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The computation of engineering data from finite element solutions based on the virtual work formulation is discussed. It is shown that, using specially chosen virtual displacement functions, it is possible to compute certain functionals from the virtual work expression with much greater efficiency than would be possible by direct methods.
A 'brick' solid finite element is presently developed on the basis of the p-version analysis, and used to demonstrate the FEM concept of 'geometric entities'. This method eliminates interelement discontinuities between low- and high-order elements, allowing very fine control over the shape-function order in various parts of the model. Attention is given to the illustrative cases of a one-element model of an elliptic pipe, and a square cross-section cantilevered beam.
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Finite-element modeling (FEM) of 3C-SiC thin-film membranes on Si substrates was used to determine the residual stress and center deflection with applied pressure. The anisotropic, three-dimensional model includes the entire 3C-SiC membrane and Si substrate with appropriate material properties and boundary conditions. Residual stress due to the thermal-expansion-coefficient mismatch between the3C-SiC film and Si substrate was included in the model. Both before-and after-etching, residual stresses were calculated. In-plane membrane stress and normal deflection with applied pressure were also calculated. FEM results predict a tensile residual stress fo 259 MPa in the 3C-SiC membrane before etching. This decreases to 247 MPa after etching the substrate below the membrane. The residual stress experimentally measured on sample made at Case Western Reserve University was 280 MPa on post-etched membranes. This is excellent agreement when an additional 30-40 MPa of residual stress to account for lattice mismatch is added to the FEM results.
The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.
A mesoscale finite element material model is proposed to analyze structures that fail by the fiber kinking damage mode. To evaluate the assumptions of the mesoscale model, the results were compared with those of a high-fidelity micromechanical model. A direct comparison between the two models shows remarkable correlation, indicating that the key features of the fiber kinking phenomenon are appropriately accounted for in the mesoscale model. The mesoscale model is applied to structural analysis cases to demonstrate the capabilities of the model. A verification study is conducted with an unnotched compression specimen and preliminary validation is demonstrated with a notched compression specimen. The results show that the model is successful at representing the kinematics of fiber kinking while at the same time highlighting the need for further verification and validation.
We present a formulation of the Finite Element Method particular to axisymmetric problems containing anisotropic media.
Finite element (FE) computational models of the whole human body are being used to investigate the injury modalities and mechanisms arising from suited astronauts’ ExtraVehicular Activities (EVAs). These FE whole body models – simplified Elemance and THUMS pedestrian versions – have undergone a series of verification and validation (V&V) assessments for applications in automotive, domestic, and contact sports arenas. However, the FE models’ Modeling and Simulation (M&S) credibility assessments for simulating suited astronaut injuries due to fall from heights in altered gravity environments are limited. The current study evaluates the M&S credibility of simplified Elemance and THUMS pedestrian FE models based on eight credibility factors – data pedigree, input pedigree, code verification, solution verification, conceptual validation, referent validation, results uncertainty, and results robustness – as per NASA-STD-7009A [1]. These credibility factors were assigned ordinal scores ranging between 0 to 4, with a score of 0 in the case of insufficient evidence and 4 when all data for the model is known, used appropriately, and traceable to the Real-World System (RWS) with acceptable accuracy, precision, and uncertainty. The credibility factor sufficiency thresholds were assigned upon guidance from NASA EVA subject matter experts. The factor scores were ascertained through the evaluation of M&S credibility assessment procedures described in the published literature and FE model reports. The M&S credibility scores for the Elemance and THUMS FE models vary between 1 and 3 for data pedigree, input pedigree, and referent validation credibility factors, and between 0 and 1 for code verification, solution verification, conceptual validation, results uncertainty and results robustness. The results show that these FE models are credible for simulating fall from heights injury scenarios in specific kinematic and kinetic ranges that correlate with highway and contact sports-related external conditions. Multiple credibility elevation strategies are prescribed to improve the Elemance and THUMS models’ credibility for use in the EVA fall from height injury scenarios.
A method for accelerating an explicit finite element analysis (FEA) simulation of a modeled system or process includes performing an initial iteration of the FEA simulation according to a baseline time interval via an FEA computing network, and calculating a criteria ratio of a predetermined set of scaling criteria for the modeled system or process. The method includes determining a time-scaling factor using the criteria ratio via the FEA computing network as a function of the criteria ratio, and then applying the time-scaling factor to the baseline time interval to generate a scaled time interval. The scaled time interval accelerates simulation time of the FEA simulation. The method includes performing a subsequent iteration of the explicit FEA simulation at the scaled time interval using the FEA computing network. The process continues for subsequent iterations, with the time-scaling factor adapting with each iteration.
