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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Stability and Convergence of Underintegrated Finite Element Approximations

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Oden, J. T.↗
NASA NTRS1983

A posteriori error indicators for the p-version of the finite element method

The existence of local a posteriori error indicators for the p-version of the finite element method is demonstrated through numerical examples. It is shown that it is possible to construct reliable error indicators from the residuums and tractions which have the same rate of convergence as the strain energy. The error indicators contribution of an element can be estimated by considering only the element and its immediate neighbors. The optimal sequence of p-distributions can be closely followed by the indicators even when there are only a very few elements, the elements vary greatly in size, the polynomial orders vary, the mesh grading is poor, and the smoothness indices and relative errors vary between wide limits.

Dunavant, D. A.↗
NASA NTRS1984

Fault friction, regional stress, and crust-mantle coupling in southern California from finite element models

To determine the correct fault rheology of the Transverse Ranges area of California, a new finite element to represent faults and a mangle drag element are introduced into a set of 63 simulation models of anelastic crustal strain. It is shown that a slip rate weakening rheology for faults is not valid in California. Assuming that mantle drag effects on the crust's base are minimal, the optimal coefficient of friction in the seismogenic portion of the fault zones is 0.4-0.6 (less than Byerly's law assumed to apply elsewhere). Depending on how the southern California upper mantle seismic velocity anomaly is interpreted, model results are improved or degraded. It is found that the location of the mantle plate boundary is the most important secondary parameter, and that the best model is either a low-stress model (fault friction = 0.3) or a high-stress model (fault friction = 0.85), each of which has strong mantel drag. It is concluded that at least the fastest moving faults in southern California have a low friction coefficient (approximtely 0.3) because they contain low strength hydrated clay gouges throughout the low-temperature seismogenic zone.

Bird, P.↗
NASA NTRS1991

A parallel algorithm for generation and assembly of finite element stiffness and mass matrices

A new algorithm is proposed for parallel generation and assembly of the finite element stiffness and mass matrices. The proposed assembly algorithm is based on a node-by-node approach rather than the more conventional element-by-element approach. The new algorithm's generality and computation speed-up when using multiple processors are demonstrated for several practical applications on multi-processor Cray Y-MP and Cray 2 supercomputers.

Storaasli, O. O.↗
NASA NTRS1992

Coupled analysis of independently modeled finite element subdomains

A new method for analyzing plate and shell structures with two or more independently modeled finite element subdomains is presented, assessed, and demonstrated. This method provides a means of coupling local and global models whose grid points do not coincide along their common interface. In general, the method provides a means of coupling structural components (e.g., wing and fuselage) which may have been modeled by different analysis. In both cases, the need for transition modeling, which is often tedious and complicated, is eliminated. The coupling is accomplished through an interface for which three formulations are considered and presented. These formulations are: collocation, least-squares, and hybrid variational. Several benchmark problems were analyzed and, based on the results, the hybrid variational formulation is identified as the preferred formulation in that it provides the most accurate solutions.

Aminpour, M. A.↗
NASA NTRS2001

Design Evaluation Using Finite Element Analysis of Cooled Silicon Nitride Plates for a Turbine Blade Application

Two- and three-dimensional finite element analyses were performed on uncoated and thermal barrier coated (TBC) silicon nitride plates with and without internal cooling by air. Steady-state heat-transfer analyses were done to optimize the size and the geometry of the cooling channels to reduce thermal stresses, and to evaluate the thermal environment experienced by the plate during burner rig testing. The limited experimental data available were used to model the thermal profile exerted by the flame on the plate. Thermal stress analyses were performed to assess the stress response due to thermal loading. Contours for the temperature and the representative stresses for the plates were generated and presented for different cooling hole sizes and shapes. Analysis indicates that the TBC experienced higher stresses, and the temperature gradient was much reduced when the plate was internally cooled by air. The advantages and disadvantages of several cooling channel layouts were evaluated.

Abdul-Aziz, Ali↗
DOE OSTI2023

COUPLING SMOOTHED PARTICLE HYDRODYNAMICS WITH FINITE ELEMENT METHOD TO SIMULATE RESIDUAL STRESSES FROM FRICTION STIR PROCESSING

