Immiscible Flow Through Soils
NASA Astrophysics Data System (ADS)
Kuppusamy, T.; Sheng, J.; Parker, J. C.; Lenhard, R. J.
1987-04-01
A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equations governing flow in a three-fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures, which are derived in a companion paper by J. C. Parker et al. (this issue) and which may be calibrated from two-phase laboratory measurements, are employed in the finite-element program. The solution procedure uses backward time integration with iteration by a modified Picard method to handle the nonlinear properties. Laboratory experiments involving water displacement from soil columns by p cymene (a benzene-derivative hydrocarbon) under constant pressure were simulated by the finite-element program to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured saturation-capillary head data agreed with observed outflow data within the limits of precision of the predictions as estimated by a first-order Taylor series approximation considering parameter uncertainty due to experimental reproducability and constitutive model accuracy. Two-dimensional simulations are presented for a hypothetical field case involving introduction of NAPL near the soil surface due to leakage from an underground storage tank. Subsequent transport of NAPL in the variably saturated vadose and groundwater zones is analyzed.
Finite-element models of continental extension
NASA Technical Reports Server (NTRS)
Lynch, H. David; Morgan, Paul
1990-01-01
Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.
The GPRIME approach to finite element modeling
NASA Technical Reports Server (NTRS)
Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.
1983-01-01
GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data.
Surface subsidence prediction by nonlinear finite-element analysis
Najjar, Y. . Dept. of Civil Engineering); Zaman, M. . School of Civil Engineering and Environmental Science)
1993-11-01
An improved two-dimensional plane-strain numerical procedure based on the incremental-iterative nonlinear finite-element is developed to predict ground subsidence caused by underground mining. The procedure emphasizes the use of the following features: (1) an appropriate constitutive model that can accurately describe the nonlinear behavior of geological strata; and (2) an accurate algorithm for simulation of excavation sequences consistent with the actual underground mining process. The computer code is used to analyze a collapse that occurred in the Blue Goose Lease [number sign]1 Mine in northeastern Oklahoma. A parametric study is conducted to investigate the effects of some selected factors on the shape and extent of subsidence profiles. Analyses of the numerical results indicate that the nonlinear finite-element technique can be employed to meaningfully predict and characterize the potential for ground subsidence due to underground mining.
Design Optimization of Coronary Stent Based on Finite Element Models
Qiu, Tianshuang; Zhu, Bao; Wu, Jinying
2013-01-01
This paper presents an effective optimization method using the Kriging surrogate model combing with modified rectangular grid sampling to reduce the stent dogboning effect in the expansion process. An infilling sampling criterion named expected improvement (EI) is used to balance local and global searches in the optimization iteration. Four commonly used finite element models of stent dilation were used to investigate stent dogboning rate. Thrombosis models of three typical shapes are built to test the effectiveness of optimization results. Numerical results show that two finite element models dilated by pressure applied inside the balloon are available, one of which with the artery and plaque can give an optimal stent with better expansion behavior, while the artery and plaque unincluded model is more efficient and takes a smaller amount of computation. PMID:24222743
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Waveguide finite elements for curved structures
NASA Astrophysics Data System (ADS)
Finnveden, Svante; Fraggstedt, Martin
2008-05-01
A waveguide finite element formulation for the analysis of curved structures is introduced. The formulation is valid for structures that along one axis have constant properties. It is based on a modified Hamilton's principle valid for general linear viscoelastic motion, which is derived here. Using this principle, material properties such as losses may be distributed in the system and may vary with frequency. Element formulations for isoparametric solid elements and deep shell elements are presented for curved waveguides as well as for straight waveguides. In earlier works, the curved elements have successfully been used to model a passenger car tyre. Here a simple validation example and convergence study is presented, which considers a finite length circular cylinder and all four elements presented are used, in turn, to model this structure. Calculated results compare favourably to those in the literature.
A Decoupled Finite Element Heterogeneous Coarse Mesh Transport Method.
Mosher, S. W.; Rahnema, Farzad
2005-01-01
In a recent paper, an original finite element (FE) method was presented for solving eigenvalue transport problems on a coarse spatial mesh. The method employed a surface Green's function expansion of the angular flux trial functions, so that heterogeneous coarse-meshes could be treated with relative ease. Numerical problems were solved using the multigroup discrete ordinates approximation in one-dimensional (1-D) slab geometry. Unfortunately, difficulties were encountered in finding solutions to the algebraic finite element equations, which led to sizeable angular flux discontinuities at coarse-mesh interfaces and significant errors. For this reason, a nonvariational iterative technique was ultimately favored for converging the angular flux distribution, and was used in conjunction with a Rayleigh quotient for converging the eigenvalue. In this paper, a new derivation of finite element equations is presented, which seems to offer a remedy for at least some of the numerical ills that plagued the previous work. First, the equations are derived in terms of a generalized response function expansion. This allows a more efficient response basis to be employed and vastly reduces the overall computational effort without a substantial loss of accuracy. Second, the tight coupling between coarse-meshes in the original equations is effectively broken by assuming that an accurate estimate of the flux distribution entering a given coarse-mesh is known. With an additional assumption that an accurate eigenvalue estimate is known, an iterative approach to solving these decoupled finite element (DFE) equations is developed. The DFE method has been applied to both 1- and 2-D heterogeneous coarse-mesh problems with a far greater degree of success than the original FE method. However, some numerical difficulties remain to be overcome before the new approach can be considered robust.
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.
Finite-approximation-error-based discrete-time iterative adaptive dynamic programming.
Wei, Qinglai; Wang, Fei-Yue; Liu, Derong; Yang, Xiong
2014-12-01
In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index function converge to the solution of the Hamilton-Jacobi-Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index function in each iteration cannot accurately be obtained, for the first time a new "design method of the convergence criteria" for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index function converge to a finite neighborhood of the optimal performance index function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method.
Massively parallel computation of RCS with finite elements
NASA Technical Reports Server (NTRS)
Parker, Jay
1993-01-01
One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary
Finite element analysis of periodic transonic flow problems
NASA Technical Reports Server (NTRS)
Fix, G. J.
1978-01-01
Flow about an oscillating thin airfoil in a transonic stream was considered. It was assumed that the flow field can be decomposed into a mean flow plus a periodic perturbation. On the surface of the airfoil the usual Neumman conditions are imposed. Two computer programs were written, both using linear basis functions over triangles for the finite element space. The first program uses a banded Gaussian elimination solver to solve the matrix problem, while the second uses an iterative technique, namely SOR. The only results obtained are for an oscillating flat plate.
Efficient finite element method for grating profile reconstruction
NASA Astrophysics Data System (ADS)
Zhang, Ruming; Sun, Jiguang
2015-12-01
This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.
Finite element modeling and analysis of tires
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1983-01-01
Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.
Visualizing higher order finite elements. Final report
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Finite Element Analysis of Pipe Elbows.
1980-02-01
AD-AO81 077 DAVD TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/B 13/11 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS .(U) FE SO M S MARCUS, B C...TAYLOR NAVAL SHIP i RESEARCH AND DEVELOPMENT CENTER Bethesda, Md. 20084 4 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS by 0 Melvyn S. Marcus and Gordon C...a 90-degree pipe elbow to determine principal stresses due to internal pressure, inplane bending, out-of-plane bending, and torsion moment loadings
Finite element methods for high speed flows
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.; Peraire, J.; Zienkiewicz, O. C.
1985-01-01
An explicit finite element based solution procedure for solving the equations of compressible viscous high speed flow is presented. The method uses domain splitting to advance the solution with different timesteps on different portions of the mesh. For steady inviscid flows, adaptive mesh refinement procedures are successfully employed to enhance the definition of discontinuities. Preliminary ideas on the application of adaptive mesh refinement to the solution of problems involving steady viscous flow are presented. Sample timings are given for the performance of the finite element code on modern supercomputers.
Studies of finite element analysis of composite material structures
NASA Technical Reports Server (NTRS)
Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.
1975-01-01
Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.
Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems
NASA Astrophysics Data System (ADS)
Ljungberg, M. P.; Koval, P.; Ferrari, F.; Foerster, D.; Sánchez-Portal, D.
2015-08-01
The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electronic excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present difficulties for simpler approaches. We present a local basis set formulation of the BSE for molecules where the optical spectrum is computed with the iterative Haydock recursion scheme, leading to a low computational complexity and memory footprint. Using a variant of the algorithm we can go beyond the Tamm-Dancoff approximation. We rederive the recursion relations for general matrix elements of a resolvent, show how they translate into continued fractions, and study the convergence of the method with the number of recursion coefficients and the role of different terminators. Due to the locality of the basis functions the computational cost of each iteration scales asymptotically as O (N3) with the number of atoms, while the number of iterations typically is much lower than the size of the underlying electron-hole basis. In practice we see that, even for systems with thousands of orbitals, the runtime will be dominated by the O (N2) operation of applying the Coulomb kernel in the atomic orbital representation.
Finite element modelling of buried structures
NASA Technical Reports Server (NTRS)
Playdon, D. K.; Simmonds, S. H.
1984-01-01
In many structures the final stress states are dependent on the sequence of construction or the stress states at various stages of construction are of interest. Such problems can be analyzed using finite element programs that have the capability of adding (birthing) elements to simulate the progress of construction. However, the usual procedure of assembling elements may lead to numerical instabilities or stress states that are unrealistic. Both problems are demonstrated in the analysis of a structure using the program ADINA. A technique which combines application of a preload with element birthing to overcome these problems is described and illustrated.
Numerical computation of transonic flows by finite-element and finite-difference methods
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
Slave finite elements: The temporal element approach to nonlinear analysis
NASA Technical Reports Server (NTRS)
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
Finite element wavelets with improved quantitative properties
NASA Astrophysics Data System (ADS)
Nguyen, Hoang; Stevenson, Rob
2009-08-01
In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319-352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for (or s<=1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.
Finite Element Simulation of Smart Structures
NASA Technical Reports Server (NTRS)
Cui, Y. Lawrence; Panahandeh, M.
1996-01-01
Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.
A multidimensional finite element method for CFD
NASA Technical Reports Server (NTRS)
Pepper, Darrell W.; Humphrey, Joseph W.
1991-01-01
A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.
Quadrilateral/hexahedral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E
2012-10-16
A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.
Adaptive finite element strategies for shell structures
NASA Technical Reports Server (NTRS)
Stanley, G.; Levit, I.; Stehlin, B.; Hurlbut, B.
1992-01-01
The present paper extends existing finite element adaptive refinement (AR) techniques to shell structures, which have heretofore been neglected in the AR literature. Specific challenges in applying AR to shell structures include: (1) physical discontinuities (e.g., stiffener intersections); (2) boundary layers; (3) sensitivity to geometric imperfections; (4) the sensitivity of most shell elements to mesh distortion, constraint definition and/or thinness; and (5) intrinsic geometric nonlinearity. All of these challenges but (5) are addressed here.
Finite element modeling of nonisothermal polymer flows
NASA Technical Reports Server (NTRS)
Roylance, D.
1981-01-01
A finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer are important is described, and the numerical model is illustrated by means of computer experiments using extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments.
Finite element analysis applied to cornea reshaping.
Cabrera Fernández, Delia; Niazy, A M; Kurtz, R M; Djotyan, G P; Juhasz, T
2005-01-01
A 2-D finite element model of the cornea is developed to simulate corneal reshaping and the resulting deformation induced by refractive surgery. In the numerical simulations, linear and nonlinear elastic models are applied when stiffness inhomogeneities varying with depth are considered. Multiple simulations are created that employ different geometric configurations for the removal of the corneal tissue. Side-by-side comparisons of the different constitutive laws are also performed. To facilitate the comparison, the material property constants are identified from the same experimental data, which are obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validate the resulting models by comparing computed refractive power changes with clinical results. Tissue deformations created by simulated corneal tissue removal using finite elements are consistent with clinically observed postsurgical results. The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the simulations. Finite element analysis is a useful tool for modeling surgical effects on the cornea and developing a better understanding of the biomechanics of the cornea. The creation of patient-specific simulations would allow surgical outcomes to be predicted based on individualized finite element models.
Finite element displacement analysis of a lung.
NASA Technical Reports Server (NTRS)
Matthews, F. L.; West, J. B.
1972-01-01
A method is given based on the technique of finite elements which determines theoretically the mechanical behavior of a lung-shaped body loaded by its own weight. The results of this theoretical analysis have been compared with actual measurements of alveolar size and pleural pressures in animal lungs.
Finite element modelling of acoustic emission sensor
NASA Astrophysics Data System (ADS)
Gerasimov, S. I.; Sych, T. V.
2017-08-01
With a validated finite element system COSMOS/M, the out-of-plane displacements corresponding to model sources of acoustic emission (AE) were calculated in three-dimensional samples. The displacement signals were calculated for positions of the receiver on the top plate surface at several different distances (in the far-field) from the source’s epicenter.
A combined finite element-boundary element formulation for solution of axially symmetric bodies
NASA Technical Reports Server (NTRS)
Collins, Jeffrey D.; Volakis, John L.
1991-01-01
A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.
A triangular thin shell finite element: Nonlinear analysis. [structural analysis
NASA Technical Reports Server (NTRS)
Thomas, G. R.; Gallagher, R. H.
1975-01-01
Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
Massively parallel finite element computation of three dimensional flow problems
NASA Astrophysics Data System (ADS)
Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S.
1992-12-01
The parallel finite element computation of three-dimensional compressible, and incompressible flows, with emphasis on the space-time formulations, mesh moving schemes and implementations on the Connection Machines CM-200 and CM-5 are presented. For computation of unsteady compressible and incompressible flows involving moving boundaries and interfaces, the Deformable-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation that previously developed are employed. In this approach, the stabilized finite element formulations of the governing equations are written over the space-time domain of the problem; therefore, the deformation of the spatial domain with respect to time is taken into account automatically. This approach gives the capability to solve a large class of problems involving free surfaces, moving interfaces, and fluid-structure and fluid-particle interactions. By using special mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors involved in remeshing and also to increase the parallelization ease of the computations. The implicit equation systems arising from the finite element discretizations are solved iteratively by using the GMRES update technique with the diagonal and nodal-block-diagonal preconditioners. These formulations have all been implemented on the CM-200 and CM-5, and have been applied to several large-scale problems. The three-dimensional problems in this report were all computed on the CM-200 and CM-5.
On Hybrid and mixed finite element methods
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Finite Element Analysis of Piping Tees.
1980-06-01
Combustion Engineering, Inc., performed an experimental stress analysis3 on an ANSI B16.9 carbon steelt tee designated T-12. Pipe extensions were welded to...AD-ASS? 353 DAVID If TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/S 13/11 FINITE ELEENT ANALYSIS OF PIPING TEES.(U) JUN 8 A J QUEZON. S C...DAVID W. TAYLOR NAVAL SHIP SRESEARCH AND DEVELOPMENT CENTER Bethesa Md. 20084 FINITE ELEMENT ANALYSIS OF PIPING TEES by Antonio J. Quezon, Gordon C
Finite Element Heat & Mass Transfer Code
Trease, Lynn
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities.
FEHM. Finite Element Heat & Mass Transfer Code
Zyvoloski, G.A.
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities.
Finite element simulations of stacked crystal filters
NASA Astrophysics Data System (ADS)
Lee, Jiunn-Horng; Tzeng, Kung-Yu; Cheng, Chih-Wei; Shih, Yu-Ching; Yao, Chih-Min
2004-03-01
Wireless networks are growing rapidly. Their applications include cellular phone, satellite communication and wireless local area networks. In order to avoid interference between all these applications, high selectivity RF filters are essential. The stacked crystal filter (SCF) is a useful configuration when low insertion loss is desired and the near-in skirt selectivity requirement is not as high as that produced by ladder filters. A SCF is an acoustically coupled resonator filter which includes a pair of thickness mode piezoelectric plates attached to each other. Mounted between adjacent sides of the two plates is a shared electrode. The common ways to model the SCF are mason model and lumped element equivalent circuit method. To accommodate complicated geometries, we need to use the other kinds of numerical analysis techniques. Finite element methods have been applied to the modeling of thin film bulk acoustic wave resonator in recent years. Advanced FEM software has the capability to do a coupled piezoelectric-circuit analysis that can connect electrical circuits directly to the piezoelectric finite element models. In this work, we integrate the SCF two-dimensional piezoelectric finite element models and electrical circuits together to simulate the performance of SCF. The influences of electrode property and acoustic loss to the performance of filter are also investigated. The results of simulation are verified by mason model. This methodology can be applied to more complicated geometry models and other types of filters simulation such as coupled resonator filters (CRF) and ladder filters.
Multiscale finite-element method for linear elastic geomechanics
NASA Astrophysics Data System (ADS)
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
Analysis of aircraft tires via semianalytic finite elements
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Kim, Kyun O.; Tanner, John A.
1990-01-01
A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell.
Finite element modelling of SAW correlator
NASA Astrophysics Data System (ADS)
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
EC Vacuum Vessel Finite Element Analysis
Rudland, D.; Luther, R.; /Fermilab
1992-02-04
This Note contains a summary of the results of the finite element analysis of the EC Cryostat vacuum vessel performed by Dave Rudland in 1987. The results are used in the structural evaluation of the EC cryostats presented in Engineering Note 194. It should also be noted that the adequacy of the design of the vacuum vessels was reviewed and verified by the Battelle Memorial Institute. Battelle used a shell of revolution program to essentially duplicate the FEA analysis with similar results. It should be noted that no plots of the finite element mesh were retained from the analysis, and these can not be easily reproduced due to a change in the version of the ANSYS computer program shortly after the analysis was completed.
Finite element substructuring methods for composite mechanics
NASA Technical Reports Server (NTRS)
Murthy, Pappu L. N.; Chamis, Christos C.
1988-01-01
Finite element substructuring strategies are presented to obtain numerical solutions for three typical problems of interest to the composites community: (1) impact and toughness characterization of composites using Charpy's impact test specimen; (2) free-edge stress analysis of composite laminates; and (3) fracture toughness predictions of composites for individual and combined fracture of modes I, II, and III. The key issue common to these problems is the presence of singular or near singular stress fields. The regions prone to see steep stress gradients are substructured with progressively refined meshes to study the local response simultaneously with the global response. The results from the select examples indicate that finite element substructuring methods are computationally effective for composite singularity mechanics.
2-d Finite Element Code Postprocessor
Sanford, L. A.; Hallquist, J. O.
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Finite element methods in fracture mechanics
NASA Technical Reports Server (NTRS)
Liebowitz, H.; Moyer, E. T., Jr.
1989-01-01
Finite-element methodology specific to the analysis of fracture mechanics problems is reviewed. Primary emphasis is on the important algorithmic developments which have enhanced the numerical modeling of fracture processes. Methodologies to address elastostatic problems in two and three dimensions, elastodynamic problems, elastoplastic problems, special considerations for three-dimensional nonlinear problems, and the modeling of stable crack growth are reviewed. In addition, the future needs of the fracture community are discussed and open questions are identified.
Finite Element Output Bounds for Hyperbolic Problems
Machiels, L.
2000-03-27
We propose a Neumann-subproblem a posteriori finite element error bound technique for linear stationary scalar advection problems. The method is similar in many respects to the previous output bound technique developed for elliptic problems. In the new approach, however, the primal residual is enhanced with a streamline diffusion term. We first formulate the bound algorithm, with particular emphasis on the proof of the bounding properties; then, we provide numerical results for an illustrative example.
Finite Element Methods: Principles for Their Selection.
1983-02-01
the finite element methods. 39 Various statements in the literature that certain mixed methods work well inspite of the fact that the LBB (BB...method, displacement and mixed methods , various adaptive approaches, etc. The examples discussed in Sections 2 and 3 show that the same computational...performance and their relation to mixed methods , SIAM J. Num. Anal., to appear. 5. F. Brezzi, On the existence uniqueness and approximation of saddle-point
EXODUS II: A finite element data model
Schoof, L.A.; Yarberry, V.R.
1994-09-01
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface (API).
Finite Element Analysis of Reverberation Chambers
NASA Technical Reports Server (NTRS)
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
Finite element based electric motor design optimization
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1993-01-01
The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.
Finite Element Results Visualization for Unstructured Grids
Speck, Douglas E.; Dovey, Donald J.
1996-07-15
GRIZ is a general-purpose post-processing application supporting interactive visualization of finite element analysis results on unstructured grids. In addition to basic pseudocolor renderings of state variables over the mesh surface, GRIZ provides modern visualization techniques such as isocontours and isosurfaces, cutting planes, vector field display, and particle traces. GRIZ accepts both command-line and mouse-driven input, and is portable to virtually any UNIX platform which provides Motif and OpenGl libraries.
TAURUS. 3-D Finite Element Code Postprocessor
Whirley, R.G.
1984-05-01
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-D Finite Element Code Postprocessor
Kennedy, T.
1992-03-03
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories, and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-D Finite Element Code Postprocessor
Whirley, R.G.
1993-11-30
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-d Finite Element Code Postprocessor
Whirley, R.G.
1991-05-01
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D (ESTSC 139), DYNA3D (ESTSC 138), TACO3D (ESTSC 287), TOPAZ3D (ESTSC 231), and GEMINI (ESTSC 455) and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-d Finite Element Code Postprocessor
Whirley, R.G.
