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At least 1,243 records · Page 69

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NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

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.

Jiang, Bo-Nan↗

NASA NTRS1973

Effect of out-of-planeness of membrane quadrilateral finite elements.

Investigation of the effect of using plane quadrilateral membrane elements for modeling nonplanar structures. The effect is assessed by analyzing a simplified finite element model with the aid of the structure network analysis program. The results obtained indicate that the use of planar quadrilateral membrane elements for modeling bending problems can lead to large errors if the four points that define the quadrilateral are not in the same plane.

Haftka, R. T.↗

DOE OSTI2023

Bound-preserving finite element approximations of the Keller–Segel equations

We report this paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the L ∞ (Ω)-norm to the L 1 (Ω)-norm limiting the growth of the singularity when supported on a macroelement.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Finite Element Analysis and Machine Learning Guided Design of Carbon Fiber Organosheet-Based Battery Enclosures for Crashworthiness

Carbon fiber composite can be a potential candidate for replacing metal-based battery enclosures of current electric vehicles (E.V.s) owing to its better strength-to-weight ratio and corrosion resistance. However, the strength of carbon fiber-based structures depends on several parameters that should be carefully chosen. Here, in this work, we implemented high throughput finite element analysis (FEA) based thermoforming simulation to virtually manufacture the battery enclosure using different design and processing parameters. Subsequently, we performed virtual crash simulations to mimic a side pole crash to evaluate the crashworthiness of the battery enclosures. This high throughput crash simulation dataset was utilized to build predictive models to understand the crashworthiness of an unknown set. Our machine learning (ML) models showed excellent performance (R 2 > 0.97) in predicting the crashworthiness metrics, i.e., crush load efficiency, absorbed energy, intrusion, and maximum deceleration during a crash. We believe that this FEA-ML work framework will be helpful in down select process parameters for carbon fiber-based component design and can be transferrable to other manufacturing technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗

NASA NTRS1975

PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual

The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.

Pifko, A.↗

NASA NTRS1978

A finite element method for transmission in non-uniform ducts without flow Comparison with the method of weighted residuals

A finite element method is derived for studying the transmission of sound in nonuniform ducts without flow. The method is based on a weighted residuals technique and eight noded isoparametric elements. The method employs two computational schemes: the Helmholtz equation found through conservation equations, and the conservation equations themselves. Solutions are found for transmission and reflection coefficients for both two-dimensional and circular geometries. Numerical solutions are compared with those for a method of weighted residuals in the form of a modified Galerkin method, showing good agreement.

Astley, R. J.↗

NASA NTRS1982

Finite-Element Analysis of Forced Convection and Conduction

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.

Wieting, A. R.↗

NASA NTRS1981

Accuracy and convergence of a finite element algorithm for laminar boundary layer flow

The Galerkin-weighted residuals formulation is employed to derive an implicit finite element solution algorithm for a generally non-linear initial-boundary value problem. Solution accuracy and convergence with discretization refinement are quantized in several error norms, for the non-linear parabolic partial differential equation system governing laminar boundary layer flow, using linear, quadratic and cubic functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the non-linear equations characteristic of laminar boundary layer flow.

Soliman, M. O.↗

NASA NTRS1981

Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow

The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.

Soliman, M. O.↗

NASA NTRS1982

Finite element models for predicting crack growth characteristics in composite materials

Two dimensional and quasi-three dimensional, linear elastic finite element models for the prediction of crack growth characteristics, including crack growth direction, in laminated composite materials are presented. Mixed mode crack growth in isotropic materials, unidirectional and laminated composites is considered. The modified crack closure method is used to predict the applied load level for crack extension and two failure theories, modifications of the point stress and the Hashin failure criteria, are proposed to predict the direction of crack extension in composites. Comparisons are made with the Tsai-Wu failure criterion and the Sih strain energy density criterion as well as with experimental results. It is shown that the modified versions of point stress and Hashin criteria compare well with experiment.

Buczek, M. B.↗

NASA NTRS1982

Chemorheology of reactive systems: Finite element analysis

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.

Douglas, C.↗

NASA NTRS1983

Potential of minicomputer/array-processor system for nonlinear finite-element analysis

The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.

Strohkorb, G. A.↗

NASA NTRS1983

Finite element calculation of buoyancy-driven convection near a melt/solid phase boundary

Two iterative schemes based on the mixed finite element method are developed for analyzing steady natural convection in a melt adjacent to its solid phase. The simplest method decouples the calculation of the field variables and the shape of the melt/solid interface into two interlocked iterations that are performed successively. The second method uses Newton's iteration to solve simultaneously for both types of unknowns and has a quadratic convergence rate. Results for a model problem of melt and solid in a cylindrical ampoule show the Newton algorithm to be a factor of three more efficient.

Chang, C. J.↗

NASA NTRS1984

On the development of hierarchical solution strategies for nonlinear finite element formulations

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.

Padovan, J.↗

NASA NTRS1987

Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

Loehner, Rainald↗

NASA NTRS1987

Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations

A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady-state examples are solved to illustrate the performance of the algorithm.

Lohner, Rainald↗

NASA NTRS1990

2-D to 3-D global/local finite element analysis of cross-ply composite laminates

An example of two-dimensional to three-dimensional global/local finite element analysis of a laminated composite plate with a hole is presented. The 'zoom' technique of global/local analysis is used, where displacements of the global/local interface from the two-dimensional global model are applied to the edges of the three-dimensional local model. Three different hole diameters, one, three, and six inches, are considered in order to compare the effect of hole size on the three-dimensional stress state around the hole. In addition, three different stacking sequences are analyzed for the six inch hole case in order to study the effect of stacking sequence. The existence of a 'critical' hole size, where the interlaminar stresses are maximum, is indicated. Dispersion of plies at the same angle, as opposed to clustering, is found to reduce the magnitude of some interlaminar stress components and increase others.

Thompson, D. Muheim↗