Friction stir processing (FSP) is a solid-state material processing technique that locally modifies the microstructure but also induces undesirable residual stresses. A robust numerical model for the FSP can help in mitigating these residual stresses. Heat source models within a finite element method (FEM) framework suffer from inaccuracies. In contrast, smoothed particle hydrodynamics (SPH) model that explicitly captures the material flow near the tool and the associated heat generation are accurate. However, the computational expense of SPH simulations can be prohibitive. In this work, we propose a coupled SPH-FEM framework. SPH is used to model the heat generation accurately near the tool and which is then inserted into to the FEM model as a heat source. To verify this proposed coupling approach, a test case is set up with typical FSP conditions and it is modeled in both SPH and SPH-FEM. The temperatures profiles were compared after the simulations have reached steady-state temperatures. The similarity of the temperature profiles from SPH-FEA and SPH validated the proposed coupling approach. This proposed approach achieves the accuracy of the SPH method while potentially retaining the low computational expense of FEM.

smoothed particle hydrodynamics, Finite Element Me↗
DOE OSTI2023

A parametric finite element study for determining burst strength of thin and thick-walled pressure vessels

To accurately predict the burst strength of both thin and thick-walled pressure vessels (PVs), a parametric study of PV burst strength was performed for a wide range of vessel geometries and materials using elastic-plastic finite element analysis (FEA). A valid FEA model was established through a detailed study of 2D versus 3D FEA models, the critical stress failure criterion versus the limit load criteria, and the thick-wall effect on the FEA simulations. Here, the results show that the stresses and strains at the mean diameter, rather than outside diameter, determines a more accurate burst strength for both thin and thick-walled PVs. On this basis, a parametrized FEA script using the ABAQUS Python application programming interface (API) was used to create a large database of PV burst strengths for a variety of vessel geometries and materials, demonstrating that Python scripting is a powerful technique for performing parametric studies or generating large databases. From the FEA results, using the regression method, a new burst pressure model was developed as a function of the vessel geometry (D/t ratio) and material properties (UTS and n). As validated by a large number of full-scale burst test data, the proposed burst model can very accurately predict the burst strength for both thin and thick-walled PVs.

42 ENGINEERING↗
NASA NTRS1984

STARS: A general-purpose finite element computer program for analysis of engineering structures

STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.

Gupta, K. K.↗
NASA NTRSDate not supplied

Developing Procedures to Implement Geometric Imperfections Beyond Right Circular Cylindrical Shells in Finite Element Method Models

Analysis of aerospace structures is frequently conducted using nominal dimensions and frequently assumes ideal conditions in loading, contact, constraints, et cetera. Off-nominal dimensions and nonideal conditions, however, are present in all structures. These are the result of widely ranging causes from coefficient of thermal expansion mismatches, manufacturing tooling anomalies, to assembly procedures that inadvertently alter the structure. Specifically, geometric imperfections can have potentially significant influence on the response of a structural test article observed in an experiment versus the response given by a numerical simulation. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS) was previously presented as a set of Python scripts to calculate and implement as-manufactured geometric midsurface and thickness imperfections into finite element method (FEM) shell models of nominally right circular cylinders. By taking advantage of the simple shape of a right circular cylinder, interpolations of the measured data points were able to be performed along directions that aligned to the cylindrical coordinate system axes of the entire structure. By taking advantage of the shell representation of the real structure as opposed to modeling using a continuum representation, the thickness variation was able to be implemented by shell section definitions instead of having to modify the position of multiple nodes in the thickness direction. Py_TIGIRS is a useful tool that established a procedural example on how to implement geometric imperfections in right circular cylindrical shell structures. Three new procedures, each expanded from concepts established in Py_TIGIRS, are proposed for various test-article designs and are intended to broaden the range of structures that can be modeled with measured geometric imperfections in the structural analysis community. Each test-article design introduces new challenges to successfully implement geometric imperfections into a FEM model. The first test-article design consists of a carbon fiber reinforced polymer square plate with a hat-shaped stiffener co-cured on one side. This test-article design was for a novel seven-point bend test that was also previously presented. Manufacturing and cure-cycle imperfections are observed using digital image correlation (DIC) techniques. As thermal expansion coefficient mismatches between the plate and stiffener materials were anticipated, a thermal analysis study with continuum shell and solid elements was conducted to capture the global shape observed prior to testing. The second test-article design is of a similar hat-stiffened plate configuration, but with a side length ratio near 3:1 with elongation in the stiffener direction. The test article was used to characterize the response to uniaxial compressive loading in the direction of the stiffener. Due to differing manufacturing steps, a thermal analysis like the one developed for the seven-point bend configuration was unable to mimic the observed geometric imperfections. Instead, a strategy based on applying deformations directly to the structure during analysis was developed for continuum shell and solid element representation of a stiffened panel.