1992-03-03
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D (ESTSC 139), DYNA3D (ESTSC 138), TACO3D (ESTSC 287), TOPAZ3D (ESTSC 231), and GEMINI (ESTSC 455) and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-D Finite Element Code Postprocessor
Whirley, R.G.
1992-03-03
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
Transient finite element method using edge elements for moving conductor
Tani, Koji; Nishio, Takayuki; Yamada, Takashi ); Kawase, Yoshihiro . Dept. of Information Science)
1999-05-01
For the next generation of high speed railway systems and automobiles new braking systems are currently under development. These braking systems take into account the eddy currents, which are produced by the movement of the conductor in the magnetic field. For their optimum design, it is necessary to know the distribution of eddy currents in the moving conductor. The finite element method (FEM) is often used to simulate them. Here, transient finite element method using edge elements for moving conductor is presented. Here the magnetic vector potential is interpolated at the upwind position and the time derivative term is discretized by the backward difference method. As a result, the system matrix becomes symmetric and the ICCG method is applicable to solve the matrix. This method is used to solve an eddy current rail brake system. The results demonstrate that this approach is suitable to solve transient problems involving movement.
Finite element-wavelet hybrid algorithm for atmospheric tomography.
Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny
2014-03-01
Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl.29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE7736, 77360X (2010)] in terms of quality.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1991-01-01
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1987-01-01
Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Finite element modeling of lipid bilayer membranes
NASA Astrophysics Data System (ADS)
Feng, Feng; Klug, William S.
2006-12-01
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.
Gauge finite element method for incompressible flows
NASA Astrophysics Data System (ADS)
E, Weinan; Liu, Jian-Guo
2000-12-01
A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher-order) finite elements. This method can achieve high-order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright
FESDIF -- Finite Element Scalar Diffraction theory code
Kraus, H.G.
1992-09-01
This document describes the theory and use of a powerful scalar diffraction theory based computer code for calculation of intensity fields due to diffraction of optical waves by two-dimensional planar apertures and lenses. This code is called FESDIF (Finite Element Scalar Diffraction). It is based upon both Fraunhofer and Kirchhoff scalar diffraction theories. Simplified routines for circular apertures are included. However, the real power of the code comes from its basis in finite element methods. These methods allow the diffracting aperture to be virtually any geometric shape, including the various secondary aperture obstructions present in telescope systems. Aperture functions, with virtually any phase and amplitude variations, are allowed in the aperture openings. Step change aperture functions are accommodated. The incident waves are considered to be monochromatic. Plane waves, spherical waves, or Gaussian laser beams may be incident upon the apertures. Both area and line integral transformations were developed for the finite element based diffraction transformations. There is some loss of aperture function generality in the line integral transformations which are typically many times more computationally efficient than the area integral transformations when applicable to a particular problem.
Solution of groundwater-flow equations using an orthogonal finite-element scheme
Yeh, G.T.
1983-01-01
A new finite-element scheme is presented for approximating the groundwater-flow equation, that will result in a matrix having the properties of the positive type and diagonal dominance. Because of these properties, the matrix equation is amenable to the pointwise iteration solution strategies. This scheme differs from the standard Galerkin scheme in that discretization is performed using a general weighted residual procedure and weighting functions orthogonal to basis functions. Numerical results have been obtained for two verification examples and are compared with results using the conventional Galerkin scheme and with analytical solutions. It is shown that both the direct elimination and pointwise iteration solutions of the new orthogonal finite-element equation yield as accurate results as those obtained by the direct elimination solution of the Galerkin finite-element scheme. However, while the pointwise iteration solution of the Galerkin finite-element method converges for one example, it generated divergent solutions for the other. A demonstration example of steady-state flow in a homogeneous medium is used to compare the utility and versatility of the new scheme with the conventional Galerkin finite-element method.
Using the finite element method to calculate sound transmission through bounded plates
NASA Astrophysics Data System (ADS)
Beshenkov, S. N.
1990-04-01
A finite element solution is obtained for the problem of sound transmission through a bounded plate mounted in an infinite absolutely rigid screen. Calculations are made of the soundproofing of quadratic and round plates. The convergence behavior of the iteration procedure used in the calculations is briefly discussed.
Finite Element approach for Density Functional Theory calculations on locally refined meshes
Fattebert, J; Hornung, R D; Wissink, A M
2007-02-23
We present a quadratic Finite Element approach to discretize the Kohn-Sham equations on structured non-uniform meshes. A multigrid FAC preconditioner is proposed to iteratively solve the equations by an accelerated steepest descent scheme. The method was implemented using SAMRAI, a parallel software infrastructure for general AMR applications. Examples of applications to small nanoclusters calculations are presented.
Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1993-01-01
Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.
NASA Technical Reports Server (NTRS)
Marr, W. A., Jr.
1972-01-01
The behavior of finite element models employing different constitutive relations to describe the stress-strain behavior of soils is investigated. Three models, which assume small strain theory is applicable, include a nondilatant, a dilatant and a strain hardening constitutive relation. Two models are formulated using large strain theory and include a hyperbolic and a Tresca elastic perfectly plastic constitutive relation. These finite element models are used to analyze retaining walls and footings. Methods of improving the finite element solutions are investigated. For nonlinear problems better solutions can be obtained by using smaller load increment sizes and more iterations per load increment than by increasing the number of elements. Suitable methods of treating tension stresses and stresses which exceed the yield criteria are discussed.
Regularised finite element model updating using measured incomplete modal data
NASA Astrophysics Data System (ADS)
Chen, Hua-Peng; Maung, Than Soe
2014-10-01
This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.
Grouped element-by-element iteration schemes for incompressible flow computations
NASA Astrophysics Data System (ADS)
Tezduyar, T. E.; Liou, J.
1989-05-01
Grouped element-by-element (GEBE) iteration schemes for incompressible flows are presented in the context of vorticity- stream function formulation. The GEBE procedure is a variation of the EBE procedure and is based on arrangement of the elements into groups with no inter-element coupling within each group. With the GEBE approach, vectorization and parallel implementation of the EBE method becomes more clear. The savings in storage and CPU time are demonstrated with two unsteady flow problems.
An iterative finite difference method for solving the quantum hydrodynamic equations of motion
Kendrick, Brian K
2010-01-01
The quantum hydrodynamic equations of motion associated with the de Broglie-Bohm description of quantum mechanics describe a time evolving probability density whose 'fluid' elements evolve as a correlated ensemble of particle trajectories. These equations are intuitively appealing due to their similarities with classical fluid dynamics and the appearance of a generalized Newton's equation of motion in which the total force contains both a classical and quantum contribution. However, the direct numerical solution of the quantum hydrodynamic equations (QHE) is fraught with challenges: the probability 'fluid' is highly-compressible, it has zero viscosity, the quantum potential ('pressure') is non-linear, and if that weren't enough the quantum potential can also become singular during the course of the calculations. Collectively these properties are responsible for the notorious numerical instabilities associated with a direct numerical solution of the QHE. The most successful and stable numerical approach that has been used to date is based on the Moving Least Squares (MLS) algorithm. The improved stability of this approach is due to the repeated local least squares fitting which effectively filters or reduces the numerical noise which tends to accumulate with time. However, this method is also subject to instabilities if it is pushed too hard. In addition, the stability of the MLS approach often comes at the expense of reduced resolution or fidelity of the calculation (i.e., the MLS filtering eliminates the higher-frequency components of the solution which may be of interest). Recently, a promising new solution method has been developed which is based on an iterative solution of the QHE using finite differences. This method (referred to as the Iterative Finite Difference Method or IFDM) is straightforward to implement, computationally efficient, stable, and its accuracy and convergence properties are well understood. A brief overview of the IFDM will be presented
The use of Galerkin finite-element methods to solve mass-transport equations
Grove, David B.
1977-01-01
The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)
Mixed Finite Element Method for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Modelling bucket excavation by finite element
NASA Astrophysics Data System (ADS)
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
NASA Technical Reports Server (NTRS)
Aberson, J. A.; Anderson, J. M.
1973-01-01
The recent introduction of special crack-tip singularity elements, usually referred to as cracked elements, has brought the power and flexibility of the finite-element method to bear much more effectively on fracture mechanics problems. This paper recalls the development of two cracked elements and presents the results of some applications proving their accuracy and economy. Judging from the available literature on numerical methods in fracture mechanics, it seems clear that the elements described have been used more extensively than any others in practical fracture mechanics applications.
Finite element implementation of state variable-based viscoplasticity models
NASA Technical Reports Server (NTRS)
Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.
1991-01-01
The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.
A responsive finite element method to aid interactive geometric modeling.
Umetani, N; Takayama, K; Mitani, J; Igarashi, T
2011-01-01
Current computer-aided engineering systems use numerical-simulation methods mainly as offline verification tools to reject designs that don't satisfy the required constraints, rather than as tools to guide users toward better designs. However, integrating real-time finite element method (FEM) into interactive geometric modeling can provide user guidance. During interactive editing, real-time feedback from numerical simulation guides users toward an improved design without tedious trial-and-error iterations. Careful reuse of previous computation results, such as meshes and matrices, on the basis of speed and accuracy trade-offs, have helped produce fast FEM analysis during interactive editing. Several 2D example applications and informal user studies show this approach's effectiveness. Such tools could help nonexpert users design objects that satisfy physical constraints and help those users understand the underlying physical properties.
Finite element modeling of pulsed eddy current NDT phenomena
Allen, B.; Ida, N.; Lord, W.
1985-05-15
Transient fields for nondestructive testing (pulsed eddy current methods) have been used experimentally for such applications as coating thickness measurements and the inspection of reactor fuel tubing. The lack of suitable models to facilitate understanding of the interaction of the pulsed field with the test specimen has hindered a wider acceptance of the method as a tool in NDT. Two models, based on the finite element technique are described. The first model, used for repetitive pulse train sources makes use of the Fourier series of the source current to solve a steady state problem for each significant harmonic. The harmonic solutions are then summed to produce the total EMF in the pickup coil. The second model is used for single pulse application. The response is calculated using an iterative time stepping solution. In both cases axisymmetric geometries are studied using a magnetic vector potential formulation. Solutions are compared with experimental results. 3 refs., 3 figs.
Finite-element analysis of nonlinear conduction problems subject to moving fields
NASA Technical Reports Server (NTRS)
Padovan, J.
1980-01-01
Through the use of a space-time warp, specialized moving finite elements are developed that can be employed to generate a nonlinear heat conduction model for situations involving traveling boundary and heat generation fields superposed on an initial state. To facilitate the solution of the resulting nonlinear finite-element formulation, a multilevel heuristic iterative solution strategy is developed. In order to demonstrate the versatility and accuracy of the moving elements and their associated nonlinear solution strategy, the results of several numerical experiments are presented.
System software for the finite element machine
NASA Technical Reports Server (NTRS)
Crockett, T. W.; Knott, J. D.
1985-01-01
The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested.
A finite element model of ultrasonic extrusion
NASA Astrophysics Data System (ADS)
Lucas, M.; Daud, Y.
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
Finite Element Modeling of Mitral Valve Repair
Morgan, Ashley E.; Pantoja, Joe Luis; Weinsaft, Jonathan; Grossi, Eugene; Guccione, Julius M.; Ge, Liang; Ratcliffe, Mark
2016-01-01
The mitral valve is a complex structure regulating forward flow of blood between the left atrium and left ventricle (LV). Multiple disease processes can affect its proper function, and when these diseases cause severe mitral regurgitation (MR), optimal treatment is repair of the native valve. The mitral valve (MV) is a dynamic structure with multiple components that have complex interactions. Computational modeling through finite element (FE) analysis is a valuable tool to delineate the biomechanical properties of the mitral valve and understand its diseases and their repairs. In this review, we present an overview of relevant mitral valve diseases, and describe the evolution of FE models of surgical valve repair techniques. PMID:26632260
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
Chemorheology of reactive systems: Finite element analysis
NASA Technical Reports Server (NTRS)
Douglas, C.; Roylance, D.
1982-01-01
The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.
A finite element Poisson solver for gyrokinetic particle simulations in a global field aligned mesh
Nishimura, Y. . E-mail: nishimuy@uci.edu; Lin, Z.; Lewandowski, J.L.V.; Ethier, S.
2006-05-20
A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations.
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.
1990-01-01
An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.
Aeroelastic Stability of Rotor Blades Using Finite Element Analysis
NASA Technical Reports Server (NTRS)
Chopra, I.; Sivaneri, N.
1982-01-01
The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.
A nonlinear dynamic finite element approach for simulating muscular hydrostats.
Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A
2014-01-01
An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.
Baradari, F.
1982-01-01
In this work the applicability of a ''Boundary Element method'' for the numerical solution of the Liouville and Helmholtz eigenvalue problem for different two dimensional geometries including a typical reactor configuration was investigated. The method is based on the discretization of the unknown along the boundary and Green's function representation of the governing equation. To compare the capability of this method with the finite element method, a finite element code which uses quadratic quadrilateral isoparametric elements was developed. A boundary element code was also written. These codes were used to determine the fundamental eigenvalue for several two dimensional geometries--square, ''L'' shaped, circular, and a quarter of a typical reactor core. The results of both codes were compared with each other and with analytical solutions where available. To optimize the computer time for the code based on the boundary element method, a powerful search technique called Fibonacci search was used to determine the fundamental eigenvalues. During the course of this study, it was found that eliminating the imaginary part of the fundamental solution of the Helmholtz equation produced an instability in the result. The results show that, due to the use of the iteration procedure in the boundary element method to evaluate the determinant of the deduced matrix, more computer time is required for the boundary element solution than the finite element solution. However, the results obtained on the basis of the boundary element technique are more accurate than those from the finite element method.
An algorithm for domain decomposition in finite element analysis
NASA Technical Reports Server (NTRS)
Al-Nasra, M.; Nguyen, D. T.
1991-01-01
A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multiprocessor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.
Nonlinear finite element analysis of solids and structures. Volume 1: Essentials
Crisfield, M.A.
1991-12-31
This book is written for the practicing engineer. It is an attempt to bring together various strands of work on nonlinear finite elements. The developments in the book are related to computer applications; there are a number of Fortran listings, and many flow charts, for solving parts of nonlinear finite element problems. (Floppy disks with the Fortran source and data files are available from the publisher). This book takes an engineering rather than a mathematical approach to nonlinear finite elements. The first three chapters deal with truss elements. The author introduces basic concepts of nonlinear finite element analysis for simple truss systems with one degree of freedom. The solution schemes considered include an incremental (Euler), an iterative (Newton-Raphson), and a combined incremental and iteration approach (full or modified Newton-Raphson or the initial stress method). In chapter 2, the author introduces the shallow truss theory of chapter 1 to derive the finite element equations for a shallow truss slement with four degrees of freedom. A set of Fortran subroutines is given to solve simple bar-spring problems; some flowcharts are also provided. This chapter also contains data and solutions from a number of bar-spring problems.
Finite Element Analysis of a Floating Microstimulator
Sahin, Mesut; Ur-Rahman, Syed S.
2011-01-01
Analytical solutions for voltage fields in a volume conductor are available only for ideal electrodes with radially symmetric contacts and infinitely extending substrates. Practical electrodes for neural stimulation may have asymmetric contacts and finite substrate dimensions and hence deviate from the ideal geometries. For instance, it needs to be determined if the analytical solutions are adequate for simulations of narrow shank electrodes where the substrate width is comparable to the size of the contacts. As an extension to this problem, a “floating” stimulator can be envisioned where the substrate would be finite in all directions. The question then becomes how small this floating stimulator can be made before its stimulation strength is compromised by the decrease in the medium impedance between the contacts as the contacts are approaching each other. We used finite element modeling to solve the voltage and current profiles generated by these radially asymmetric electrode geometries in a volume conductor. The simulation results suggest that both the substrate size and the bipolar contact separation influence the voltage field when these parameters are as small as a few times the contact size. Both of these effects are larger for increasing elevations from the contact surface, and even stronger for floating electrodes (finite substrate in all directions) than the shank-type electrodes. Location of the contacts on the floating electrode also plays a role in determining the voltage field. The voltage field for any device size and current, and any specific resistance of the volume conductor can be predicted from these results so long as the aspect ratios are preserved. PMID:17601192
Impeller deflection and modal finite element analysis.
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A.; Mrozek, Randy A.; Lenhart, Joseph Ludlow; Rao, Rekha Ranjana; Collins, Robert; Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
Finite element analysis of bolted flange connections
NASA Astrophysics Data System (ADS)
Hwang, D. Y.; Stallings, J. M.
1994-06-01
A 2-D axisymmetric finite element model and a 3-D solid finite element model of a high pressure bolted flange joint were generated to investigate the stress behaviors. This investigation includes comparisons for axisymmetric loading of both the 2-D and 3-D models, the effects of non-axisymmetric bolt pretensions in the 3-D models, and the differences between 2-D and 3-D models subjected to non-axisymmetric loading. Comparisons indicated differences in von Mises stress up to 12% at various points due to the non-axisymmetric bolt pretensions. Applied bending moments were converted to equivalent axial forces for use in the 2-D model. It was found that the largest von Mises stresses in 3-D model did not occur on the side of the connection where the bending stresses and applied axial stresses were additive. Hence, in the 2-D model where the equivalent axial force (for bending moment) and applied axial forces were added, the 2-D model under estimated the maximum von Mises stress obtained from the 3-D model by 30%.
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Accurate finite element modeling of acoustic waves
NASA Astrophysics Data System (ADS)
Idesman, A.; Pham, D.
2014-07-01
In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analyses is presented. New thermal finite elements which yield exact nodal and element temperature for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal-structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
Finite element analysis enhancement of cryogenic testing
NASA Astrophysics Data System (ADS)
Thiem, Clare D.; Norton, Douglas A.
1991-12-01
Finite element analysis (FEA) of large space optics enhances cryogenic testing by providing an analytical method by which to ensure that a test article survives proposed testing. The analyses presented in this paper were concerned with determining the reliability of a half meter mirror in an environment where the exact environmental profile was unknown. FEA allows the interaction between the test object and the environment to be simulated to detect potential problems prior to actual testing. These analyses examined worse case scenerios related to cooling the mirror, its structural integrity for the proposed test environment, and deformation of the reflective surface. The FEA was conducted in-house on the System's Reliability Division's VAX 11-750 and Decstation 3100 using Engineering Mechanics Research Corporation's numerically integrated elements for systems analysis finite element software. The results of the analyses showed that it would take at least 48 hours to cool the mirror to its desired testing temperature. It was also determined that the proposed mirror mount would not cause critical concentrated thermal stresses that would fracture the mirror. FEA and actual measurements of the front reflective face were compared and good agreement between computer simulation and physical tests were seen. Space deployment of large optics requires lightweight mirrors which can perform under the harsh conditions of space. The physical characteristics of these mirrors must be well understood in order that their deployment and operation are successful. Evaluating design approaches by analytical simulation, like FEA, verifies the reliability and structural integrity of a space optic during design prior to prototyping and testing. Eliminating an optic's poor design early in its life saves money, materials, and human resources while ensuring performance.
Mixed Finite Element Methods for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.
2005-01-01
A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.
Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.
2005-01-01
A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.
Finite element models and feedback control of flexible aerospace structures
NASA Technical Reports Server (NTRS)
Balas, M. J.
1980-01-01
Large flexible aerospace structures, such as the solar power satellite, are distributed parameter systems with very complex continuum descriptions. This paper investigates the use of finite element methods to produce reduced-order models and finite dimensional feedback controllers for these structures. The main results give conditions under which stable control of the finite element model will produce stable control of the actual structure.
TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures
NASA Technical Reports Server (NTRS)
Thornton, E. A.
1976-01-01
The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.
Patient-specific finite element modeling of bones.
Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A
2013-04-01
Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.
NASA Astrophysics Data System (ADS)
Conley, Rebecca; Delaney, Tristan J.; Jiao, Xiangmin
2016-11-01
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES-FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial (GLP) basis functions, which we construct using local weighted least-squares approximations. The method preserves the theoretical framework of FEM, and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES-FEM can use higher-degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES-FEM, and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poison equation and a time-independent convection-diffusion equation. The numerical results demonstrate that AES-FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor-quality meshes
Efficient finite element modeling of elastodynamic scattering
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2009-03-01
The scattering of elastic waves by defects is the physical basis of ultrasonic NDE. Although analytical models exist for some canonical problems, the general case of scattering from an arbitrarily-shaped defect requires numerical methods such as finite elements (FE). In this paper, a robust and efficient FE technique is presented that is based on the premise of meshing a relatively small domain sufficient to enclose the scatterer. Plane waves are then excited from a particular direction by a numerical implementation of the Helmholtz-Kirchhoff integral that uses an encircling array of uni-modal point sources. The scattered field displacements are recorded at the same points and the field decomposed into plane waves of different modes at different angles. By repeating this procedure for different incident angles it is possible to generate the scattering- or S-matrix for the scatterer. For a given size of scatterer, all the information in an S-matrix can be represented in the Fourier domain by a limited number of complex coefficients. Thus the complete scattering behavior of an arbitrary-shaped scatterer can be characterized by a finite number of complex coefficients, that can be obtained from a relatively small number of FE model executions.