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.
Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.
Sikorsky Aircraft, together with the other major helicopter airframe manufacturers, is engaged in a study to improve the use of finite element analysis to predict the dynamic behavior of helicopter airframes, under a rotorcraft structural dynamics program called DAMVIBS (Design Analysis Methods for VIBrationS), sponsored by the NASA-Langley. The test plan and test results are presented for a shake test of the UH-60A BLACK HAWK helicopter. A comparison is also presented of test results with results obtained from analysis using a NASTRAN finite element model.
The aeroacoustic problem associated with the radiation of fan noise from the inlet of a turbofan aircraft engine, the dimensions of which are generally many times larger than the acoustical wavelengths of the major energy-carrying frequencies, is considered. In the present approach, a conventional finite element solution in the inner region is compatibly matched to a 'wave envelope' finite element solution in a large but finite outer region. The inclusion of a wavelike variation with the correct asymptotic decay in the shape functions for the outer region preserves the correct behavior of the solution at large distances. The method is initially presented for a simple one-dimensional model based on the solution of Webster's horn equation. Results are presented for the specific case of a uniform cylindrical section joined to a conical expansion, and also for a simple axisymmetric test case of the calculation of acoustical pressure generated by a vibrating circular piston located at the center of an infinite rigid baffle.
During a drop weight impact test, the kinetic energy of the falling weight is transferred into the sample resting on the anvil. The plastic deformation in the sample is an important mechanism for the dissipation of the input kinetic energy. We use Eulerian finite element analysis to simulate the deformation and temperature evolution in a 1,3,5-trinitro-1,3,5-triazine (RDX) sample consisting of multiple crystals. In Eulerian finite element simulations, the mesh moves relative to the material. After every change of position between the mesh and the material, the state variables are interpolated to the new mesh position, i.e., advection. In an effort to reduce the advection errors, we use a rate form of a dislocation density-based continuum model by Luscher et al. Here, the simulations predict localization of plastic deformation, and plastic dissipation as a significant source of heat generation.
This paper considers the stress concentration problems of two types of cracked composite systems: (1) a composite system with a broken fiber (a penny-shaped crack problem), and (2) a composite system with a cracked matrix (an annular crack problem). The cracked composite systems are modeled with triangular and trapezoidal ring finite elements. Using NASTRAN (NASA Structural Analysis) finite element computer program, the stress and deformation fields in the cracked composite systems are calculated. The effect of fiber-matrix material combination on the stress concentrations and on the crack opening displacements is studied.
The present paper describes a transient translating elastoplastic thermomechanical finite element model to study two-dimensional frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a nonuniform thermomechanical distribution across the surface of an elastoplastic half space. The half space is represented by a two-dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermophysical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on (1) the temperature gradients and (2) the magnitudes of the normal and tangential tractions.
A method is presented for formulating stiffness terms and thermal coefficients of fiber-reinforced composite, stiffened panels for input to finite element analysis (FEA). The method is robust enough to handle panels with general cross sectional shapes, including those which are unsymmetric and/or unbalanced. New thermal coefficients are introduced to quantify panel response from through-the-thickness temperature gradients. Equations are defined for stiffness, thermal expansion, and thermal bending that consider the full complement of membrane, bending, membrane-bending coupling, and transverse shear behavior. A technique of implementing this capability with a single plane of shell finite elements using the MSC/NASTRAN(TradeMark) FEA program is revealed. Finally, an example of a composite, hat-stiffened panel is included to demonstrate errors that occur when an unsymmetric panel is symmetrically formulated as traditionally done. These erroneous values and the correct ones produced from the presented method are listed for the panel's stiffness matrices, thermal expansion and bending vectors, and the forces and moments that are thermally induced from in-plane and through-the-thickness temperature gradients.
ALEGRA is a multiphysics finite-element shock hydrodynamics code, under development at Sandia National Laboratories since 1990. Fully coupled multiphysics capabilities include transient magnetics, magnetohydrodynamics, electromechanics, and radiation transport. Importantly, ALEGRA is used to study hypervelocity impact, pulsed power devices, and radiation effects. The breadth of physics represented in ALEGRA is outlined here, along with simulated results for a selected hypervelocity impact experiment.