Geometric imperfections↗
DOE OSTI2020

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

FINITE ELEMENT MODEL MESH REFINEMENT EFFECTS ON QUALIFICATION OF NUCLEAR GRADE GRAPHITE COMPONENTS

The American Society of Mechanical Engineers (ASME) provides the full and simplified design-by-analysis probabilistic assessments for determining acceptance of nuclear grade graphite core components. The assessments can be characterized by three parts: (1) a component stress distribution, often determined by a finite element (FE) model; (2) a Weibull probability density function (pdf) that characterizes the experimental tensile strength distribution; and (3) the post-processor, which combines the FE model and the Weibull strength distribution in accordance with the full and simplified assessments to determine component acceptance. It is known that the level of mesh refinement in FE models can affect the modeled component’s calculated stress distribution. Depending on the component geometry, the stress distribution may converge with sufficient refinement. It was previously unknown whether the acceptance decision resulting from the full and simplified assessments might change even with sufficient mesh refinement. This study explores that question using experimental strength results for a dog-bone geometry for two graphite grades, IG-110 and PCEA. The simplified assessment has two criteria that must be met, the first limits the combined membrane stress by the allowable stress and the second limits the peak equivalent stress by the allowable stress scaled by the ratio of flexural to tensile strength. In the application of the simplified assessment, convergence of the peak equivalent stress required extreme mesh refinement, however, the acceptance decision was not affected. It is hypothesized that more complex geometries with stress concentrations may present mesh refinement effects on the simplified assessment acceptance decision. Mesh refinement did affect the acceptance decision in the full assessment for the applied pressure loadings in this study. This work suggests component stress distribution convergence is not a sufficient criteria for POF convergence in the full assessment and that mesh refinement should continue until the POF has converged, especially where the resulting POF is bordering the SRC acceptable POF limit.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

A Realistic Full-Scale 3D Modeling of Turning Using Coupled Smoothed Particle Hydrodynamics and Finite Element Method for Predicting Cutting Forces

Computational modelling is an effective technique for understanding the complex physics of machining. Large deformations, material separation, and high computational requirements are the key challenges faced while simulating machining. This work introduces a full-scale three-dimensional model of turning operations using a combined approach based on the Smoothed Particle Hydrodynamics (SPH) and Finite Element (FE) methods. By exploiting the advantages of each method, this approach leads to high-fidelity coupled SPH-FE machining models. Cutting forces and chip morphology are the primary results of interest. The machining models are validated with the results of turning experiments. Two-dimensional machining model underpredicts the cutting force and feed force by approximately 49% and 70%, respectively. Moreover, passive force cannot be predicted using the two-dimensional model. On the other hand, with the three-dimensional models developed in this manuscript, the difference between the total simulated force and experimentally measured force is ∼17%. The chip morphologies correlate with experiments in terms of the direction of the chip movement and the “long” continuous chips observed while turning Al 6061. This work expands the realm of machining simulations from two-dimensional orthogonal machining or sectional three-dimensional model to a full-scale realistic simulation. The encouraging simulation results show the potential to study more complex phenomena, such as machining stability and tool path modulation.

42 ENGINEERING↗
DOE OSTI2024

A Study on Particle Trajectory Error in Finite-Element Particle-in-Cell Algorithms

Particle-in-cell (PIC) algorithms are widely used for the simulation of kinetic plasmas. PIC algorithms account for the interaction between charged particles in a plasma and the electromagnetic field in ambient space, including self-field interactions. The objective of this article is to study the error in charged particle trajectories present in finite-element (FE)-based PIC algorithms on unstructured meshes. We study how the trajectory error behaves according to the FE mesh resolution and the matrix solver employed in the FE algorithm. The study is performed by considering a trajectory established by a parabolic electric potential and an axial magnetic force acting on the charged particle. Under a proper choice combination of electric and magnetic field parameters, the 2-D particle trajectories comprise closed orbits. Numerical errors cause small perturbations on the trajectories, with cumulative effects. As a result, the resulting orbital trajectories exhibit distortions including spurious apsidal precession. These distortions provide a clear imprint of the numerical error. Here, we also study the numerical error in a quantitative fashion by computing the distance norm between the trajectories obtained by the exact fields and numerical fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1968

Duality in finite element methods.

Duality between basic equations and dependent variables in problems of plate stretching and bending applied to finite element method

Elias, Z. M.↗
NASA NTRS1971

Finite element solution of lubrication problems

A variational formulation of the transient lubrication problem is presented and the corresponding finite element equations derived for three and six point triangles, and, four and eight point quadrilaterals. Test solutions for a one dimensional slider bearing used in validating the computer program are given. Utility of the method is demonstrated by a solution of the shrouded step bearing.

Reddi, M. M.↗
NASA NTRS1972

A finite element procedure for nonlinear prebuckling and initial postbuckling analysis

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.

Mau, S. T.↗