Elastic buckling of stiffened plates by the finite element method
Sabir, A.B.; Djoudi, M.S.
1995-09-01
The finite element method is used to obtain the elastic buckling loads of stiffened plates. The plates are modeled by rectangular plate elements and the stiffeners which are rectangular in cross section are modeled by exact beam elements. Eccentrically located stiffeners as well as stiffeners having centroids coinciding with the middle surface of the plates are considered. The effect of the flexural rigidity of the stiffeners relative to that of the plates on the buckling load is investigated. Square plates simply supported along the four edges are considered when subjected to uniform uniaxial compressive loads. Further investigations are carried out to examine the effect of the number of stiffeners and their locations on the buckling load and the mode of buckling. Stiffeners positioned in the direction of the applied compressive load or in the transverse direction are also considered. The method used in the calculation of the buckling load is the subspace iteration technique. This method is shown to produce acceptable results for the eigenvalues and the associated eigenvectors of the transidental equations for the combined stiffness and geometric matrices for the stiffened plates. The buckling loads as well as the modes of buckling are determined and compared where possible with existing solutions.
Structural optimization of thin shells using finite element method
NASA Technical Reports Server (NTRS)
Gotsis, Pascal K.
1992-01-01
The objective of the present work was the structural optimization of thin shell structures that are subjected to stress and displacement constraints. In order to accomplish this, the structural optimization computer program DESAP1 was modified and improved. In the static analysis part of the DESAP1 computer program the torsional spring elements, which are used to analyze thin, shallow shell structures, were eliminated by modifying the membrane stiffness matrix of the triangular elements in the local coordinate system and adding a fictitious rotational stiffness matrix. This simplified the DESAP1 program input, improved the accuracy of the analysis, and saved computation time. In the optimization part of the DESAP1 program the stress ratio formula, which redesigns the thickness of each finite element of the structure, was solved by an analytical method. This scheme replaced the iterative solution that was previously used in the DESAP1 program, thus increasing the accuracy and speed of the design. The modified program was used to design a thin, cylindrical shell structure with optimum weight, and the results are reported in this paper.
Immersed molecular electrokinetic finite element method
NASA Astrophysics Data System (ADS)
Kopacz, Adrian M.; Liu, Wing K.
2013-07-01
A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier-Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid-structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.
Quality management of finite element analysis
NASA Astrophysics Data System (ADS)
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
Finite element or Galerkin type semidiscrete schemes
NASA Technical Reports Server (NTRS)
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
Adaptive finite element methods in electrochemistry.
Gavaghan, David J; Gillow, Kathryn; Süli, Endre
2006-12-05
In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.
NASA Technical Reports Server (NTRS)
Cooke, C. H.; Blanchard, D. K.
1975-01-01
A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.
Improved finite-element methods for rotorcraft structures
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1991-01-01
An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1989-01-01
The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
NASA Technical Reports Server (NTRS)
1976-01-01
The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.
Yoshida, Hiroaki; Tada, Mitsunori; Mochimaru, Masaaki
2011-03-01
Since the tactile perception detects skin deformation due to the contact of an object, it is important to understand contact mechanics, especially, frictional behavior of the human fingertip. The coefficient of friction is recently modeled as a function of the applied normal load in which case the traditional Coulomb's law does not provide a description for the skin surface. When a surface is a rubber-like material, the frictional behavior follows the frictional law of the rubber-like material. Therefore, we developed a three-dimensional Finite Element model of the fingertip and analyzed frictional behavior based on the frictional law of rubber-like material. We proposed a combined technique using both experimental and Finite Element analyses in order to investigate the frictional property of the fingertip. A three-dimensional Finite Element model of the fingertip was developed using MRI images. We hypothesized a frictional equation of the critical shear stress. Squared differences between equivalent coefficient of friction of the FE analysis and the coefficient of kinetic friction of the experiment while sliding was decreased and the Finite Element analysis iterated until the error was minimized, and thus the frictional equation was determined. We obtained the equation of the critical shear stress and simulated kinetic friction of the fingertip while sliding under arbitrary normal loading condition by using the Finite Element analysis. We think this study is an appropriate method for understanding the frictional property of the human fingertip using the Finite Element analysis.
Ablative Thermal Response Analysis Using the Finite Element Method
NASA Technical Reports Server (NTRS)
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Leapfrog/Finite Element Method for Fractional Diffusion Equation
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L 2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis. PMID:24955431
Cwik, T.; Katz, D.S.
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
An efficient finite element solution for gear dynamics
NASA Astrophysics Data System (ADS)
Cooley, C. G.; Parker, R. G.; Vijayakar, S. M.
2010-06-01
A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.
Finite Element Analysis (FEA) in Design and Production.
ERIC Educational Resources Information Center
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
Finite Element Analysis (FEA) in Design and Production.
ERIC Educational Resources Information Center
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
Finite element modelling of fabric shear
NASA Astrophysics Data System (ADS)
Lin, Hua; Clifford, Mike J.; Long, Andrew C.; Sherburn, Martin
2009-01-01
In this study, a finite element model to predict shear force versus shear angle for woven fabrics is developed. The model is based on the TexGen geometric modelling schema, developed at the University of Nottingham and orthotropic constitutive models for yarn behaviour, coupled with a unified displacement-difference periodic boundary condition. A major distinction from prior modelling of fabric shear is that the details of picture frame kinematics are included in the model, which allows the mechanisms of fabric shear to be represented more accurately. Meso- and micro-mechanisms of deformation are modelled to determine their contributions to energy dissipation during shear. The model is evaluated using results obtained for a glass fibre plain woven fabric, and the importance of boundary conditions in the analysis of deformation mechanisms is highlighted. The simulation results show that the simple rotation boundary condition is adequate for predicting shear force at large deformations, with most of the energy being dissipated at higher shear angles due to yarn compaction. For small deformations, a detailed kinematic analysis is needed, enabling the yarn shear and rotation deformation mechanisms to be modelled accurately.
TACO: a finite element heat transfer code
Mason, W.E. Jr.
1980-02-01
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code.
VALIDATION OF ANSYS FINITE ELEMENT ANALYSIS SOFTWARE
HAMM, E.R.
2003-06-27
This document provides a record of the verification and Validation of the ANSYS Version 7.0 software that is installed on selected CH2M HILL computers. The issues addressed include: Software verification, installation, validation, configuration management and error reporting. The ANSYS{reg_sign} computer program is a large scale multi-purpose finite element program which may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS Full Mechanical Version 7.0 installed on selected CH2M Hill Hanford Group (CH2M HILL) Intel processor based computers include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses and various types of field and coupled-field applications. The program contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and thermal radiation. The ANSYS program has been in commercial use since 1970, and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil and steel industries.
Intra Plate Stresses Using Finite Element Modelling
NASA Astrophysics Data System (ADS)
Jayalakshmi, S.; Raghukanth, S. T. G.
2016-10-01
One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo- Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma).
Wang, Wansheng; Chen, Long; Zhou, Jie
2016-05-01
A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures.
Thermal-structural finite element analysis using linear flux formulation
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Wieting, Allan R.
1990-01-01
A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.
Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan
2017-05-01
Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.
NASA Astrophysics Data System (ADS)
Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan
2017-05-01
Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.
Block Iterative Methods for Elliptic Finite Element Equations.
1983-03-01
inverse inequalities (5.3) hold, then Landau’s inequality implies that there is a constant Eo such that hmllull. !- U0o lllo. (5.6) This inverse inequality...a! n E, P 0. (a.23) Let V be the eigenfunction associated with a. Then rLF= qgP inO, b9=O onO( (0J!9m-1). (a.24) -71- Equivalently, aB (go’v) f q rp7dz
An efficient finite-element algorithm for 3D layered complex structure modelling.
Sahalos, J N; Kyriacou, G A; Vafiadis, E
1994-05-01
In this paper an efficient finite-element method (FEM) algorithm for complicated three-dimensional (3D) layered type models has been developed. Its unique feature is that it can handle, with memory requirements within the abilities of a simple PC, arbitrarily shaped 3D elements. This task is achieved by storing only the non-zero coefficients of the sparse FEM system of equations. The algorithm is applied to the solution of the Laplace equation in models with up to 79 layers of trilinear general hexahedron elements. The system of equations is solved with the Gauss-Seidel iterative technique.
Solution-adaptive finite element method in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
Modular Finite Element Methods Library Version: 1.0
2010-06-22
MFEM is a general, modular library for finite element methods. It provides a variety of finite element spaces and bilinear/linear forms in 2D and 3D. MFEM also includes classes for dealing with various types of meshes and their refinement.
Generating Finite-Element Models Of Composite Materials
NASA Technical Reports Server (NTRS)
Melis, M. E.
1993-01-01
Program starts at micromechanical level, from simple inputs supplied by user. COMGEN, COmposite Model GENerator, is interactive FORTRAN program used to create wide variety of finite-element models of continuous-fiber composite materials at micromechanical level. Quickly generates batch or "session files" to be submitted to finite-element preprocessor and postprocessor program, PATRAN. COMGEN requires PATRAN to complete model.
A computer graphics program for general finite element analyses
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1978-01-01
Documentation for a computer graphics program for displays from general finite element analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid finite element analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.
Finite element meshing of ANSYS (trademark) solid models
NASA Technical Reports Server (NTRS)
Kelley, F. S.
1987-01-01
A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.
TAURUS96. 3-D Finite Element Code Postprocessor
Brown, B.; Hallquist, J.O.; Spelce, T.E.
1993-11-30
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
Finite-element analysis of a weld-penetration problem
NASA Technical Reports Server (NTRS)
Rogge, T. R.
1977-01-01
The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.
Practical Application of Finite Element Analysis to Aircraft Structural Design
1986-08-01
t] Cook, Robert D., "Concepts and Applications of Finite element Analysis," John Wiley & Sons, Inc., New York, 1981. [5] Rao, S. S., "The Finite...generation large-scale computer programs is discussed. V.P. Analysis of aircraft structure using applied fracture mechanics (AA) WILHEM , D. P. Northrop...Analytical, finite element for surface flaws, holes (AA) WILHEM , D. P. Northrop Corp., Hawthorne, Calif. (N5631231) Aircraft Group. In AGARD Fracture
Application of modified integration rule to time-domain finite-element acoustic simulation of rooms.
Okuzono, Takeshi; Otsuru, Toru; Tomiku, Reiji; Okamoto, Noriko
2012-08-01
The applicability of the modified integration rule for time-domain finite-element analysis is tested in sound field analysis of rooms involving rectangular elements, distorted elements, and finite impedance boundary conditions. Dispersion error analysis in three dimensions is conducted to evaluate the dispersion error in time-domain finite-element analysis using eight-node hexahedral elements. The results of analysis confirmed that fourth-order accuracy with respect to dispersion error is obtainable using the Fox-Goodwin method (FG) with a modified integration rule, even for rectangular elements. The stability condition in three-dimensional analysis using the modified integration rule is also presented. Numerical experiments demonstrate that FG with a modified integration rule performs much better than FG with the conventional integration rule for problems with rectangular elements, distorted elements, and with finite impedance boundary conditions. Further, as another advantage, numerical results revealed that the use of modified integration rule engenders faster convergence of the iterative solver than a conventional rule for problems with the same degrees of freedom.
Analysis of finite deformations of elastic solids by the finite element method.
NASA Technical Reports Server (NTRS)
Oden, J. T.; Key, J. E.
1971-01-01
Finite element applications, particularly to analyses of finite deformations in elastic solids, are reviewed, along with the difficulties encountered in the formulation of certain problems and in their numerical solution. Various approaches are discussed for overcoming these and other difficulties. A computer program designed for finite elasticity problems is described, and several numerical examples are presented.
Nondestructive Evaluation Correlated with Finite Element Analysis
NASA Technical Reports Server (NTRS)
Abdul-Azid, Ali; Baaklini, George Y.
1999-01-01
Advanced materials are being developed for use in high-temperature gas turbine applications. For these new materials to be fully utilized, their deformation properties, their nondestructive evaluation (NDE) quality and material durability, and their creep and fatigue fracture characteristics need to be determined by suitable experiments. The experimental findings must be analyzed, characterized, modeled and translated into constitutive equations for stress analysis and life prediction. Only when these ingredients - together with the appropriate computational tools - are available, can durability analysis be performed in the design stage, long before the component is built. One of the many structural components being evaluated by the NDE group at the NASA Lewis Research Center is the flywheel system. It is being considered as an energy storage device for advanced space vehicles. Such devices offer advantages over electrochemical batteries in situations demanding high power delivery and high energy storage per unit weight. In addition, flywheels have potentially higher efficiency and longer lifetimes with proper motor-generator and rotor design. Flywheels made of fiber-reinforced polymer composite material show great promise for energy applications because of the high energy and power densities that they can achieve along with a burst failure mode that is relatively benign in comparison to those of flywheels made of metallic materials Therefore, to help improve durability and reduce structural uncertainties, we are developing a comprehensive analytical approach to predict the reliability and life of these components under these harsh loading conditions. The combination of NDE and two- and three-dimensional finite element analyses (e.g., stress analyses and fracture mechanics) is expected to set a standardized procedure to accurately assess the applicability of using various composite materials to design a suitable rotor/flywheel assembly.
Finite element simulation of thick sheet thermoforming
NASA Astrophysics Data System (ADS)
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
Finite Element analyses of soil bioengineered slopes
NASA Astrophysics Data System (ADS)
Tamagnini, Roberto; Switala, Barbara Maria; Sudan Acharya, Madhu; Wu, Wei; Graf, Frank; Auer, Michael; te Kamp, Lothar
2014-05-01
Soil Bioengineering methods are not only effective from an economical point of view, but they are also interesting as fully ecological solutions. The presented project is aimed to define a numerical model which includes the impact of vegetation on slope stability, considering both mechanical and hydrological effects. In this project, a constitutive model has been developed that accounts for the multi-phase nature of the soil, namely the partly saturated condition and it also includes the effects of a biological component. The constitutive equation is implemented in the Finite Element (FE) software Comes-Geo with an implicit integration scheme that accounts for the collapse of the soils structure due to wetting. The mathematical formulation of the constitutive equations is introduced by means of thermodynamics and it simulates the growth of the biological system during the time. The numerical code is then applied in the analysis of an ideal rainfall induced landslide. The slope is analyzed for vegetated and non-vegetated conditions. The final results allow to quantitatively assessing the impact of vegetation on slope stability. This allows drawing conclusions and choosing whenever it is worthful to use soil bioengineering methods in slope stabilization instead of traditional approaches. The application of the FE methods show some advantages with respect to the commonly used limit equilibrium analyses, because it can account for the real coupled strain-diffusion nature of the problem. The mechanical strength of roots is in fact influenced by the stress evolution into the slope. Moreover, FE method does not need a pre-definition of any failure surface. FE method can also be used in monitoring the progressive failure of the soil bio-engineered system as it calculates the amount of displacements and strains of the model slope. The preliminary study results show that the formulated equations can be useful for analysis and evaluation of different soil bio
Finite element analysis of posterior cervical fixation.
Duan, Y; Wang, H H; Jin, A M; Zhang, L; Min, S X; Liu, C L; Qiu, S J; Shu, X Q
2015-02-01
Despite largely, used in the past, biomechanical test, to investigate the fixation techniques of subaxial cervical spine, information is lacking about the internal structural response to external loading. It is not yet clear which technique represents the best choice and whether stabilization devices can be efficient and beneficial for three-column injuries (TCI). The different posterior cervical fixation techniques (pedicle screw PS, lateral mass screw LS, and transarticular screw TS) have respective indications. A detailed, geometrically accurate, nonlinear C3-C7 finite element model (FEM) had been successfully developed and validated. Then three FEMs were reconstructed from different fixation techniques after C4-C6 TCI. A compressive preload of 74N combined with a pure moment of 1.8 Nm in flexion, extension, left-right lateral bending, and left-right axial rotation was applied to the FEMs. The ROM results showed that there were obvious significant differences when comparing the different fixation techniques. PS and TS techniques can provide better immediate stabilization, compared to LS technique. The stress results showed that the variability of von Mises stress in the TS fixation device was minimum and LS fixation device was maximum. Furthermore, the screws inserted by TS technique had high stress concentration at the middle part of the screws. Screw inserted by PS and LS techniques had higher stress concentration at the actual cap-rod-screw interface. The research considers that spinal surgeon should first consider using the TS technique to treat cervical TCI. If PS technique is used, we should eventually prolong the need for external bracing in order to reduce the higher risk of fracture on fixation devices. If LS technique is used, we should add anterior cervical operation for acquire a better immediate stabilization. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
FEWA: a Finite Element model of Water flow through Aquifers
Yeh, G.T.; Huff, D.D.
1983-11-01
This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables.
The L sub 1 finite element method for pure convection problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1991-01-01
The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.
Viscoelastic characterization of soft tissue from dynamic finite element models.
Eskandari, Hani; Salcudean, Septimiu E; Rohling, Robert; Ohayon, Jacques
2008-11-21
An iterative solution to the inverse problem of elasticity and viscosity is proposed in this paper. A new dynamic finite element model that is consistent with known rheological models has been derived to account for the viscoelastic changes in soft tissue. The model assumes known lumped masses at the nodes, and comprises two vectors of elasticity and viscosity parameters that depend on the material elasticity and viscosity distribution, respectively. Using this deformation model and the observed dynamic data for harmonic excitation, the inverse problem is solved to reconstruct the viscosity and elasticity in the medium by using a Gauss-Newton-based approach. As in other inverse problems, previous knowledge of the parameters on the boundaries of the medium is necessary to assure uniqueness and convergence and to obtain an accurate map of the viscoelastic properties. The sensitivity of the solutions to noise, model and boundary conditions has been studied through numerical simulations. Experimental results are also presented. The viscosity and elasticity of a gelatin-based phantom with inclusion of known properties have been reconstructed and have been shown to be close to the values obtained using standard rheometry.
Three dimensional inelastic finite element analysis of laminated composites
NASA Technical Reports Server (NTRS)
Griffin, O. H., Jr.; Kamat, M. P.
1980-01-01
Formulations of the inelastic response of laminated composites to thermal and mechanical loading are used as the basis for development of the computer NALCOM (Nonlinear Analysis of Laminated Composites) computer program which uses a fully three dimensional isoparametric finite element with 24 nodes and 72 degrees of freedom. An incremental solution is performed with nonlinearities introduced as pseudoloads computed for initial strains. Equilibrium iteration may be performed at every step. Elastic and elastic-plastic response of boron/epoxy and graphite/epoxy graphite/epoxy and problems of curing 0/90 sub s Gr/Ep laminates with and without circular holes are analyzed. Mechanical loading of + or - 45sub s Gr/Ep laminates is modeled and symmetry conditions which exist in angle-ply laminates are discussed. Results are compared to experiments and other analytical models when possible. All models are seen to agree reasonably well with experimetnal results for off-axis tensile coupons. The laminate analyses show the three dimensional effects which are present near holes and free corners.
A hybrid finite-difference and analytic element groundwater model.
Haitjema, H M; Feinstein, D T; Hunt, R J; Gusyev, M A
2010-01-01
Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-03-22
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
Combined Finite- and Boundary-Element Analysis of SCC Crack Growth
NASA Astrophysics Data System (ADS)
Nikishkov, Gennadiy
2010-05-01
Modeling of stress corrosion cracking (SCC) is performed using the combination of the finite element method and the symmetric Galerkin boundary element method. The uncracked structural component is represented with finite elements. The crack is simulated using the boundary element method. The superposition principle is employed for combining two solutions. The equilibrium state for the system of the structural component and the crack is reached after several iterations that alternate between two methods. It is adopted that the crack develops in the direction of the J-integral vector and the crack growth rate is determined by the mechanochemical model using the effective stress intensity factor based on the J-integral value. Results of SCC crack growth modeling are presented for inclined semi-elliptical surface cracks under tensile loading.
Static Implicit vs. Dynamic Explicit Finite Element Analysis for Ring Rolling Process Modeling
NASA Astrophysics Data System (ADS)
Pauskar, P. M.; Sawamiphakdi, K.; Jin, D. Q.
2004-06-01
Over the past two decades, various finite element formulations and solution techniques for metal forming analysis have been developed. Most finite element codes for bulk metal forming used in the industry today are based on static implicit solution schemes wherein a non-linear system of equations is solved iteratively for each time increment. For simple 2D problems, static implicit analysis models are generally known to be more accurate and efficient than dynamic explicit analysis models. However, for complex 3D forming problems, the static implicit procedures encounter a number of inherent difficulties especially in incremental forming processes such as ring rolling in which several surface nodes repeatedly make contact with and separate from the dies. Static implicit finite element formulations require a very long computational time for the analysis of ring rolling. Several solution techniques have been developed to reduce the computational time of static implicit finite element analysis, namely the dual mesh technique, Arbitrary Lagrangian Eulerian (ALE) technique, etc. The dynamic explicit method on the other hand appears to be very effective in analyzing complex incremental forming problems. In this paper, a comparison of the analysis results obtained using dynamic explicit finite element method and static implicit method using a dual mesh approach is presented.
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.
Discontinuous Galerkin finite element solution for poromechanics
NASA Astrophysics Data System (ADS)
Liu, Ruijie
This dissertation focuses on applying discontinuous Galerkin (DG) methods to poromechanics problems. A few challenges have been presented in traditional and popular continuous Galerkin (CG) finite element methods for solving complex coupled thermal, flow and solid mechanics. For example, nonphysical pore pressure oscillations often occur in CG solutions for poroelasticity problems with low permeability. A robust and practical numerical scheme for removing or alleviating the oscillation is not available. In modeling thermoporoelastoplasticity, CG methods require the use of very small time steps to obtain a convergent solution. The temperature profile predicted by CG methods in the fine mesh zones is often seriously polluted by large errors produced in coarse mesh zones in the case where the convection dominates the thermal process. The nonphysical oscillations in pore pressure and temperature solutions induced by CG methods at very early time stages seriously corrupt the solutions at longer time. We propose DG methods to handle these challenges because they are physics driven, provide local conservation of mass and momentum, have high stability and robustness, are locking-free, and because of their meshing and implementation capabilities. We first apply a family of DG methods, including Oden-Babuska-Baumann (OBB), Nonsymmetric Interior Penalty Galerkin (NIPG), Symmetric Interior Penalty Galerkin (SIPG) and Incomplete Interior Penalty Galerkin (IIPG), to 3D linear elasticity problems. This family of DG methods is tested and evaluated by using a cantilever beam problem with nearly incompressible materials. It is shown that DG methods are simple, robust and locking-free in dealing with nearly incompressible materials. Based on the success of DG methods in elasticity, we extend the DG theory into plasticity problems. A DG formulation has been implemented for solving 3D poroelasticity problems with low permeability. Numerical examples solved by DG methods demonstrate
Design of fast tuning elements for the ITER ICH system
Swain, D.W.; Goulding, R.H.
1996-05-01
The coupling between the ion cyclotron (IC) antenna and the ITER plasma (as expressed by the load resistance the antenna sees) will experience relatively fast variations due to plasma edge profile modifications. If uncompensated, these will cause an increase in the amount of power reflected back to the transmitter and ultimately a decrease in the amount of radio frequency (rf) power to the plasma caused by protective suppression of the amount of rf power generated by the transmitter. The goals of this task were to study several alternate designs for a tuning and matching (T&M) system and to recommend some research and development (R&D) tasks that could be carried out to test some of the most promising concepts. Analyses of five different T&M configurations are presented in this report. They each have different advantages and disadvantages, and the choice among them must be made depending on the requirements for the IC system. Several general conclusions emerge from our study: The use of a hybrid splitter as a passive reflected-power dump [``edge localized mode (ELM)-dump``] appears very promising; this configuration will protect the rf power sources from reflected power during changes in plasma loading due to plasma motion or profile changes (e.g., ELM- induced changes in the plasma scrape-off region) and requires no active control of the rf system. Trade-offs between simplicity of design and capability of the system must be made. Simple system designs with few components near the antenna either have high voltages over considerable distances of transmission lines, or they are not easily tuned to operate at different frequencies. Designs using frequency shifts and/or fast tuning elements can provide fast matching over a wide range of plasma loading; however, the designs studied here require components near the antenna, complicating assembly and maintenance. Capacitor-tuned resonant systems may offer a good compromise.
NASA Astrophysics Data System (ADS)
Whiteley, J. P.
2017-06-01
Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.
NASA Astrophysics Data System (ADS)
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Pointwise interactions of finite element modeling of advection-diffusion equations
Yeh, G.T.
1984-07-01
Pointwise iteration techniques including successive under-relaxation (SUR), Gauss-Seidel (G-S), and successive over-relaxation (SOR) schemes, are applied to advection-diffusion equations to derive the matrix equation with finite element methods. These schemes are tested using two simple examples for which analytical solutions are available so that numerical results can be checked to ensure code consistency. Numerical experiments indicate that the iteration schemes, if convergent, produce almost identical solutions as those obtained by the direct elimination scheme. For diffusion dominant transport, all three iteration schemes generate convergent computations. However, for advection-diffusion equally dominant or advection dominant transport, only SUR and G-S schemes yield convergent calculations, the SOR scheme leads to divergent computations. Pointwise iteration schemes offer substantial savings in central process unit (CPU) memory over the direct elimination scheme, even for the small, two-dimensional verification example, without complicating the programming efforts and, in the meantime, keeps the CPU time comparable. A realistic, hypothetical problem is used to demonstrate the applicability and versatility of pointwise iterations and direct elimination schemes. The saving in CPU memory using the pointwise iterations is more than tenfold that using the direct elimination solution for this hypothetical problem. The saving in CPU time is even better, more than 40 fold.
Application of the Finite Element Method to Rotary Wing Aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Friedmann, P. P.
1982-01-01
A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.
Finite-element mesh generation from mappable features
Kuniansky, Eve L.; Lowther, Robert A.
1993-01-01
A vector-based geographical information system (GIS) is used to generate a variably-sized triangular element finite-element mesh from mappable features. Important digitally-mapped features are automatically linked to nodes in the finite-element model, ensuring an efficient, virtually error-free alternative to the tedious process of mesh design and data-input preparation by other methods. The procedure permits the user to work interactively with graphically-displayed hydrologic information about the study area allowing different mesh sizes to be used as needed, based on hydrologic complexity. The mesh-generaiion programs are stand-alone macros within the GIS that set up the basic data defining a finite-element mesh for many different finite-element model programs.
NASA Astrophysics Data System (ADS)
Chien, C.-C.; Wu, T.-Y.
This work presents an improved predictor/multi-corrector algorithm for linear structural dynamics problems, based on the time-discontinuous Galerkin finite element method. The improved algorithm employs the Gauss-Seidel method to calculate iteratively the solutions that exist in the phase of the predictor/multi-corrector of the numerical implementation. Stability analyses of iterative algorithms reveal that such an improved scheme retains the unconditionally stable behavior with greater efficiency than another iterative algorithm. Also, numerical examples are presented, demonstrating that the proposed method is more stable and accurate than several commonly used algorithms in structural dynamic applications.
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Hybrid stress finite elements for large deformations of inelastic solids
NASA Technical Reports Server (NTRS)
Reed, K. W.; Atluri, S. N.
1984-01-01
A new hybrid stress finite element algorithm, based on a generalization of Fraeijs de Veubeke's complementary energy principle is presented. Analyses of large quasistatic deformation of inelastic solids (hypoelastic, plastic, viscoplastic) are within its capability. Principle variables in the formulation are the nominal stress rate and spin. A brief account is given of the boundary value problem in these variables, and the 'equivalent' variational principle. The finite element equation, along with initial positions and stresses, comprise an initial value problem. Factors affecting the choice of time integration schemes are discussed. Results found by application of the new algorithm are compared to those obtained by a velocity based finite element algorithm.
Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms
NASA Technical Reports Server (NTRS)
Kurdila, Andrew J.; Sharpley, Robert C.
1999-01-01
This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
NASA Technical Reports Server (NTRS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Quality assessment and control of finite element solutions
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Babuska, Ivo
1987-01-01
Status and some recent developments in the techniques for assessing the reliability of finite element solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the finite element solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the finite element solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
Finite Element Anlaysis of Laminated Composite Plates
1988-09-01
4.2, results depicting maximum displacement obtained using 2 x 2 integration points, 3 x 3 integration points and ’ heterosis ’ [Ref. 4] elements are...thick and thin plates. This element gives better predictions for thick plates than heterosis ele- ment, however, for thin plates, heterosis element...results showing the normalized maximum displacements are shown in Figure 4.8. The heterosis element results in about ten percent error while the
Validating Finite Element Models of Assembled Shell Structures
NASA Technical Reports Server (NTRS)
Hoff, Claus
2006-01-01
The validation of finite element models of assembled shell elements is presented. The topics include: 1) Problems with membrane rotations in assembled shell models; 2) Penalty stiffness for membrane rotations; 3) Physical stiffness for membrane rotations using shell elements with 6 dof per node; and 4) Connections avoiding rotations.
Finite elements and the method of conjugate gradients on a concurrent processor
NASA Technical Reports Server (NTRS)
Lyzenga, G. A.; Raefsky, A.; Hager, B. H.
1984-01-01
An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.
On the development of hierarchical solution strategies for nonlinear finite element formulations
NASA Technical Reports Server (NTRS)
Padovan, J.; Lackney, J.
1984-01-01
This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.
A comparative study of an ABC and an artificial absorber for truncating finite element meshes
NASA Technical Reports Server (NTRS)
Oezdemir, T.; Volakis, John L.
1993-01-01
The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.
NASA Astrophysics Data System (ADS)
Huang, Chen
2016-03-01
A key element in the density functional embedding theory (DFET) is the embedding potential. We discuss two major issues related to the embedding potential: (1) its non-uniqueness and (2) the numerical difficulty for solving for it, especially for the spin-polarized systems. To resolve the first issue, we extend DFET to finite temperature: all quantities, such as the subsystem densities and the total system's density, are calculated at a finite temperature. This is a physical extension since materials work at finite temperatures. We show that the embedding potential is strictly unique at T > 0. To resolve the second issue, we introduce an efficient iterative embedding potential solver. We discuss how to relax the magnetic moments in subsystems and how to equilibrate the chemical potentials across subsystems. The solver is robust and efficient for several non-trivial examples, in all of which good quality spin-polarized embedding potentials were obtained. We also demonstrate the solver on an extended periodic system: iron body-centered cubic (110) surface, which is related to the modeling of the heterogeneous catalysis involving iron, such as the Fischer-Tropsch and the Haber processes. This work would make it efficient and accurate to perform embedding simulations of some challenging material problems, such as the heterogeneous catalysis and the defects of complicated spin configurations in electronic materials.
North Atlantic Finite Element Ocean Modeling
NASA Astrophysics Data System (ADS)
Veluthedathekuzhiyil, Praveen
This thesis presents a modified version of the Finite Element Ocean Model (FEOM) developed at Alfred Wegener Institute for Polar and Marine Research (AWI) for the North Atlantic Ocean. A reasonable North Atlantic Ocean simulation is obtained against the observational data sets in a Control simulation (CS) where the surface boundary conditions are relaxed to a climatology. The vertical mixing in the model was tuned to represent convection in the model, also the horizontal mixing and diffusion coefficients to represent the changes in the resolution of the model’s unstructured grid. In addition, the open boundaries in the model are treated with a sponge layer where tracers are relaxed to climatology. The model is then further modified to accept the atmospheric flux forcing at the surface boundary with an added net heat flux correction and freshwater forcing from major rivers that are flowing into the North Atlantic Ocean. The impact of this boundary condition on the simulation results is then analyzed and shows many improvements albeit the drift in tracer properties around the Gulf Stream region remains as that of the CS case. However a comparison of the vertical sections at Cape Desolation and Cape Farewell with the available observational data sets shows many improvements in this simulation compared to that of the CS case. But the freshwater content in the Labrador Sea interior shows a continued drift as that of the CS case with an improvement towards the 10th model year. A detailed analysis of the boundary currents around the Labrador Sea shows the weak offshore transport of freshwater from the West Greenland Current (WGC) as one of the causes. To further improve the model and reasonably represent the boundary currents and associated sub-grid scale eddies in the model, a modified sub-grid scale parameterization based on Gent and McWilliams, (1990) is adopted. The sensitivity of using various approaches in the thickness diffusion parameter ( Kgm) for this
Superconvergence in the Generalized Finite Element Method
2005-01-01
Galerkin method for elliptic equations based on tensor products of piecewise polynomials. RAIRO Anal. Numer., 8:61– 66, 1974. [19] M. Kř́ıžek...London, 1986. [22] P. Lesaint and M. Zlámal. Superconvergence of the gradient of finite ele- ment solutions. RAIRO Anal. Numer., 13:139–166, 1979. [23] Q
Application of Mass Lumped Higher Order Finite Elements
Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.
2005-11-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.
NASA Astrophysics Data System (ADS)
Kanber, Bahattin; Bozkurt, O. Yavuz
2006-08-01
In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.
Finite element analysis to evaluate optical mirror deformations
NASA Astrophysics Data System (ADS)
Izazaga-Pérez, R.; Aguirre-Aguirre, D.; Villalobos-Mendoza, B.
2015-10-01
In this work we describe the use of Finite Element Analysis software to simulate the deformations of an optical mirror. We use Finite Element Method software as a tool to simulate the mirror deformations assuming that it is a thin plate that can be mechanically tensed or compressed; the Finite Element Analysis give us information about the displacements of the mirror from an initial position and the tensions that remains in the surface. The information obtained by means of Finite Element Analysis can be easily exported to a coordinate system and processed in a simulation environment. Finally, a ray-tracing subroutine is used in the obtained data giving us information in terms of aberration coefficients. We present some results of the simulations describing the followed procedure.
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
Validation of High Displacement Piezoelectric Actuator Finite Element Models
NASA Technical Reports Server (NTRS)
Taleghani, B. K.
2000-01-01
The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
NASA Technical Reports Server (NTRS)
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Error analysis of finite element solutions for postbuckled cylinders
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1989-01-01
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
NASA Technical Reports Server (NTRS)
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
The finite element machine: An experiment in parallel processing
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Peebles, S. W.; Crockett, T. W.; Knott, J. D.; Adams, L.
1982-01-01
The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described.
Validation of high displacement piezoelectric actuator finite element models
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.
2000-08-01
The paper presents the results obtained by using NASTRAN and ANSYS finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness and important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN and ANSYS used different methods for modeling piezoelectric effects. In NASTRAN, a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
Examples of finite element mesh generation using SDRC IDEAS
NASA Technical Reports Server (NTRS)
Zapp, John; Volakis, John L.
1990-01-01
IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.
Integration of geometric modeling and advanced finite element preprocessing
NASA Technical Reports Server (NTRS)
Shephard, Mark S.; Finnigan, Peter M.
1987-01-01
The structure to a geometry based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary based data structure for the major data sets within the system. The approach presented can support the finite element modeling procedures used today as well as the fully automated procedures under development.
Global/local finite element analysis of composite materials
NASA Technical Reports Server (NTRS)
Griffin, O. Hayden, Jr.; Vidussoni, M. A.
1988-01-01
The motivation for performing global/local finite element analysis in composite materials is described. An example of such an analysis of a composite plate with a central circular hole is presented. Deformed finite element grids and interlaminar normal stress distributions are presented to aid understanding of the plate response. Such distribution at the plate edge is shown to be basically unaffected, although transverse displacements of the edge were slightly different from an analysis of a similar plate with no hole.
Finite element analysis to model complex mitral valve repair.
Labrosse, Michel; Mesana, Thierry; Baxter, Ian; Chan, Vincent
2016-01-01
Although finite element analysis has been used to model simple mitral repair, it has not been used to model complex repair. A virtual mitral valve model was successful in simulating normal and abnormal valve function. Models were then developed to simulate an edge-to-edge repair and repair employing quadrangular resection. Stress contour plots demonstrated increased stresses along the mitral annulus, corresponding to the annuloplasty. The role of finite element analysis in guiding clinical practice remains undetermined.
Finite element analysis of a composite wheelchair wheel design
NASA Technical Reports Server (NTRS)
Ortega, Rene
1994-01-01
The finite element analysis of a composite wheelchair wheel design is presented. The design is the result of a technology utilization request. The designer's intent is to soften the riding feeling by incorporating a mechanism attaching the wheel rim to the spokes that would allow considerable deflection upon compressive loads. A finite element analysis was conducted to verify proper structural function. Displacement and stress results are presented and conclusions are provided.
An Adaptive Multiscale Finite Element Method for Large Scale Simulations
2015-09-28
the method . Using the above definitions , the weak statement of the non-linear local problem at the kth 4 DISTRIBUTION A: Distribution approved for...AFRL-AFOSR-VA-TR-2015-0305 An Adaptive Multiscale Finite Element Method for Large Scale Simulations Carlos Duarte UNIVERSITY OF ILLINOIS CHAMPAIGN...14-07-2015 4. TITLE AND SUBTITLE An Adaptive Multiscale Generalized Finite Element Method for Large Scale Simulations 5a. CONTRACT NUMBER 5b
Nonlinear Finite Element Analysis of Composite Flextensional Transducer Shell
1993-03-01
4 TITLE AND SUBTITLE s FUNDING NUMbE;h NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE FLEXTENSIONAL PR: SV70 TRANSDUCER SHELL PE: 020431 IN 6 AUFTHOA...D NSN 7540-01-280-5500 ,ssard tr,298 IBACI UiNCLA-SSIFlED NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE FLEXTENSIONAL TRANSDUCER SHELL R. C. SliAW...its correlation with test data for a Class IV flextensional underwater acoustic transducer . The thick. elliptical fiberglass/epoxy shell of the
Finite element modeling of electromagnetic propagation in composite structures
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1987-01-01
A finite element Galerkin formulation has been developed to study electromagnetic propagation in complex two-dimensional absorbing ducts. The reflection and transmission at entrance and exit boundaries are determined by coupling the finite element solutions at the entrance and exit to the eigenfunctions of an infinite uniform perfect conducting duct. Example solutions are presented for electromagnetic propagation with absorbing duct walls and propagating through dielectric-metallic matrix materials.
Mathematical aspects of finite element methods for incompressible viscous flows
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Evaluation of a hybrid, anisotropic, multilayered, quadrilateral finite element
NASA Technical Reports Server (NTRS)
Robinson, J. C.; Blackburn, C. L.
1978-01-01
A multilayered finite element with bending-extensional coupling is evaluated for: (1) buckling of general laminated plates; (2) thermal stresses of laminated plates cured at elevated temperatures; (3) displacements of a bimetallic beam; and (4) displacement and stresses of a single-cell box beam with warped cover panels. Also, displacements and stresses for flat and spherical orthotropic and anisotropic segments are compared with results from higher order plate and shell finite-element analyses.
Microwave imaging using the finite-element method and a sensitivity analysis approach.
Rekanos, I T; Panas, S M; Tsiboukis, T D
1999-11-01
A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.
NASA Astrophysics Data System (ADS)
Iotti, Robert
2015-04-01
ITER is an international experimental facility being built by seven Parties to demonstrate the long term potential of fusion energy. The ITER Joint Implementation Agreement (JIA) defines the structure and governance model of such cooperation. There are a number of necessary conditions for such international projects to be successful: a complete design, strong systems engineering working with an agreed set of requirements, an experienced organization with systems and plans in place to manage the project, a cost estimate backed by industry, and someone in charge. Unfortunately for ITER many of these conditions were not present. The paper discusses the priorities in the JIA which led to setting up the project with a Central Integrating Organization (IO) in Cadarache, France as the ITER HQ, and seven Domestic Agencies (DAs) located in the countries of the Parties, responsible for delivering 90%+ of the project hardware as Contributions-in-Kind and also financial contributions to the IO, as ``Contributions-in-Cash.'' Theoretically the Director General (DG) is responsible for everything. In practice the DG does not have the power to control the work of the DAs, and there is not an effective management structure enabling the IO and the DAs to arbitrate disputes, so the project is not really managed, but is a loose collaboration of competing interests. Any DA can effectively block a decision reached by the DG. Inefficiencies in completing design while setting up a competent organization from scratch contributed to the delays and cost increases during the initial few years. So did the fact that the original estimate was not developed from industry input. Unforeseen inflation and market demand on certain commodities/materials further exacerbated the cost increases. Since then, improvements are debatable. Does this mean that the governance model of ITER is a wrong model for international scientific cooperation? I do not believe so. Had the necessary conditions for success
An adaptive discontinuous finite element method for the transport equation
Lang, J.; Walter, A.
1995-03-01
In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary varying flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators.
Least-squares finite element methods for compressible Euler equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Carey, G. F.
1990-01-01
A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
Nonlinear finite element analysis: An alternative formulation
NASA Technical Reports Server (NTRS)
Merazzi, S.; Stehlin, P.
1980-01-01
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
Finite element analysis of electric bicycle frame geometries
NASA Astrophysics Data System (ADS)
Cahyono, Sukmaji Indro; Anwar, Miftahul; Diharjo, Kuncoro; Triyono, Teguh; Hapid, Abdul; Kaleg, Sunarto
2017-01-01
This paper presents a simulation Finite Element Analysis (FEA) model of electric trike frames. The model of electric trike frame is a standard bicycle frame with addition modification on the back side for battery pack component and passenger loads. The electric motor is driven to put in front wheel for easy maintenance. Due to gain maximum safety in the passenger area and easy assembling, the frame is manufactured by circular steel tube in the front side and square steel tube in the back side. FEA simulation has been investigating proper model based on steel tube profile. The profiles is circular and oval steel tube 1.65mm thickness, (1, 1 ½, and 1 ½) inch diameter in front and square steel tube 2 mm thickness, (30×30, 40×40 and 50×50) mm size in the back. The support tube of the electric bicycle frame is similar to the National Standard road bicycle (SNI).The validation of this simulation is using experiment method and adaption method for optimizing iteration time and accuracy. The result of the simulation is a factor of safety. Von misses stress distribution from simulation result is showed the critical are in joining tube under driver of the frame structure. The oval tube is reached safety factor better than the circular tube, and it's had a better performance against the vertical load. The best variable is variable 3 oval tube 56.6×40 mm diagonal size with 1.65 thickness. It maximum passenger load is 700Kg. It can be a recommendation to redesign future frame of the electric bicycle.
Recent developments in finite element analysis for transonic airfoils
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.
1979-01-01
The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.
Dynamical observer for a flexible beam via finite element approximations
NASA Technical Reports Server (NTRS)
Manitius, Andre; Xia, Hong-Xing
1994-01-01
The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.
Nonlinear Finite Element Analysis of Sandwich Composites.
1981-03-01
to the element midsurface z - z(x,y) at all points. An additional coordinate r is used to describe the distance away from the midsurface at any point...It is assumed that on the element level, the shell is shallow, so that z2 2 (56) ,y everywhere. The unit vector normal to the shell midsurface at a...relations above do not involve the orientation of the displaced midsurface normal, and, therefore, apply to arbitrarily large displacements and rotations
SULEC: Benchmarking a new ALE finite-element code
NASA Astrophysics Data System (ADS)
Buiter, S.; Ellis, S.
2012-04-01
We have developed a 2-D/3-D arbitrary lagrangian-eulerian (ALE) finite-element code, SULEC, based on known techniques from literature. SULEC is successful in tackling many of the problems faced by numerical models of lithosphere and mantle processes, such as the combination of viscous, elastic, and plastic rheologies, the presence of a free surface, the contrast in viscosity between lithosphere and the underlying asthenosphere, and the occurrence of large deformations including viscous flow and offset on shear zones. The aim of our presentation is (1) to describe SULEC, and (2) to present a set of analytical and numerical benchmarks that we use to continuously test our code. SULEC solves the incompressible momentum equation coupled with the energy equation. It uses a structured mesh that is built of quadrilateral or brick elements that can vary in size in all dimensions, allowing to achieve high resolutions where required. The elements are either linear in velocity with constant pressure, or quadratic in velocity with linear pressure. An accurate pressure field is obtained through an iterative penalty (Uzawa) formulation. Material properties are carried on tracer particles that are advected through the Eulerian mesh. Shear elasticity is implemented following the approach of Moresi et al. [J. Comp. Phys. 184, 2003], brittle materials deform following a Drucker-Prager criterion, and viscous flow is by temperature- and pressure-dependent power-law creep. The top boundary of our models is a true free surface (with free surface stabilisation) on which simple surface processes models may be imposed. We use a set of benchmarks that test viscous, viscoelastic, elastic and plastic deformation, temperature advection and conduction, free surface behaviour, and pressure computation. Part of our benchmark set is automated allowing easy testing of new code versions. Examples include Poiseuille flow, Couette flow, Stokes flow, relaxation of viscous topography, viscous pure shear
Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions
Carpenter, D.C.
1997-04-01
Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions.
Kolotilina, L.; Nikishin, A.; Yeremin, A.
1994-12-31
The solution of large systems of linear equations is a crucial bottleneck when performing 3D finite element analysis of structures. Also, in many cases the reliability and robustness of iterative solution strategies, and their efficiency when exploiting hardware resources, fully determine the scope of industrial applications which can be solved on a particular computer platform. This is especially true for modern vector/parallel supercomputers with large vector length and for modern massively parallel supercomputers. Preconditioned iterative methods have been successfully applied to industrial class finite element analysis of structures. The construction and application of high quality preconditioners constitutes a high percentage of the total solution time. Parallel implementation of high quality preconditioners on such architectures is a formidable challenge. Two common types of existing preconditioners are the implicit preconditioners and the explicit preconditioners. The implicit preconditioners (e.g. incomplete factorizations of several types) are generally high quality but require solution of lower and upper triangular systems of equations per iteration which are difficult to parallelize without deteriorating the convergence rate. The explicit type of preconditionings (e.g. polynomial preconditioners or Jacobi-like preconditioners) require sparse matrix-vector multiplications and can be parallelized but their preconditioning qualities are less than desirable. The authors present results of numerical experiments with Factorized Sparse Approximate Inverses (FSAI) for symmetric positive definite linear systems. These are high quality preconditioners that possess a large resource of parallelism by construction without increasing the serial complexity.
Overall design of actively controlled smart structures by the finite element method
NASA Astrophysics Data System (ADS)
Gabbert, Ulrich; Koeppe, Heinz; Seeger, Falko
2001-08-01
The design process of engineering smart structures requires a virtual overall model, which includes the main functional parts such as the passive structure, the actuators and sensors as well as the control algorithm. The objective of the paper is to pre-sent such a design concept for vibration suppression of thin-walled shell structures controlled by piezoelectric wafers and fi-bers. This concept is based on a recently developed finite element package for the simulation of multi-physics problems. At first a rough design of actuator and sensor distributions is estimated which is based on the controllability and observabilty indices. Then the Matlab/Simulink software tool is used for controller design. From the finite element model all required data and information are transferred to Matlab/Simulink via a data exchange interface. After having designed the controller the result in form of the controller matrices or as C-codes can be transferred back into the finite element simulation package. Within the finite element code the controlled structural behavior can be studied under different disturbances. The structural design can be improved in an iterative way, e.g. by changing the actuator and sensor positions based on a sensitivity analy-sis. As an example an actively controlled smart plate structure is designed and tested to demonstrate the proposed procedure.
Large deformations of reconfigurable active membranes: a finite element model
NASA Astrophysics Data System (ADS)
Son, Seyul; Goulbourne, N. C.
2010-04-01
In this paper, a finite element model is used to describe the inhomogeneous deformations of dielectric elastomers (DE). In our previous work, inhomogeneous deformations of the DE with simple boundary conditions represented by a system of highly nonlinear coupled differential equations (ordinary and partial) were solved using numerical approaches [1-3]. To solve for the electromechanical response for complex shapes (asymmetric), nonuniform loading, and complex boundary conditions a finite element scheme is required. This paper describes a finite element implementation of the DE material model proposed in our previous work in a commercial FE code (ABAQUS 6.8-1, PAWTUCKET, R.I, USA). The total stress is postulated as the summation of the elastic stress tensor and the Maxwell stress tensor, or more generally the electrostatic stress tensor. The finite element model is verified by analytical solutions and experimental results for planar membrane extensions subject to mechanical loads and an electric field: (i) equibiaxial extension and (ii) generalized biaxial extension. Specifically, the analytical solutions for equibiaxial extension of the DE is obtained by combining a modified large deformation membrane theory that accounts for the electromechanical coupling effect in actuation commonly referred to as the Maxwell stress [4]. A Mooney-Rivlin strain energy function is employed to describe the constitutive stress strain behavior of the DE. For the finite element implementation, the constitutive relationships from our previously proposed mathematical model [4] are implemented into the finite element code. Experimentally, a 250% equibiaxially prestretched DE sample is attached to a rigid joint frame and inhomogeneous deformations of the reconfigurable DE are observed with respect to mechanical loads and an applied electric field. The computational result for the reconfigurable DE is compared with the test result to validate the accuracy and robustness of the finite
Finite Element Model Development For Aircraft Fuselage Structures
NASA Technical Reports Server (NTRS)
Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.
2000-01-01
The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S.
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Radiosity algorithms using higher order finite element methods
Troutman, R.; Max, N.
1993-08-01
Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.
Finite element analysis of two disk rotor system
Dixit, Harsh Kumar
2016-05-06
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
Finite element analysis of shear deformable laminated composite plates
Kam, T.Y.; Chang, R.R. )
1993-03-01
A shear deformable finite element is developed for the analysis of thick laminated composite plates. The finite element formulation is based on Mindlin's plate theory in which shear correction factors are derived from the exact expressions for orthotropic materials. The element is used to solve a variety of problems on deflection, stress distribution, natural frequency and buckling of laminated composite plates. The effects of material properties, plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle on the mechanical behaviors of laminated composite plates are investigated. Optimal lamination arrangements of layers for laminated composite plates of particular applications are determined.
Time domain finite element analysis of multimode microwave applicators
Dibben, D.C.; Metaxas, R.
1996-05-01
Analysis of multimode applicators in the frequency domain via the finite element technique produces a set of very ill-conditioned equations. This paper outlines a time domain finite element method (TDFE) for analyzing three dimensional microwave applicators where this ill-conditioning is avoided. Edge elements are used in order to handle sharp metal edges and to avoid spurious solutions. Analysis in the time domain allows field distributions at a range of different frequencies to be obtained with a single calculation. Lumping is investigated as a means of reducing the time taken for the calculation. The reflection coefficient is also obtained.
Probabilistic finite elements for fatigue and fracture analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Liu, Wing Kam
1992-01-01
Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.
Adaptive grid finite element model of the tokamak scrapeoff layer
Kuprat, A.P.; Glasser, A.H.
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
Finite element analysis of two disk rotor system
NASA Astrophysics Data System (ADS)
Dixit, Harsh Kumar
2016-05-01
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
A finite element method to study multimaterial wind towers
NASA Astrophysics Data System (ADS)
Pascoal-Faria, P.; Dias, C.; Oliveira, M.; Alves, N.
2017-07-01
Wind towers are used to produce electrical energy from the wind. A significant number of towers is manufactured using tubular separately steel or concrete, having limitations such as maximum diameter and height imposed essentially by transportation limitations. Developed computational studies on structural design of towers have been mainly focused on a single material. This investigation aims to develop a finite element method able to study structural design of wind towers combining different materials. The finite element model combines solid and shell elements encompassing different geometries. Several case studies are considered to validate the proposed method and accurate results are obtained.
Numerical Differentiation for Adaptively Refined Finite Element Meshes
NASA Technical Reports Server (NTRS)
Borgioli, Andrea; Cwik, Tom
1998-01-01
Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.
Footbridge between finite volumes and finite elements with applications to CFD
NASA Astrophysics Data System (ADS)
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
Design and finite element analysis of oval man way
Hari, Y.; Gryder, B.
1996-12-01
This paper presents the design of an oval man way in the side wall of a cylindrical pressure vessel. ASME Code Section 8 is used to obtain the design parameters of the oval man way, man way cover and bolts. The code calculations require some assumptions which may not be valid. A typical design example is taken. STAAD III finite element code with plate elements is used to model the oval man way, man way cover and bolts. The stresses calculated using ASME Code Section 8 and other analytical formulas for plate and shells are compared with the stresses obtained by Finite Element Modeling. This paper gives the designer of oval man way the ability to perform a finite element analysis and compare it with the analytical calculations and assumptions made. This gives added confidence to the designer as to the validity of his calculations and assumptions.
A finite element simulation scheme for biological muscular hydrostats.
Liang, Y; McMeeking, R M; Evans, A G
2006-09-07
An explicit finite element scheme is developed for biological muscular hydrostats such as squid tentacles, octopus arms and elephant trunks. The scheme is implemented by embedding muscle fibers in finite elements. In any given element, the fiber orientation can be assigned arbitrarily and multiple muscle directions can be simulated. The mechanical stress in each muscle fiber is the sum of active and passive parts. The active stress is taken to be a function of activation state, muscle fiber shortening velocity and fiber strain; while the passive stress depends only on the strain. This scheme is tested by simulating extension of a squid tentacle during prey capture; our numerical predictions are in close correspondence with existing experimental results. It is shown that the present finite element scheme can successfully simulate more complex behaviors such as torsion of a squid tentacle and the bending behavior of octopus arms or elephant trunks.
Finite element analysis for acoustic characteristics of a magnetostrictive transducer
NASA Astrophysics Data System (ADS)
Kim, Jaehwan; Jung, Eunmi
2005-12-01
This paper presents a finite element analysis for a magnetostrictive transducer by taking into account the nonlinear behavior of the magnetostrictive material and fluid interaction. A finite element formulation is derived for the coupling of magnetostrictive and elastic materials based upon a separated magnetic and displacement field calculation and a curve fitting technique of material properties. The fluid and structure coupled problem is taken into account based upon pressure and velocity potential fields formulation. Infinite wave envelope elements are introduced at an artificial boundary to deal with the infinite fluid domain. A finite element code for the analysis of a magnetostrictive transducer is developed. A magnetostrictive tonpilz transducer is taken as an example and verification for the developed program is made by comparing with a commercial code. The acoustic characteristics of the magnetostrictive tonpilz transducer are calculated in terms of radiation pattern and transmitted current response.
MHOST: An efficient finite element program for inelastic analysis of solids and structures
NASA Technical Reports Server (NTRS)
Nakazawa, S.
1988-01-01
An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.
A singular finite element technique for calculating continuum damping of Alfvén eigenmodes
Bowden, G. W.; Hole, M. J.
2015-02-15
Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode in a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.
Finite element study of plate buckling induced by spatial temperature gradients
NASA Technical Reports Server (NTRS)
Thornton, Earl A.; Kolenski, James D.; Marino, Robert P.
1993-01-01
Finite element analyses of thermal buckling of thin metallic plates with prescribed spatial temperature distributions are described. Thermally induced compressive membrane stresses and transverse plate displacement imperfections initiate plates buckling. A finite element formulation based on von Karman plate theory is presented. The resulting nonlinear equations are solved for incremental temperature increases by Newton-Raphson iteration. The computational method is used to investigate the buckling response of rectangular plates with steady and unsteady spatially varying temperature distributions. The role of initial plate imperfections and temperature distributions on the nonlinear response of plate displacements and stresses is described. The relatively high levels of stress induced by spatial temperature gradients should be considered carefully in the postbuckling design of panels for aerospace vehicles subjected to combined mechanical and thermal loads.
Finite element study of plate buckling induced by spatial temperature gradients
Thornton, E.A.; Kolenski, J.D.; Marino, R.P.
1993-01-01
Finite element analyses of thermal buckling of thin metallic plates with prescribed spatial temperature distributions are described. Thermally induced compressive membrane stresses and transverse plate displacement imperfections initiate plates buckling. A finite element formulation based on von Karman plate theory is presented. The resulting nonlinear equations are solved for incremental temperature increases by Newton-Raphson iteration. The computational method is used to investigate the buckling response of rectangular plates with steady and unsteady spatially varying temperature distributions. The role of initial plate imperfections and temperature distributions on the nonlinear response of plate displacements and stresses is described. The relatively high levels of stress induced by spatial temperature gradients should be considered carefully in the postbuckling design of panels for aerospace vehicles subjected to combined mechanical and thermal loads. 31 refs.
Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods
NASA Astrophysics Data System (ADS)
Bause, M.; Knabner, P.
2004-06-01
We present adaptive mixed hybrid finite element discretizations of the Richards equation, a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated porous medium. The approach simultaneously constructs approximations of the flux and the pressure head in Raviart-Thomas spaces. The resulting nonlinear systems of equations are solved by a Newton method. For the linear problems of the Newton iteration a multigrid algorithm is used. We consider two different kinds of error indicators for space adaptive grid refinement: superconvergence and residual based indicators. They can be calculated easily by means of the available finite element approximations. This seems attractive for computations since no additional (sub-)problems have to be solved. Computational experiments conducted for realistic water table recharge problems illustrate the effectiveness and robustness of the approach.
NASA Astrophysics Data System (ADS)
Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie
2017-03-01
Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.
Solution Techniques in Finite Element Analysis.
1983-05-01
7. we show a plane strain rubber block subjected to large deforma- tion. We employ a 4-node element and a Mooney - Rivlin material as described in...0 Rubber Block U: 0.30 Figure 7. Large Deformation Analysis of the R ubber Block with Mooney - Rivlin Material Model. GEOMETRY node iE 10 4 -0.3 1.0 1
Guo, Hongqiang; Shah, Mitul; Spilker, Robert L.
2014-01-01
The study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. However, to date, few biphasic finite element contact analysis for 3D physiological geometries under finite deformation has been developed. The objective of this paper is to develop a hyperelastic biphasic contact implementation for finite deformation and sliding problem. An augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The finite element implementation was based on a general purpose software, COMSOL Multiphysics. The accuracy of the implementation is verified using example problems, for which solutions are available by alternative analyses. The implementation was proven to be robust and able to handle finite deformation and sliding. PMID:24496915
Coupled finite-difference/finite-element approach for wing-body aeroelasticity
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
1992-01-01
Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
New triangular and quadrilateral plate-bending finite elements
NASA Technical Reports Server (NTRS)
Narayanaswami, R.
1974-01-01
A nonconforming plate-bending finite element of triangular shape and associated quadrilateral elements are developed. The transverse displacement is approximated within the element by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.
Variational formulation of high performance finite elements: Parametrized variational principles
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Militello, Carmello
1991-01-01
High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational basis of high-performance elements, with emphasis on those constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parametrized variational principles that provide a foundation for the FF and ANS methods, as well as for a combination of both are presented.
Effective Finite Elements for Shell Analysis.
1984-02-20
important mode of deformation , and when an element is not capable of representing inextensional bending, parasitic membrane energy is generated in many modes...of deformation . In the same manner that parasitic shear causes shear locking, this spurious membrane energy causes membrane locking. Membrane locking...dominant mode of deformation . (cont.) 20. OISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION UNCLASSIFIEO/UNLIMITEO X SAME AS
The Mathematics of Finite Elements and Applications
1993-04-30
suitable geometrical mapping between the parametric u,v-plane and the physical xy- plane. In the u,v-plane the geometry of the elements is linear. In...the plate. For thin plates there may be a boundary layer, the existence and structure of which depends on the boundary conditions, the plate geometry ...exhibits a boundary layer except for very special data or plate geometry . The bending moment tensor and shear force vector have more pronounced boundary
Spectral finite-element methods for parametric constrained optimization problems.
Anitescu, M.; Mathematics and Computer Science
2009-01-01
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.
Cooley, Richard L.
1992-01-01
MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.
Stabilized plane and axisymmetric Lobatto finite element models
NASA Astrophysics Data System (ADS)
Hu, Y. C.; Sze, K. Y.; Zhou, Y. X.
2015-11-01
High order elements are renowned for their high accuracy and convergence. Among them, Lobatto spectral finite elements are commonly used in explicit dynamic analyses as their mass matrices when evaluated by the Lobatto integration rule are diagonal. While there are numerous advanced first and second order elements, advanced high order elements are rarely seen. In this paper, generic stabilization schemes are devised for the reduced integrated plane and axisymmetric elements. Static and explicit dynamic tests are considered for evaluating the relatively merits of the stabilized and conventional elements. The displacement errors of the stabilized elements are less than those of the conventional Lobatto elements. When the material is nearly incompressible, the stabilized elements are also more accurate in terms of the energy error norm. This advantage is of practical importance for bio-tissue and hydrated soil analyses.
Parallel implementation of the finite element method using compressed data structures
NASA Astrophysics Data System (ADS)
Ribeiro, F. L. B.; Ferreira, I. A.
2007-12-01
This paper presents a parallel implementation of the finite element method designed for coarse-grain distributed memory architectures. The MPI standard is used for message passing and tests are run on a PC cluster and on an SGI Altix 350. Compressed data structures are employed to store the coefficient matrix and obtain iterative solutions, based on Krylov methods, in a subdomain-by-subdomain approach. Two mesh partitioning schemes are compared: non-overlapping and overlapping. The pros and cons of these partitioning methods are discussed. Numerical examples of symmetric and non-symmetric problems in two and three dimensions are presented.
Surface chemistry effects in finite element modeling of heat transfer in (micron)-fuel cells
Havstad, M
2000-12-07
Equations for modeling surface chemical kinetics by the interaction of gaseous and surface species are presented. The formulation is embedded in a finite element heat transfer code and an ordinary differential equation package is used to solve the surface system of chemical kinetic equations for each iteration within the heat transfer solver. The method is applied to a flow which includes methane and methanol in a microreactor on a chip. A simpler more conventional method, a plug flow reactor model, is then applied to a similar problem. Initial results for steam reforming of methanol are given.
Freels, J.D.; Baker, A.J. ); Ianelli, G.S. )
1991-01-01
A weak statement forms the theoretical basis for identifying the range of choices/decisions for constructing approximate solutions to the compressible Navier-Stokes equations. The Galerkin form is intrinsically non-dissipative, and a Taylor series analysis identifies the extension needed for shock capturing. Thereafter, the approximation trial space is constructed with compact support using a spatial domain semi-discretization into finite elements. An implicit temporal algorithm produces the terminal algebraic form, which is iteratively solved using a tensor product factorization quasi-Newton procedure. Computational results verify algorithm performance for a range of aerodynamics specifications. 6 refs., 3 figs.
NASA Astrophysics Data System (ADS)
Chen, Jiefu
2015-03-01
A discontinuous Galerkin finite element method is employed to study the responses of microresistivity imaging tools used in the oil and gas exploration industry. The multiscale structure of an imaging problem is decomposed into several nested subdomains based on its geometric characteristics. Each subdomain is discretized independently, and numerical flux is used to couple all subdomains together. The nested domain decomposition scheme will lead to a block tridiagonal linear system, and the block Thomas algorithm is utilized here to eliminate the subdomain based iteration in the step of solving the linear system. Numerical results demonstrate the validity and efficiency of this method.
A method of limit point calculation in finite element structural analysis
NASA Technical Reports Server (NTRS)
Gallagher, R. H.; Mau, S. T.
1972-01-01
An approach is presented for the calculation of limit points for structures described by discrete coordinates, and whose governing equations derive from finite element concepts. The nonlinear load-displacement path of the imperfect structure is first traced by use of a direct iteration scheme and the determinant of the governing algebraic equations is calculated at each solution point. The limit point is then established by extrapolation and imposition of the condition of zero slope of the plot of load vs. determinant. Three problems are solved in illustration of the approach and in comparison with alternative procedures and test data.
A finite element procedure for nonlinear prebuckling and initial postbuckling analysis
NASA Technical Reports Server (NTRS)
Mau, S. T.; Gallagher, R. H.
1972-01-01
A procedure cast in a form appropriate to the finite element method is presented for geometrically nonlinear prebuckling and postbuckling structural analysis, including the identification of snap-through type of buckling. The principal features of this procedure are the use of direct iteration for solution of the nonlinear algebraic equations in the prebuckling range, an interpolation scheme for determination of the initial bifurcation point, a perturbation method in definition of the load-displacement behavior through the postbuckling regime, and extrapolation in determination of the limit point for snap-through buckling. Three numerical examples are presented in illustration of the procedure and in comparison with alternative approaches.
Gaston, L.; Glut, B.; Bellet, M.; Chenot, J.L.
1995-12-31
This paper presents a two-dimensional lagrangian-eulerian finite element approach of non-steady state Navier-Stokes fluid flows with free surfaces, like those occurring during the mould filling stage in casting processes. The proposed model is based on a mixed velocity-pressure finite element formulation, including an augmented Lagrangian technique and an iterative solver of Uzawa type. Mesh updating is carried out through an arbitrary lagrangian-eulerian method in order to describe properly the free surface evolution. Heat transfer through the fluid flow is solved by a convection-diffusion splitting technique. The efficiency of the method is illustrated on an example of gravity casting.
NASA Technical Reports Server (NTRS)
Liou, W. J.; Sun, C. T.
1987-01-01
A method of analysis of dynamic response of laminated composite plates is presented. The analysis is carried by using a hybrid-stress finite element numerical technique. By using this approach, the response of simply supported laminated plates subjected to sinusoidal loading are investigated. For the solution of the finite element equations of motion of free vibrations and dynamic response problems, two effective methods of solution, the space iteration method and the Newmark direct integration method are used. These two methods are discussed here.
NASA Astrophysics Data System (ADS)
Hano, Mitsuo; Hotta, Masashi
A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.
The Constraint Method for Solid Finite Elements.
1982-11-30
Sciences 13 . NUMBER S Bolling Air Force Base, DC 20332 - -Jfi’ 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) IS. SECURITY CVASS...1- 4)Q2 (n) (’+C) Higher degree elements add edge modes, face modes and internal modes. More details are given in [12, 13 ]. triangular prism A...23) N2 (L2 , L3)(l-z) edge u (31) N2 (L3 ’ L)(1-z) nodes s u s (45). N2 (L1, L2 )z uso (56) N2 (L2, L3 )z K - 13 - nodal variable shape function u
Shadid, J.N.; Moffat, H.K.; Hutchinson, S.A.; Hennigan, G.L.; Devine, K.D.; Salinger, A.G.
1996-05-01
The theoretical background for the finite element computer program, MPSalsa, is presented in detail. MPSalsa is designed to solve laminar, low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow, heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solver coupled multiple Poisson or advection-diffusion- reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurring in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMKIN, respectively. The code employs unstructured meshes, using the EXODUS II finite element data base suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec solver library.
Variance analysis for model updating with a finite element based subspace fitting approach
NASA Astrophysics Data System (ADS)
Gautier, Guillaume; Mevel, Laurent; Mencik, Jean-Mathieu; Serra, Roger; Döhler, Michael
2017-07-01
Recently, a subspace fitting approach has been proposed for vibration-based finite element model updating. The approach makes use of subspace-based system identification, where the extended observability matrix is estimated from vibration measurements. Finite element model updating is performed by correlating the model-based observability matrix with the estimated one, by using a single set of experimental data. Hence, the updated finite element model only reflects this single test case. However, estimates from vibration measurements are inherently exposed to uncertainty due to unknown excitation, measurement noise and finite data length. In this paper, a covariance estimation procedure for the updated model parameters is proposed, which propagates the data-related covariance to the updated model parameters by considering a first-order sensitivity analysis. In particular, this propagation is performed through each iteration step of the updating minimization problem, by taking into account the covariance between the updated parameters and the data-related quantities. Simulated vibration signals are used to demonstrate the accuracy and practicability of the derived expressions. Furthermore, an application is shown on experimental data of a beam.
Finite Element Method for Capturing Ultra-relativistic Shocks
NASA Technical Reports Server (NTRS)
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Optimal mapping of irregular finite element domains to parallel processors
NASA Technical Reports Server (NTRS)
Flower, J.; Otto, S.; Salama, M.
1987-01-01
Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.
Finite element methods for nonlinear acoustics in fluids.
Walsh, Timothy Francis
2005-06-01
In this paper, weak formulations and finite element discretizations of the governing partial differential equations of three-dimensional nonlinear acoustics in absorbing fluids are presented. The fluid equations are considered in an Eulerian framework, rather than a displacement framework, since in the latter case the corresponding finite element formulations suffer from spurious modes and numerical instabilities. When taken with the governing partial differential equations of a solid body and the continuity conditions, a coupled formulation is derived. The change in solid/fluid interface conditions when going from a linear acoustic fluid to a nonlinear acoustic fluid is demonstrated. Finite element discretizations of the coupled problem are then derived, and verification examples are presented that demonstrate the correctness of the implementations. We demonstrate that the time step size necessary to resolve the wave decreases as steepening occurs. Finally, simulation results are presented on a resonating acoustic cavity, and a coupled elastic/acoustic system consisting of a fluid-filled spherical tank.
Finite element methods on supercomputers - The scatter-problem
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.
1985-01-01
Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.
Finite element method for eigenvalue problems in electromagnetics
NASA Technical Reports Server (NTRS)
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
An Object Oriented, Finite Element Framework for Linear Wave Equations
Koning, Joseph M.
2004-03-01
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Probabilistic finite elements for transient analysis in nonlinear continua
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Optimal mapping of irregular finite element domains to parallel processors
NASA Technical Reports Server (NTRS)
Flower, J.; Otto, S.; Salama, M.
1987-01-01
Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Finite element method for non-linear dispersive wave analysis
NASA Astrophysics Data System (ADS)
Cheng, Jung-Yu; Kawahara, Mutsuto
1993-09-01
This report presents the finite element method for the analysis of the short wave problem expressed by the Boussinesq equation. The Boussinesq equation considers the effect of wave crest curvature. The standard Galerkin finite element method is employed for the spatial discretization using the triangular finite element based on the linear interpolation function. The combination of the explicit and the quasi-explicit schemes-- i.e., the explicit scheme for the continuum equation and the quasi-explicit scheme for the momentum equation--is employed for the discretization in time. To show the applicability of the present method to the practical problem, the simulation of wave propagation in one-dimensional and two-dimensional channel flows is carried out. The numerical results are in good agreement with the experimental results being. The practical example for Miyako Bay is presented.
Derivation of a Tappered p-Version Beam Finite Element
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1989-01-01
A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.
NASA Astrophysics Data System (ADS)
Begue, C.; Periaux, J.; Perrier, P.; Pouletty, C.
1985-11-01
A self-adaptive finite-element method, coupled to a homogenization model of turbulence, is presented for the numerical simulation of unsteady turbulent flow of viscous fluids in air intakes. The nonlinear subproblem due to the convection is solved by an iterative algorithm, and the linear Stokes subproblem due to the diffusion is solved by a Hood-Taylor type iterative algorithm. An efficient and precise minielement approximation is used, and the adaptive mesh procedure is automatic in the calculation, using the physical criteria of rotation and divergence to determine the submeshing zones. The numerical method is demonstrated for the example of three-dimensional laminar flow around and in air intake at a Reynolds number of 200.
On nonlinear finite element analysis in single-, multi- and parallel-processors
NASA Technical Reports Server (NTRS)
Utku, S.; Melosh, R.; Islam, M.; Salama, M.
1982-01-01
Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.
Life assessment of structural components using inelastic finite element analyses
NASA Astrophysics Data System (ADS)
Arya, Vinod K.; Halford, Gary R.
1993-10-01
The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.
Life assessment of structural components using inelastic finite element analyses
NASA Technical Reports Server (NTRS)
Arya, Vinod K.; Halford, Gary R.
1993-01-01
The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.
NASA Astrophysics Data System (ADS)
Vitale, Stefano
2014-11-01
A new technique for estimating the finite strain of deformed elliptical markers is presented. This method is based on the property of the arithmetic mean Rfbar of the deformed object aspect ratios Rf to reach its minimum value in the undeformed state when they correspond to the initial aspect ratios Ri. The minimized Ribar (MIRi) iterative method furnishes the best results when, in the pre-strain state, the markers are uniformly orientated for every aspect ratio (Ri) class. A Matlab code, provided in this study, finds the best values of strain Rs and maximum stretching direction X that minimize the arithmetic mean Ribar by means of several iterations. In order to define the uncertainties of Rs and X, the code: (i) re-samples h-times the original (Ri, θ) dataset; (ii) assigns random values to the initial long axis angles θ; (iii) deforms newly the synthetic dataset; (iv) re-applies the MIRi method; and finally (v) estimates the standard deviation for the (Rs, X) values. Tests of the method on synthetic aggregates of elliptical markers and two naturally deformed rocks provide strain values that are compared with estimations from other available methods.
Finite Element Modelling and Analysis of Conventional Pultrusion Processes
NASA Astrophysics Data System (ADS)
Akishin, P.; Barkanov, E.; Bondarchuk, A.
2015-11-01
Pultrusion is one of many composite manufacturing techniques and one of the most efficient methods for producing fiber reinforced polymer composite parts with a constant cross-section. Numerical simulation is helpful for understanding the manufacturing process and developing scientific means for the pultrusion tooling design. Numerical technique based on the finite element method has been developed for the simulation of pultrusion processes. It uses the general purpose finite element software ANSYS Mechanical. It is shown that the developed technique predicts the temperature and cure profiles, which are in good agreement with those published in the open literature.
Predicting Rediated Noise With Power Flow Finite Element Analysis
2007-02-01
Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow Finite Element Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW FINITE ELEMENT ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated
Correlation of composite material test results with finite element analysis
NASA Astrophysics Data System (ADS)
Guƫu, M.
2016-08-01
In this paper are presented some aspects regarding the method of simulation of composite materials testing with finite element analysis software. There were simulated tensile and shear tests of specimens manufactured from glass fiber reinforced polyester. For specimens manufacturing two types of fabrics were used: unidirectional and bidirectional. Experimentally determined elastic properties of composite material were used as input data. Modeling of composite architecture of the specimens was performed with ANSYS Composite PrepPost software. Finite element analysis stresses and strains on strain gauges bonding area were considered and compared with the real values in a diagram. After results comparison, potential causes of deviations were identified.
Finite element models of the space shuttle main engine
NASA Technical Reports Server (NTRS)
Muller, G. R.
1980-01-01
Finite element models were developed as input to dynamic simulations of the high pressure fuel turbopump (HPFTP), the high pressure oxidizer turbopump (HPOTP), and the space shuttle main engine (SSME). Descriptions are provided for the five basic finite element models: HPFTP rotor, HPFTP case, HPOTP rotor, HPOTP case, and SSME (excluding turbopumps). Modal results are presented for the HPFTP rotor, HPFTP case, HPOTP rotor, coupled HPFTP rotor and case, HPOTP case, coupled HPOTP rotor and case, SSME (excluding turbopumps), and SSME (including turbopumps). Results for the SSME (including turbopumps) model are compared to data from a SSME HPOTP modal survey.
Development of non-linear finite element computer code
NASA Technical Reports Server (NTRS)
Becker, E. B.; Miller, T.
1985-01-01
Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.
Finite element methods for nonlinear elastostatic problems in rubber elasticity
NASA Technical Reports Server (NTRS)
Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.
1983-01-01
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element...SM4), 1,435-1,457. Fernando Dams During the Earthquakes of February Davis, E. H., and Poulos, H. G. (1972). “Rate of Report EERC-73-2, Berkeley, CA
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
NASA Astrophysics Data System (ADS)
Smith, N. A. S.; Rokosz, M. K.; Correia, T. M.
2014-07-01
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna.; Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Verification of a Finite Element Model for Pyrolyzing Ablative Materials
NASA Technical Reports Server (NTRS)
Risch, Timothy K.
2017-01-01
Ablating thermal protection system (TPS) materials have been used in many reentering spacecraft and in other applications such as rocket nozzle linings, fire protection materials, and as countermeasures for directed energy weapons. The introduction of the finite element model to the analysis of ablation has arguably resulted in improved computational capabilities due the flexibility and extended applicability of the method, especially to complex geometries. Commercial finite element codes often provide enhanced capability compared to custom, specially written programs based on versatility, usability, pre- and post-processing, grid generation, total life-cycle costs, and speed.
Error analysis of finite element solutions for postbuckled plates
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1988-01-01
An error analysis of results from finite-element solutions of problems in shell structures is further developed, incorporating the results of an additional numerical analysis by which oscillatory behavior is eliminated. The theory is extended to plates with initial geometric imperfections, and this novel analysis is programmed as a postprocessor for a general-purpose finite-element code. Numerical results are given for the case of a stiffened panel in compression and a plate loaded in shear by a 'picture-frame' test fixture.
Differentiating a Finite Element Biodegradation Simulation Model for Optimal Control
NASA Astrophysics Data System (ADS)
Minsker, Barbara S.; Shoemaker, Christine A.
1996-01-01
An optimal control model for improving the design of in situ bioremediation of groundwater has been developed. The model uses a finite element biodegradation simulation model called Bio2D to find optimal pumping strategies. Analytical derivatives of the bioremediation finite element model are derived; these derivatives must be computed for the optimal control algorithm. The derivatives are complex and nonlinear; the bulk of the computational effort in solving the optimal control problem is required to calculate the derivatives. An overview of the optimal control and simulation model formulations is also given.
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
Smith, N. A. S. E-mail: maciej.rokosz@npl.co.uk Correia, T. M. E-mail: maciej.rokosz@npl.co.uk; Rokosz, M. K. E-mail: maciej.rokosz@npl.co.uk
2014-07-28
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Analysis of the Performance of Mixed Finite Element Methods.
1986-10-01
October 1986 SUMMARY The initial goal of this project is to analyze various mixed methods based on the p- and h-p versions of the finite element methods...The convergence of mixed methods depends on two factors: (1) Approximability of polynomial spaces used (2) Stability. In the past year, the question...significant portion of the research is geared towards the investigation of mixed methods based on the ’p’ and ’h-p’ versions of the finite element method
Chemically pre-strained dielectric elastomers finite element analysis
NASA Astrophysics Data System (ADS)
Newell, Brittany; Krutz, Gary; Stewart, Frank; Pascal, Kevin
2017-04-01
The applications and feasibility of utilizing dielectric elastomer electroactive polymers in the industrial and medical sectors has drastically increased in recent years due to significant improvements in actuation potential, manufacturing, the introduction of new materials and modeling capabilities. One such development is the introduction of chemical pre-strain as a method of providing enhanced actuation. The purpose of this study was to utilize finite element analysis to analyze the mechanical actuation of an industrial fluoropolymer with chemical induced pre-strain and validate the model with experiential results. Results generated from the finite element analysis showed similar trends to results produced experimentally.
Convergence of finite element approximations of large eddy motion.
Iliescu, T.; John, V.; Layton, W. J.; Mathematics and Computer Science; Otto-von-Guericke Univ.; Univ. of Pittsburgh
2002-11-01
This report considers 'numerical errors' in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. Keywords: Navier Stokes equations, large eddy simulation, finite element method I. INTRODUCTION Consider the (turbulent) flow of an incompressible fluid. One promising and common approach to the simulation of the motion of the large fluid structures is Large Eddy Simulation (LES). Various models are used in LES; a common one is to find (w, q), where w : {Omega}
A weak Galerkin generalized multiscale finite element method
Mu, Lin; Wang, Junping; Ye, Xiu
2016-03-31
In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.
Using Finite-Element Analysis In Estimating Reliability
NASA Technical Reports Server (NTRS)
Zaretsky, Erwin V.; August, Richard
1994-01-01
Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.
Substructure System Identification for Finite Element Model Updating
NASA Technical Reports Server (NTRS)
Craig, Roy R., Jr.; Blades, Eric L.
1997-01-01
This report summarizes research conducted under a NASA grant on the topic 'Substructure System Identification for Finite Element Model Updating.' The research concerns ongoing development of the Substructure System Identification Algorithm (SSID Algorithm), a system identification algorithm that can be used to obtain mathematical models of substructures, like Space Shuttle payloads. In the present study, particular attention was given to the following topics: making the algorithm robust to noisy test data, extending the algorithm to accept experimental FRF data that covers a broad frequency bandwidth, and developing a test analytical model (TAM) for use in relating test data to reduced-order finite element models.
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
Diffusive mesh relaxation in ALE finite element numerical simulations
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-01-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
Identification of Molecular Laser Transitions Using the Finite Element Method
1995-12-01
11-19 Numerical Solution of Schr~dinger’s Equation .......................... 11-23 Conclusion...element solution of Schr6dinger’s Equation . The purpose of this research is to extend this previous work, and develop a chemical laser engineering tool for...Schr6dinger’s Equation . The eigenvalues from these solutions are then compared to the experimental values. Through this iterative process, the best potential
Finite Element Model Development and Validation for Aircraft Fuselage Structures
NASA Technical Reports Server (NTRS)
Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.
2000-01-01
The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results. The increased frequency range results in a corresponding increase in the number of modes, modal density and spatial resolution requirements. In this study, conventional modal tests using accelerometers are complemented with Scanning Laser Doppler Velocimetry and Electro-Optic Holography measurements to further resolve the spatial response characteristics. Whenever possible, component and subassembly modal tests are used to validate the finite element models at lower levels of assembly. Normal mode predictions for different finite element representations of components and assemblies are compared with experimental results to assess the most accurate techniques for modeling aircraft fuselage type structures.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-11-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-01-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Maker, B.N.
1995-04-14
This report provides a user`s manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.
Finite Element Aircraft Simulation of Turbulence
NASA Technical Reports Server (NTRS)
McFarland, R. E.
1997-01-01
A turbulence model has been developed for realtime aircraft simulation that accommodates stochastic turbulence and distributed discrete gusts as a function of the terrain. This model is applicable to conventional aircraft, V/STOL aircraft, and disc rotor model helicopter simulations. Vehicle angular activity in response to turbulence is computed from geometrical and temporal relationships rather than by using the conventional continuum approximations that assume uniform gust immersion and low frequency responses. By using techniques similar to those recently developed for blade-element rotor models, the angular-rate filters of conventional turbulence models are not required. The model produces rotational rates as well as air mass translational velocities in response to both stochastic and deterministic disturbances, where the discrete gusts and turbulence magnitudes may be correlated with significant terrain features or ship models. Assuming isotropy, a two-dimensional vertical turbulence field is created. A novel Gaussian interpolation technique is used to distribute vertical turbulence on the wing span or lateral rotor disc, and this distribution is used to compute roll responses. Air mass velocities are applied at significant centers of pressure in the computation of the aircraft's pitch and roll responses.
A finite element based method for solution of optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.
1989-01-01
A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.
Least-squares finite element solution of 3D incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.
1992-01-01
Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.
New hybrid quadrilateral finite element for Mindlin plate
NASA Astrophysics Data System (ADS)
Chin, Yi; Zhang, Jingyu
1994-02-01
A new quadrilateral plate element concerning the effect of transverse shear strain was presented. It was derived from the hybrid finite element model based on the principles of virtual work. The outstanding advantage of this element was to use more rational trial functions of the displacements. For this reason, every variety of plate deformation can be simulated really while the least degrees of freedom was employed. A wide range of numerical tests was conducted and the results illustrate that this element has a very wide application scope to the thickness of plates and satisfactory accuracy can be obtained by coarse mesh for all kinds of examples.
Finite element approach for transient analysis of multibody systems
NASA Technical Reports Server (NTRS)
Wu, Shih-Chin; Chang, Che-Wei; Housner, Jerrold M.
1992-01-01
A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.
A new formulation of hybrid/mixed finite element
NASA Technical Reports Server (NTRS)
Pian, T. H. H.; Kang, D.; Chen, D.-P.
1983-01-01
A new formulation of finite element method is accomplished by the Hellinger-Reissner principle for which the stress equilibrium conditions are not introduced initially but are brought-in through the use of additional internal displacement parameters. The method can lead to the same result as the assumed stress hybrid model. However, it is more general and more flexible. The use of natural coordinates for stress assumptions leads to elements which are less sensitive to the choice of reference coordinates. Numerical solutions by 3-D solid element indicate that more efficient elements can be constructed by assumed stresses which only partially satisfy the equilibrium conditions.
Numerical techniques in linear duct acoustics. [finite difference and finite element analyses
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1980-01-01
Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.
NASA Technical Reports Server (NTRS)
Atluri, S. N.
1986-01-01
Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.
A Demonstration of the Method of Stochastic Finite Element Analysis
1989-03-01
Lfl A DENONSTATION OF THE METHO -D OF DTIC STOCHASTIC FINITE ELEMENT ANALYSIS At LECTE S APR 0418 THESIS Paul R. Bryant Captain, USAF - AFIT/GA/A.A...Sample ASTROS Output) ....................... 78 Appendix D (Random Element Selection) .................... 83 Appendix E ( Weight Estimation...ensuring satisfactory performance? If weight is a concern, then the answer is yes. In the quest for higher performance aircraft and greater useful
A finite element code for electric motor design
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1994-01-01
FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.
NASA Astrophysics Data System (ADS)
Wille, S. Ø.
1996-06-01
An iterative adaptive equation multigrid solver for solving the implicit Navier-Stokes equations simultaneously with tri-tree grid generation is developed. The tri-tree grid generator builds a hierarchical grid structur e which is mapped to a finite element grid at each hierarchical level. For each hierarchical finite element multigrid the Navier-Stokes equations are solved approximately. The solution at each level is projected onto the next finer grid and used as a start vector for the iterative equation solver at the finer level. When the finest grid is reached, the equation solver is iterated until a tolerated solution is reached. The iterative multigrid equation solver is preconditioned by incomplete LU factorization with coupled node fill-in.The non-linear Navier-Stokes equations are linearized by both the Newton method and grid adaption. The efficiency and behaviour of the present adaptive method are compared with those of the previously developed iterative equation solver which is preconditioned by incomplete LU factorization with coupled node fill-in.
Finite Element Modeling of the Buckling Response of Sandwich Panels
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.
2002-01-01
A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.
Finite element modeling of the deformation of magnetoelastic film
Barham, Matthew I.; White, Daniel A.; Steigmann, David J.
2010-09-01
Recently a new class of biocompatible elastic polymers loaded with small ferrous particles, a magnetoelastic polymer, has been developed. This engineered material is formed into a thin film using spin casting. An applied magnetic field will deform the film. The magnetic deformation of this film has many possible applications, particularly in microfluidic pumps and pressure regulators. In this paper a finite element method suitable for the transient simulation of arbitrarily shaped three-dimensional magnetoelastic polymers subjected to time-varying magnetic fields is developed. The approach is similar to that employed in finite elment magnetohydrodynamic simulations, the key difference is a more complex hyperelastic material model. In order to confirm the validity of the approach, finite element solutions for an axially symmetric thin film are compared to an analytical solution based on the membrane (infinitely thin) approximation. For this particular problem the two approaches give qualitatively similar results and converge as the film thickness approaches zero.
Dedicated finite elements for electrode thin films on quartz resonators.
Srivastava, Sonal A; Yong, Yook-Kong; Tanaka, Masako; Imai, Tsutomu
2008-08-01
The accuracy of the finite element analysis for thickness shear quartz resonators is a function of the mesh resolution; the finer the mesh resolution, the more accurate the finite element solution. A certain minimum number of elements are required in each direction for the solution to converge. This places a high demand on memory for computation, and often the available memory is insufficient. Typically the thickness of the electrode films is very small compared with the thickness of the resonator itself; as a result, electrode elements have very poor aspect ratios, and this is detrimental to the accuracy of the result. In this paper, we propose special methods to model the electrodes at the crystal interface of an AT cut crystal. This reduces the overall problem size and eliminates electrode elements having poor aspect ratios. First, experimental data are presented to demonstrate the effects of electrode film boundary conditions on the frequency-temperature curves of an AT cut plate. Finite element analysis is performed on a mesh representing the resonator, and the results are compared for testing the accuracy of the analysis itself and thus validating the results of analysis. Approximations such as lumping and Guyan reduction are then used to model the electrode thin films at the electrode interface and their results are studied. In addition, a new approximation called merging is proposed to model electrodes at the electrode interface.
Finite-Element Analysis of Forced Convection and Conduction
NASA Technical Reports Server (NTRS)
Wieting, A. R.
1982-01-01
TAP2 thermal-analysis program was developed as part of research on finite element methodology for thermal analysis of convectively cooled structures, such as scramjet engines and hypersonic aircraft. Program simplifies computations when both structural and thermal analyses are required and is suited for thermal analysis of nuclear reactors and solar-panel heating systems.
Finite-element analysis of end-notch flexure specimens
NASA Technical Reports Server (NTRS)
Mall, S.; Kochhar, N. K.
1986-01-01
A finite-element analysis of the end-notch flexure specimen for Mode II interlaminar fracture toughness measurement was conducted. The effects of friction between the crack faces and large deflection on the evaluation of G(IIc) from this specimen were investigated. Results of this study are presented in this paper.
Finite element analysis of end notch flexure specimen
NASA Technical Reports Server (NTRS)
Mall, S.; Kochhar, N. K.
1986-01-01
A finite element analysis of the end notch flexure specimen for mode II interlaminar fracture toughness measurement was conducted. The effect of friction between the crack faces and large deflection on the evaluation of G sub IIc from this specimen were investigated. Results of this study are presented in this paper.
Finite element corroboration of buckling phenomena observed in corrugated boxes
Thomas J. Urbanik; Edmond P. Saliklis
2003-01-01
Conventional compression strength formulas for corrugated fiberboard boxes are limited to geometry and material that produce an elastic postbuckling failure. Inelastic postbuckling can occur in squatty boxes and trays, but a mechanistic rationale for unifying observed strength data is lacking. This study combines a finite element model with a parametric design of the...
Design, development and use of the finite element machine
NASA Technical Reports Server (NTRS)
Adams, L. M.; Voigt, R. C.
1983-01-01
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.
Modeling of resistive sheets in finite element solutions
NASA Astrophysics Data System (ADS)
Jin, J. M.; Volakis, John L.; Yu, C. L.; Woo, Alex C.
1992-01-01
A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for variational purposes results are presented for the scattering by a metal-backed cavity loaded with a resistive card.
Modeling of resistive sheets in finite element solutions
NASA Astrophysics Data System (ADS)
Jin, J. M.; Volakis, J. L.; Yu, C. L.; Woo, A. C.
1992-06-01
A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for variational purposes results are presented for the scattering by metal-backed cavity loaded with a resistive card.
Finite element analysis of aeroelasticity of plates and shells
Bismarck-Nasr, M.N.
1992-12-01
A review of the finite element method applied to the problem of supersonic aeroelastic stability of plates and shells is presented. The review is limited to linear models. Some new contributions in the field are presented and future trends are discussed. 105 refs., 18 figs., 6 tabs.
Finite element analyses of wood laminated composite poles
Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse
2005-01-01
Finite element analyses using ANSYS were conducted on orthotropic, polygonal, wood laminated composite poles subjected to a body force and a concentrated load at the free end. Deflections and stress distributions of small-scale and full-size composite poles were analyzed and compared to the results obtained in an experimental study. The predicted deflection for both...
Three Dimensional Finite Element Simulation of the Fretting Wear Problems
NASA Astrophysics Data System (ADS)
Lee, Choon Yeol; Bae, Joon Woo; Choi, Byung Sun; Chai, Young Suck
The structural integrity of steam generators in nuclear power plants is very much dependent upon the fretting wear characteristics of Inconel 690 U-tubes. In this study, a finite element analysis was used to investigate fretting wear on the secondary side of the steam generator, which arises from flow-induced vibrations (FIV) between the U-tubes and supports or foreign objects. Two-dimensional and three-dimensional finite element analyses were adopted to investigate the fretting wear problems. The purpose of the two-dimensional analysis, which simulated the contact between a punch and a plate, was to demonstrate the validity of using finite element analysis to analyze fretting wear problems. This was achieved by controlling the value of the wear constant and the number of cycles. The two-dimensional solutions obtained from this study were in good agreement with previous results reported by Strömberg. In the three-dimensional finite element analysis, a quarterly symmetric model was used to simulate tubes contacting at right angles. The results of the analyses showed donut-shaped wear along the contacting boundary, which is a typical feature of fretting wear.
Coupling finite element and spectral methods: First results
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Debit, Naima; Maday, Yvon
1987-01-01
A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.
2-D Finite Element Cable and Box IEMP Analysis
Scivner, G.J.; Turner, C.D.
1998-12-17
A 2-D finite element code has been developed for the solution of arbitrary geometry cable SGEMP and box IEMP problems. The quasi- static electric field equations with radiation- induced charge deposition and radiation-induced conductivity y are numerically solved on a triangular mesh. Multiple regions of different dielectric materials and multiple conductors are permitted.
Finite-element analysis of an epoxy-curing process
Gartling, D K; Hickox, C E; Nunziato, J W
1983-01-01
A finite element numerical procedure is used to study the curing of an epoxy compound. The problem involves the gelation of an incompressible liquid due to an exothermic chemical reaction. Nonuniform temperature fields produce buoyancy-driven fluid motions that interact with the solidifying material. The numerical simulations provide temperature histories and the progression of the gel front that are compared with experimental data.
A finite element approach for prediction of aerothermal loads
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Vemaganti, G.
1986-01-01
A Taylor-Galerkin finite element approach is presented for analysis of high speed viscous flows with an emphasis on predicting heating rates. Five computational issues relevant to the computation of steady flows are examined. Numerical results for supersonic and hypersonic problems address the computational issues and demonstrate the validity for the approach for analysis of high speed flows.
SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications
NASA Technical Reports Server (NTRS)
Kirk, Benjamin S.
2007-01-01
This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.
Coupling of Peridynamics and Finite Element Formulation for Multiscale Simulations
2012-10-16
state-based peridynamic method, Warren et al. [46] studied the elastic deformation and fracture of a bar. Littlewood [47] presented fragmentation of an...Journal of Solids and Structures 46 (2009) 1186-1195. [47] D. J. Littlewood , Simulation of dynamic fracture using peridynamics, finite element modeling
Finite-Element Fracture Analysis of Pins and Bolts
NASA Technical Reports Server (NTRS)
Nord, K. J.
1986-01-01
Stress intensities calculated in bending and tension. Finite-element stress-analysis method gives stress-intensity estimates for surface flaws on smooth and threaded round bars. Calculations done for purely tensile and purely bending loads. Results, presented in dimensionless form, useful for determining fatigue lives of bolts and pins.
A split finite element algorithm for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Baker, A. J.
1979-01-01
An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.
A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains
NASA Technical Reports Server (NTRS)
Kandil, Osama A.
1998-01-01
Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.
Modelling of orbital deformation using finite-element analysis
Al-Sukhun, Jehad; Lindqvist, Christian; Kontio, Risto
2005-01-01
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury. This study investigated the hypothesis that such deformation could be modelled using finite-element techniques. One patient who had CT-scan examination to the maxillofacial skeleton including the orbits, as part of her treatment, was selected for this study. A FEM of one of the orbits containing the globe was constructed, based on CT-scan images. Simulations were performed with a computer using the finite-element software NISA (EMRC, Troy, USA). The orbit was subjected to a blunt injury of a 0.5 kg missile with 30 m s−1 velocity. The FEM was then used to predict principal and shear stresses or strains at each node position. Two types of orbital deformation were predicted during different impact simulations: (i) horizontal distortion and (ii) rotational distortion. Stress values ranged from 213.4 to 363.3 MPa for the maximum principal stress, from −327.8 to −653.1 MPa for the minimum principal stress, and from 212.3 to 444.3 MPa for the maximum shear stress. This is the first finite-element study, which demonstrates different and concurrent patterns of orbital deformation in a subject following a blunt injury. Finite element modelling is a powerful and invaluable tool to study the multifaceted phenomenon of orbital deformation. PMID:16849235
Advance finite element modeling of rotor blade aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Sangha, K. B.; Panda, B.
1994-01-01
An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.
High-order Finite Element Analysis of Boundary Layer Flows
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2014-11-01
Numerical analysis of boundary layer flows requires careful approximations, specifically the use of a mesh with layered and graded elements near the (viscous) walls. This is referred to as a boundary layer mesh, which for complex geometries is composed of triangular elements on the walls that are inflated or extruded into the volume along the wall-normal direction up to a desired height while the rest of the domain is filled with unstructured tetrahedral elements. Linear elements with C0 inter-element continuity are employed and in some situations higher order C0 elements are also used. However, these elements only enforce continuity whereas high-order smoothness is not attained as will be the case with C1 inter-element continuity and higher. As a result, C0 elements result in a poor approximation of the high-order boundary layer behavior. To achieve greater inter-element continuity in boundary layer region, we employ B-spline basis functions along the wall-normal direction (i.e., only in the layered portion of the mesh). In the rest of the fully unstructured mesh, linear or higher order C0 elements are used as appropriate. In this study we demonstrate the benefits of finite-element analysis based on such higher order and continuity basis functions for boundary layer flows.
NASA Astrophysics Data System (ADS)
Baca, R. G.; Chung, J. N.; Mulla, D. J.
1997-03-01
A new computational method is developed for numerical solution of the Richards equation for flow in variably saturated porous media. The new method, referred to as the mixed transform finite element method, employs the mixed formulation of the Richards equation but expressed in terms of a partitioned transform. An iterative finite element algorithm is derived using a Newton-Galerkin weak statement. Specific advantages of the new method are demonstrated with applications to a set of one- dimensional test problems. Comparisons with the modified Picard method show that the new method produces more robust solutions for a broad range of soil- moisture regimes, including flow in desiccated soils, in heterogeneous media and in layered soils with formation of perched water zones. In addition, the mixed transform finite element method is shown to converge faster than the modified Picard method in a number of cases and to accurately represent pressure head and moisture content profiles with very steep fronts.
An FCT finite element scheme for ideal MHD equations in 1D and 2D
NASA Astrophysics Data System (ADS)
Basting, Melanie; Kuzmin, Dmitri
2017-06-01
This paper presents an implicit finite element (FE) scheme for solving the equations of ideal magnetohydrodynamics in 1D and 2D. The continuous Galerkin approximation is constrained using a flux-corrected transport (FCT) algorithm. The underlying low-order scheme is constructed using a Rusanov-type artificial viscosity operator based on scalar dissipation proportional to the fast wave speed. The accuracy of the low-order solution can be improved using a shock detector which makes it possible to prelimit the added viscosity in a monotonicity-preserving iterative manner. At the FCT correction step, the changes of conserved quantities are limited in a way which guarantees positivity preservation for the density and thermal pressure. Divergence-free magnetic fields are extracted using projections of the FCT predictor into staggered finite element spaces forming exact sequences. In the 2D case, the magnetic field is projected into the space of Raviart-Thomas finite elements. Numerical studies for standard test problems are performed to verify the ability of the proposed algorithms to enforce relevant constraints in applications to ideal MHD flows.
Noakes, Kimberley F.; Bissett, Ian P.; Pullan, Andrew J.; Cheng, Leo K.
2014-01-01
Three anatomically realistic meshes, suitable for finite element analysis, of the pelvic floor and anal canal regions have been developed to provide a framework with which to examine the mechanics, via finite element analysis of normal function within the pelvic floor. Two cadaver-based meshes were produced using the Visible Human Project (male and female) cryosection data sets, and a third mesh was produced based on MR image data from a live subject. The Visible Man (VM) mesh included 10 different pelvic structures while the Visible Woman and MRI meshes contained 14 and 13 structures respectively. Each image set was digitized and then finite element meshes were created using an iterative fitting procedure with smoothing constraints calculated from ‘L’-curves. These weights produced accurate geometric meshes of each pelvic structure with average Root Mean Square (RMS) fitting errors of less than 1.15 mm. The Visible Human cadaveric data provided high resolution images, however, the cadaveric meshes lacked the normal dynamic form of living tissue and suffered from artifacts related to postmortem changes. The lower resolution MRI mesh was able to accurately portray structure of the living subject and paves the way for dynamic, functional modeling. PMID:18317929
Sensitivity analysis based preform die shape design using the finite element method
NASA Astrophysics Data System (ADS)
Zhao, G. Q.; Hufi, R.; Hutter, A.; Grandhi, R. V.
1997-06-01
This paper uses a finite element-based sensitivity analysis method to design the preform die shape for metal forming processes. The sensitivity analysis was developed using the rigid visco-plastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of the B-spline are used as the design variables. The optimization problem is to minimize the difference between the realized and the desired final forging shapes. The sensitivity analysis includes the sensitivities of the objective function, nodal coordinates, and nodal velocities with respect to the design variables. The remeshing procedure and the interpolation/transfer of the history/dependent parameters are considered. An adjustment of the volume loss resulting from the finite element analysis is used to make the workpiece volume consistent in each optimization iteration and improve the optimization convergence. In addition, a technique for dealing with fold-over defects during the forming simulation is employed in order to continue the optimization procedures of the preform die shape design. The method developed in this paper is used to design the preform die shape for both plane strain and axisymmetric deformations with shaped cavities. The analysis shows that satisfactory final forging shapes are obtained using the optimized preform die shapes.
Finite Element Modeling of the NASA Langley Aluminum Testbed Cylinder
NASA Technical Reports Server (NTRS)
Grosveld, Ferdinand W.; Pritchard, Joselyn I.; Buehrle, Ralph D.; Pappa, Richard S.
2002-01-01
The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC configurations were compared with experimental modal survey data. The finite element models were updated and refined, using physical parameters, to increase correlation with the measured modal data. Excellent agreement, within an average 1.5% to 2.9%, was obtained between the predicted and measured modal frequencies of the stringer, frame and dome components. The predictions for the modal frequencies of the assembled component Configurations I through V were within an average 2.9% and 9.1%. Finite element modal analyses were performed for comparison with 3 psi and 6 psi internal pressurization conditions in Configuration VI. The modal frequencies were predicted by applying differential stiffness to the elements with pressure loading and creating reduced matrices for beam elements with offsets inside external superelements. The average disagreement between the measured and predicted differences for the 0 psi and 6 psi internal pressure conditions was less than 0.5%. Comparably good agreement was obtained for the differences between the 0 psi and 3 psi measured and predicted internal pressure conditions.
Discontinuous dual-primal mixed finite elements for elliptic problems
NASA Technical Reports Server (NTRS)
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
2000-01-01
We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.
Dynamic quasistatic characterization of finite elements for shell structures.
Thomas, Jesse David
2010-11-01
Finite elements for shell structures have been investigated extensively, with numerous formulations offered in the literature. These elements are vital in modern computational solid mechanics due to their computational efficiency and accuracy for thin and moderately thick shell structures, allowing larger and more comprehensive (e.g. multi-scale and multi-physics) simulations. Problems now of interest in the research and development community are routinely pushing our computational capabilities, and thus shell finite elements are being used to deliver efficient yet high quality computations. Much work in the literature is devoted to the formulation of shell elements and their numerical accuracy, but there is little published work on the computational characterization and comparison of shell elements for modern solid mechanics problems. The present study is a comparison of three disparate shell element formulations in the Sandia National Laboratories massively parallel Sierra Solid Mechanics code. A constant membrane and bending stress shell element (Key and Hoff, 1995), a thick shell hex element (Key et al., 2004) and a 7-parameter shell element (Buechter et al., 1994) are available in Sierra Solid Mechanics for explicit transient dynamic, implicit transient dynamic and quasistatic calculations. Herein these three elements are applied to a set of canonical dynamic and quasistatic problems, and their numerical accuracy, computational efficiency and scalability are investigated. The results show the trade-off between the relative inefficiency and improved accuracy of the latter two high quality element types when compared with the highly optimized and more widely used constant membrane and bending stress shell element.
Linear and nonlinear finite element analysis of laminated composite structures at high temperatures
NASA Astrophysics Data System (ADS)
Wilt, Thomas Edmund
The use of composite materials in aerospace applications, particularly engine components, is becoming more prevalent due to the materials high strength, yet low weight. In addition to thermomechanical deformation response, life prediction and damage modeling analysis is also required to assess the component's service life. These complex and computationally intensive analyses require the development of simple, efficient and robust finite element analysis capabilities. A simple robust finite element which can effectively model the multi-layer composite material is developed. This will include thermal gradient capabilities necessary for a complete thermomechanical analysis. In order to integrate the numerically stiff rate dependent viscoplastic equations, efficient, stable numerical algorithms are developed. In addition, consistent viscoplastic/plastic tangent matrices will also be formulated. The finite element is formulated based upon a generalized mixed variational principle with independently assumed displacements and layer number independent strains. A unique scheme utilizing nodal temperatures is used to model a linear thermal gradient through the thickness of the composite. The numerical integration algorithms are formulated in the context of a fully implicit backward Euler scheme. The consistent tangent matrices arise directly from the formulation. The multi-layer composite finite element demonstrates good performance in terms of static displacement and stress predictions, and dynamic response. Also, the element appears to be relatively insensitive to mesh distortions. The robustness and efficiency of the fully implicit integration algorithms is effectively demonstrated in the numerical results. That is, large time steps and a significant reduction in global iterations, as a direct result of utilizing the consistent tangent matrices, is shown.
Visualization of transient finite element analyses on large unstructured grids
Dovey, D.
1995-03-22
Three-dimensional transient finite element analysis is performed on unstructured grids. A trend toward running larger analysis problems, combined with a desire for interactive animation of analysis results, demands efficient visualization techniques. This paper discusses a set of data structures and algorithms for visualizing transient analysis results on unstructured grids and introduces some modifications in order to better support large grids. In particular, an element grouping approach is used to reduce the amount of memory needed for external surface determination and to speed up ``point in element`` tests. The techniques described lend themselves to visualization of analyses carried out in parallel on a massively parallel computer (MPC).
PWSCC Assessment by Using Extended Finite Element Method
NASA Astrophysics Data System (ADS)
Lee, Sung-Jun; Lee, Sang-Hwan; Chang, Yoon-Suk
2015-12-01
The head penetration nozzle of control rod driving mechanism (CRDM) is known to be susceptible to primary water stress corrosion cracking (PWSCC) due to the welding-induced residual stress. Especially, the J-groove dissimilar metal weld regions have received many attentions in the previous studies. However, even though several advanced techniques such as weight function and finite element alternating methods have been introduced to predict the occurrence of PWSCC, there are still difficulties in respect of applicability and efficiency. In this study, the extended finite element method (XFEM), which allows convenient crack element modeling by enriching degree of freedom (DOF) with special displacement function, was employed to evaluate structural integrity of the CRDM head penetration nozzle. The resulting stress intensity factors of surface cracks were verified for the reliability of proposed method through the comparison with those suggested in the American Society of Mechanical Engineering (ASME) code. The detailed results from the FE analyses are fully discussed in the manuscript.
Finite element dynamic analysis on CDC STAR-100 computer
NASA Technical Reports Server (NTRS)
Noor, A. K.; Lambiotte, J. J., Jr.
1978-01-01
Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.
Finite Element Modelling of Fluid Coupling in the Coiled Cochlea
NASA Astrophysics Data System (ADS)
Ni, Guangjian; Elliott, S. J.; Lineton, B.; Saba, R.
2011-11-01
A finite element model is first used to calculate the modal pressure difference for a box model of the cochlea, which shows that the number of fluid elements across the width of the cochlea determines the accuracy with which the near field, or short wavenumber, component of the fluid coupling is reproduced. Then results are compared with the analytic results to validate the accuracy of the FE model. It is, however, the far field, or long wavelength, component of the fluid coupling that is most affected by the geometry. A finite element model of the coiled cochlea is then used to calculate fluid coupling in this case, which has similar characteristics to the uncoiled model.
Edge-based finite element scheme for the Euler equations
NASA Astrophysics Data System (ADS)
Luo, Hong; Baum, Joseph D.; Loehner, Rainald
1994-06-01
This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of the upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.
Edge-based finite element scheme for the Euler equations
NASA Astrophysics Data System (ADS)
Luo, Hong; Baum, Joseph D.; Lohner, Rainald
1994-06-01
This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more traditional element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well-documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.
Finite element analysis of inviscid subsonic boattail flow
NASA Technical Reports Server (NTRS)
Chima, R. V.; Gerhart, P. M.
1981-01-01
A finite element code for analysis of inviscid subsonic flows over arbitrary nonlifting planar or axisymmetric bodies is described. The code solves a novel primitive variable formulation of the coupled irrotationality and compressible continuity equations. Results for flow over a cylinder, a sphere, and a NACA 0012 airfoil verify the code. Computed subcritical flows over an axisymmetric boattailed afterbody compare well with finite difference results and experimental data. Interative coupling with an integral turbulent boundary layer code shows strong viscous effects on the inviscid flow. Improvements in code efficiency and extensions to transonic flows are discussed.
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
NASA Technical Reports Server (NTRS)
Hughes, T. J. R.; Winget, J.; Levit, I.; Tezduyar, T. E.
1983-01-01
Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in computational mechanics. A variety of techniques are compared on problems of structural mechanics, heat conduction and fluid mechanics. The results obtained suggest considerable potential for the methods described.
A nonlinear viscoelastic finite element model of polyethylene.
Chen, P C; Colwell, C W; D'Lima, D D
2011-06-01
A nonlinear viscoelastic finite element model of ultra-high molecular weight polyethylene (UHMWPE) was developed in this study. Eight cylindrical specimens were machined from ram extruded UHMWPE bar stock (GUR 1020) and tested under constant compression at 7% strain for 100 sec. The stress strain data during the initial ramp up to 7% strain was utilized to model the "instantaneous" stress-strain response using a Mooney-Rivlin material model. The viscoelastic behavior was modeled using the time-dependent relaxation in stress seen after the initial maximum stress was achieved using a stored energy formulation. A cylindrical model of similar dimensions was created using a finite element analysis software program. The cylinder was made up of hexahedral elements, which were given the material properties utilizing the "instantaneous" stress-strain curve and the energy-relaxation curve obtained from the experimental data. The cylinder was compressed between two flat rigid bodies that simulated the fixtures of the testing machine. Experimental stress-relaxation, creep and dynamic testing data were then used to validate the model. The mean error for predicted versus experimental data for stress relaxation at different strain levels was 4.2%. The mean error for the creep test was 7% and for dynamic test was 5.4%. Finally, dynamic loading in a hip arthroplasty was modeled and validated experimentally with an error of 8%. This study establishes a working finite element material model of UHMWPE that can be utilized to simulate a variety of postoperative arthroplasty conditions.
NASA Astrophysics Data System (ADS)
Chang, S. S.; Tan, K. K.; Lee, H. W. J.; Chan, Chi Kin
2006-01-01
The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357-1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351-358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767-773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911-921].
FECAP - FINITE ELEMENT COMPOSITE ANALYSIS PROGRAM FOR A MICROCOMPUTER
NASA Technical Reports Server (NTRS)
Bowles, D. E.
1994-01-01
Advanced composite materials have gained use in the aerospace industry over the last 20 years because of their high specific strength and stiffness, and low coefficient of thermal expansion. Design of composite structures requires the analysis of composite material behavior. The Finite Element Composite Analysis Program, FECAP, is a special purpose finite element analysis program for analyzing composite material behavior with a microcomputer. Composite materials, in regard to this program, are defined as the combination of at least two distinct materials to form one nonhomogeneous anisotropic material. FECAP assumes a state of generalized plane strain exists in a material consisting of two or more orthotropic phases, subjected to mechanical and/or thermal loading. The finite element formulation used in FECAP is displacement based and requires the minimization of the total potential energy for each element with respect to the unknown variables. This procedure leads to a set of linear simultaneous equations relating the unknown nodal displacements to the applied loads. The equations for each element are assembled into a global system, the boundary conditions are applied, and the system is solved for the nodal displacements. The analysis may be performed using either 4-mode linear or 8-mode quadratic isoparametric elements. Output includes the nodal displacements, and the element stresses and strains. FECAP was written for a Hewlett Packard HP9000 Series 200 Microcomputer with the HP Basic operating system. It was written in HP BASIC 3.0 and requires approximately 0.5 Mbytes of RAM in addition to what is required for the operating system. A math coprocessor card is highly recommended. FECAP was developed in 1988.
Microbuckle initiation in fibre composites : A finite element study
NASA Astrophysics Data System (ADS)
Fleck, Norman A.; Shu, John Y.
1995-12-01
A finite strain continuum theory is presented for unidirectional fibre reinforced composites under in-plane loading. The constitutive response is expressed in terms of couple stress theory, and is deduced from a unit cell of a linear elastic Timoshenko beam embedded in a non-linear elastic-plastic matrix. The continuum theory is implemented within a finite element framework and is used to analyse compressive failure of polymer matrix composites by fibre microbuckling. It is assumed that microbuckling initiates from an imperfection in the form of a finite elliptical region of fibre waviness. The calculations show that the compressive strength decreases with increasing imperfection spatial size from the elastic bifurcation value of Rosen (1965, Fibre Composite Materials, pp. 37-75, American Society Metals Seminar) to the imperfection-sensitive infinite band strength given by Fleck et al. [1995, J. Appl. Mech.62, 329-337.].
Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements
NASA Technical Reports Server (NTRS)
Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.
1990-01-01
A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.
Evaluation of damage models by finite element prediction of fracture in cylindrical tensile test.
Eom, Jaegun; Kim, Mincheol; Lee, Seongwon; Ryu, Hoyeun; Joun, Mansoo
2014-10-01
In this research, tensile tests of cylindrical specimens of a mild steel are predicted via the finite element method, with emphasis on the fracture predictions of various damage models. An analytical model is introduced for this purpose. An iterative material identification procedure is used to obtain the flow stress, making it possible to exactly predict a tensile test up to the fracture point, in the engineering sense. A node-splitting technique is used to generate the cracks on the damaged elements. The damage models of McClintock, Rice-Tracey, Cockcroft-Latham, Freudenthal, Brozzo et al. and Oyane et al. are evaluated by comparing their predictions from the tensile test perspective.
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
NASA Technical Reports Server (NTRS)
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
Wang, C.Y.
1985-01-01
This taper describes an implicit three-dimensional finite-element formulation for the structural analysis of reactor piping system. The numerical algorithm considers hoop, flexural, axial, and torsion modes of the piping structures. It is unconditionally stable and can be used for calculation of piping response under static or long duration dynamic loads. The method uses a predictor-corrector, successive iterative scheme which satisfies the equilibrium equations. A set of stiffness equations representing the discretized equations of motion are derived to predict the displacement increments. The calculated displacement increments are then used to correct the element nodal forces. The algorithm is fairly general, and is capable of treating large displacements and elastic-plastic materials with thermal and strain-rate effects. 7 refs., 7 figs.
Finite element structural redesign by large admissible perturbations
NASA Technical Reports Server (NTRS)
Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.
1991-01-01
In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.
Reliability of elasto-plastic structure using finite element method
NASA Astrophysics Data System (ADS)
Ning, Liu; Wilson H, Tang; Jiashou, Zhuo
2002-02-01
A solution of probabilistic FEM for elastic-plastic materials is presented based on the incremental theory of plasticity and a modified initial stress method. The formulations are deduced through a direct differentiation scheme. Partial differentiation of displacement, stress and the performance function can be iteratively performed with the computation of the mean values of displacement and stress. The presented method enjoys the efficiency of both the perturbation method and the finite difference method, but avoids the approximation during the partial differentiation calculation. In order to improve the efficiency, the adjoint vector method is introduced to calculate the differentiation of stress and displacement with respect to random variables. In addition, a time-saving computational method for reliability index of elastic-plastic materials is suggested based upon the advanced First Order Second Moment (FOSM) and by the usage of Taylor expansion for displacement. The suggested method is also applicable to 3-D cases.
Barnes, Derek N; George, John S; Ng, Kwong T
2008-09-01
Currently the resolution of the head models used in electroencephalography (EEG) studies is limited by the speed of the forward solver. Here, we present a parallel finite difference technique that can reduce the solution time of the governing Poisson equation for a head model. Multiple processors are used to work on the problem simultaneously in order to speed up the solution and provide the memory for solving large problems. The original computational domain is divided into multiple rectangular partitions. Each partition is then assigned to a processor, which is responsible for all the computations and inter-processor communication associated with the nodes in that particular partition. Since the forward solution time is mainly spent on solving the associated matrix equation, it is desirable to find the optimum matrix solver. A detailed comparison of various iterative solvers was performed for both isotropic and anisotropic realistic head models constructed from MRI images. The conjugate gradient (CG) method preconditioned with an advanced geometric multigrid technique was found to provide the best overall performance. For an anisotropic model with 256 x 128 x 256 cells, this technique provides a speedup of 508 on 32 processors over the serial CG solution, with a speedup of 20.1 and 25.3 through multigrid preconditioning and parallelization, respectively.
Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes.
Einstein, D R; Reinhall, P; Nicosia, M; Cochran, R P; Kunzelman, K
2003-02-01
We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function.
Finite-element modelling of multilayer X-ray optics.
Cheng, Xianchao; Zhang, Lin
2017-05-01
Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100-300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10(7)) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10(16) elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10(6)), which causes low solution accuracy; and the number of elements is still very large (10(6)). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.
Parallel, adaptive finite element methods for conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.
1994-01-01
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
Compatibility conditions of structural mechanics for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.
1990-01-01
The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown.
A finite element model of ferroelectric/ferroelastic polycrystals
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices
Oria, Roger; Otero, Jorge; González, Laura; Botaya, Luis; Carmona, Manuel; Puig-Vidal, Manel
2013-01-01
Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement. PMID:23722828
Finite element calculation of residual stress in dental restorative material
NASA Astrophysics Data System (ADS)
Grassia, Luigi; D'Amore, Alberto
2012-07-01
A finite element methodology for residual stresses calculation in dental restorative materials is proposed. The material under concern is a multifunctional methacrylate-based composite for dental restorations, activated by visible light. Reaction kinetics, curing shrinkage, and viscoelastic relaxation functions were required as input data on a structural finite element solver. Post cure effects were considered in order to quantify the residual stresses coming out from natural contraction with respect to those debited to the chemical shrinkage. The analysis showed for a given test case that residual stresses frozen in the dental restoration at uniform temperature of 37°C are of the same order of magnitude of the strength of the dental composite material per se.
An emulator for minimizing finite element analysis implementation resources
NASA Technical Reports Server (NTRS)
Melosh, R. J.; Utku, S.; Salama, M.; Islam, M.
1982-01-01
A finite element analysis emulator providing a basis for efficiently establishing an optimum computer implementation strategy when many calculations are involved is described. The SCOPE emulator determines computer resources required as a function of the structural model, structural load-deflection equation characteristics, the storage allocation plan, and computer hardware capabilities. Thereby, it provides data for trading analysis implementation options to arrive at a best strategy. The models contained in SCOPE lead to micro-operation computer counts of each finite element operation as well as overall computer resource cost estimates. Application of SCOPE to the Memphis-Arkansas bridge analysis provides measures of the accuracy of resource assessments. Data indicate that predictions are within 17.3 percent for calculation times and within 3.2 percent for peripheral storage resources for the ELAS code.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Finite Element Modeling of Micromachined MEMS Photon Devices
Datskos, P.G.; Evans, B.M.; Schonberger, D.
1999-09-20
The technology of microelectronics that has evolved over the past half century is one of great power and sophistication and can now be extended to many applications (MEMS and MOEMS) other than electronics. An interesting application of MEMS quantum devices is the detection of electromagnetic radiation. The operation principle of MEMS quantum devices is based on the photoinduced stress in semiconductors, and the photon detection results from the measurement of the photoinduced bending. These devices can be described as micromechanical photon detectors. In this work, we have developed a technique for simulating electronic stresses using finite element analysis. We have used our technique to model the response of micromechanical photon devices to external stimuli and compared these results with experimental data. Material properties, geometry, and bimaterial design play an important role in the performance of micromechanical photon detectors. We have modeled these effects using finite element analysis and included the effects of bimaterial thickness coating, effective length of the device, width, and thickness.
Compatibility conditions of structural mechanics for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Berke, L.; Gallagher, R. H.
1991-01-01
The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown.
An emulator for minimizing finite element analysis implementation resources
NASA Technical Reports Server (NTRS)
Melosh, R. J.; Utku, S.; Salama, M.; Islam, M.
1982-01-01
A finite element analysis emulator providing a basis for efficiently establishing an optimum computer implementation strategy when many calculations are involved is described. The SCOPE emulator determines computer resources required as a function of the structural model, structural load-deflection equation characteristics, the storage allocation plan, and computer hardware capabilities. Thereby, it provides data for trading analysis implementation options to arrive at a best strategy. The models contained in SCOPE lead to micro-operation computer counts of each finite element operation as well as overall computer resource cost estimates. Application of SCOPE to the Memphis-Arkansas bridge analysis provides measures of the accuracy of resource assessments. Data indicate that predictions are within 17.3 percent for calculation times and within 3.2 percent for peripheral storage resources for the ELAS code.
Finite element analysis applied to dentoalveolar trauma: methodology description.
da Silva, B R; Moreira Neto, J J S; da Silva, F I; de Aguiar, A S W
2011-01-01
Dentoalveolar traumatic injuries are among the clinical conditions most frequently treated in dental practice. However, few studies so far have addressed the biomechanical aspects of these events, probably as a result of difficulties in carrying out satisfactory experimental and clinical studies as well as the unavailability of truly scientific methodologies. The aim of this paper was to describe the use of finite element analysis applied to the biomechanical evaluation of dentoalveolar trauma. For didactic purposes, the methodological process was divided into steps that go from the creation of a geometric model to the evaluation of final results, always with a focus on methodological characteristics, advantages, and disadvantages, so as to allow the reader to customize the methodology according to specific needs. Our description shows that the finite element method can faithfully reproduce dentoalveolar trauma, provided the methodology is closely followed and thoroughly evaluated.
Finite Element Analysis Applied to Dentoalveolar Trauma: Methodology Description
da Silva, B. R.; Moreira Neto, J. J. S.; da Silva, F. I.; de Aguiar, A. S. W.
2011-01-01
Dentoalveolar traumatic injuries are among the clinical conditions most frequently treated in dental practice. However, few studies so far have addressed the biomechanical aspects of these events, probably as a result of difficulties in carrying out satisfactory experimental and clinical studies as well as the unavailability of truly scientific methodologies. The aim of this paper was to describe the use of finite element analysis applied to the biomechanical evaluation of dentoalveolar trauma. For didactic purposes, the methodological process was divided into steps that go from the creation of a geometric model to the evaluation of final results, always with a focus on methodological characteristics, advantages, and disadvantages, so as to allow the reader to customize the methodology according to specific needs. Our description shows that the finite element method can faithfully reproduce dentoalveolar trauma, provided the methodology is closely followed and thoroughly evaluated. PMID:21991463
Finite element thermo-viscoplastic analysis of aerospace structures
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
Total quality management of forged products through finite element simulation
NASA Astrophysics Data System (ADS)
Chandra, U.; Rachakonda, S.; Chandrasekharan, S.
The paper reviews the entire thermo-mechanical history experienced by a complex shaped, high strength forged part during all stages of its manufacturing process, i.e. forging, heat treatment, and machining. It examines the current practice of selecting the process parameters using finite element simulation of forging and quenching operations on an individual basis. Some recent work related to the simulation of aging and machining operations is summarized. The capabilities of several well-known finite element codes for these individual simulations are compared. Then, an integrated simulation approach is presented which will permit the optimization of process parameters for all operations, as opposed to a single operation. This approach will ensure a total quality management of forged products by avoiding costly problems which, under the current practice, are detected only at the end of the manufacturing cycle, i.e. after final machining.
Weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Pavement nondestructive evaluation using finite-element dynamic simulation
NASA Astrophysics Data System (ADS)
Uddin, W.; Hackett, R. M.
1996-11-01
This paper describes the nondestructive evaluation devices, visual distress survey and coring used to investigate jointed concrete pavement performance in northern Mississippi. 3D finite-element models were developed to simulate in-service conditions and to characterize in-situ material properties. Reasonable good agreement is found between in-situ moduli backcalculated from the dynamic analysis of falling weight deflectometer (FWD) deflections measured on selected pavements and laboratory moduli. Effects of load pulse shape, cracking, and discontinuities on the surface deflection response of pavements subjected to FWD load wee also investigated. It is shown that 3D analysis of temperature distribution and resulting thermal stresses play a significant role int he performance of concrete pavements. The study results demonstrated the extensive usefulness of the finite-element dynamic analysis and limitations of the static multilayered analysis and other pavement analysis programs which do not allow for crack modeling and dynamic analysis.
Cyclic creep analysis from elastic finite-element solutions
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hwang, S. Y.
1986-01-01
A uniaxial approach was developed for calculating cyclic creep and stress relaxation at the critical location of a structure subjected to cyclic thermomechanical loading. This approach was incorporated into a simplified analytical procedure for predicting the stress-strain history at a crack initiation site for life prediction purposes. An elastic finite-element solution for the problem was used as input for the simplified procedure. The creep analysis includes a self-adaptive time incrementing scheme. Cumulative creep is the sum of the initial creep, the recovery from the stress relaxation and the incremental creep. The simplified analysis was exercised for four cases involving a benchmark notched plate problem. Comparisons were made with elastic-plastic-creep solutions for these cases using the MARC nonlinear finite-element computer code.
A fast hidden line algorithm for plotting finite element models
NASA Technical Reports Server (NTRS)
Jones, G. K.
1982-01-01
Effective plotting of finite element models requires the use of fast hidden line plot techniques that provide interactive response. A high speed hidden line technique was developed to facilitate the plotting of NASTRAN finite element models. Based on testing using 14 different models, the new hidden line algorithm (JONES-D) appears to be very fast: its speed equals that for normal (all lines visible) plotting and when compared to other existing methods it appears to be substantially faster. It also appears to be very reliable: no plot errors were observed using the new method to plot NASTRAN models. The new algorithm was made part of the NPLOT NASTRAN plot package and was used by structural analysts for normal production tasks.
Finite Element Analysis of Extrusion of Multifilamentary Superconductor Precursor
Peng, X.; Sumption, M.D.; Collings, E.W.
2004-06-28
The extrusion of multifilamentary superconductor precursor billets has been modeled using finite element analysis. The billet configuration was 6 around 1, with the subelement consisting of Nb rods, and the outer can or sleeve was Cu. Two general cases were investigated, those in which the re-stack rods were initially; (i) round, and (ii) hexed. A thermo-mechanical, elasto-plastic, finite-element method was used to analyze the extrusion process. In this 3D FEM model, the initial state of the billet was assumed to be absent of bonding. A typical die angle (2{alpha}=45 deg.) and a series of extrusion ratios were selected to perform the simulation and the corresponding stress and strain distributions of the two billet variants processed were compared. Based on the stress and deformation created at the rod/rod and rod/sleeve interfaces, the bonding conditions generated through the extrusion were investigated.
ORION96. 2-d Finite Element Code Postprocessor
Sanford, L.A.; Hallquist, J.O.
1992-02-02
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.