SEARCH · Search NASA

Results for “compatible finite element method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics

Here, we present compatible finite element space discretizations for the ideal compressible magnetohydrodynamic equations. The magnetic field is considered both in div- and curl-conforming spaces, leading to a strongly or weakly preserved zero-divergence condition, respectively. The equations are discretized in space such that transfers between the kinetic, internal, and magnetic energies are consistent, leading to a preserved total energy. We also discuss further adjustments to the discretization required to additionally achieve magnetic helicity preservation. Finally, we describe new transport stabilization methods for the magnetic field equation which maintain the zero-divergence and energy conservation properties, including one method which also preserves magnetic helicity. The methods' preservation and improved stability properties are confirmed numerically using a steady state and a magnetic dynamo test case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1991

Finite element modeling of truss structures with frequency-dependent material damping

A physically motivated modelling technique for structural dynamic analysis that accommodates frequency dependent material damping was developed. Key features of the technique are the introduction of augmenting thermodynamic fields (AFT) to interact with the usual mechanical displacement field, and the treatment of the resulting coupled governing equations using finite element analysis methods. The AFT method is fully compatible with current structural finite element analysis techniques. The method is demonstrated in the dynamic analysis of a 10-bay planar truss structure, a structure representative of those contemplated for use in future space systems.

Lesieutre, George A.↗

NASA NTRS1991

Integrated force method - Compatibility conditions of structural mechanics for finite element analysis

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. The utilization of CC's has resulted in the novel integrated force method (IFM). The solution that is obtained by the IFM converges with a significantly fewer number of elements, compared to the stiffness and the hybrid methods.

Patnaik, Surya N.↗

NASA NTRS1997

Micromechanics Analysis Code (MAC) Developed

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers in performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions, it must be based on a micromechanics approach that uses physically based deformation and life constitutive models, and it must allow one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Only then can such a model be used by a material scientist to investigate the effect of different deformation mechanisms on the overall response of the composite and, thereby, identify the appropriate constituents for a given application. However, if a micromechanical model is to be used in a large-scale structural analysis it must be (1) computationally efficient, (2) able to generate accurate displacement and stress fields at both the macro and micro level, and (3) compatible with the finite element method. In addition, new advancements in processing and fabrication techniques now make it possible to engineer the architectures of these advanced composite systems. Full utilization of these emerging manufacturing capabilities require the development of a computationally efficient micromechanics analysis tool that can accurately predict the effect of microstructural details on the internal and macroscopic behavior of composites. Computational efficiency is required because (1) a large number of parameters must be varied in the course of engineering (or designing) composite materials and (2) the optimization of a material's microstructure requires that the micromechanics model be integrated with optimization algorithms. From this perspective, analytical approaches that produce closed-form expressions which describe the effect of a material's internal architecture on the overall material behavior are preferable to numerical methods such as the finite element or finite difference schemes.

Source record↗

NASA NTRS2001

Micromechanics-Based Inelastic Finite Element Analysis Accomplished Via Seamless Integration of MAC/GMC

A critical issue in the micromechanics-based analysis of composite structures becomes the availability of a computationally efficient homogenization technique: one that is 1) Capable of handling the sophisticated, physically based, viscoelastoplastic constitutive and life models for each constituent; 2) Able to generate accurate displacement and stress fields at both the macro and the micro levels; 3) Compatible with the finite element method. The Generalized Method of Cells (GMC) developed by Paley and Aboudi is one such micromechanical model that has been shown to predict accurately the overall macro behavior of various types of composites given the required constituent properties. Specifically, the method provides "closed-form" expressions for the macroscopic composite response in terms of the properties, size, shape, distribution, and response of the individual constituents or phases that make up the material. Furthermore, expressions relating the internal stress and strain fields in the individual constituents in terms of the macroscopically applied stresses and strains are available through strain or stress concentration matrices. These expressions make possible the investigation of failure processes at the microscopic level at each step of an applied load history.

Arnold, Steven M.↗

NASA NTRS1990

Improved Stress Analysis Of Multicomponent Rotors

Suitable formulation of finite-element model speeds computation. Improved method developed for analysis of stress and compatibility of components in multicomponent rotating assembly. In method, single finite-element mathematical model represents all of components. Made possible by use of gap elements to represent contact surfaces between components.

Carek, Gerald A.↗

NASA NTRS1993

A comparison of viscoelastic damping models

Modern finite element methods (FEM's) enable the precise modeling of mass and stiffness properties in what were in the past overwhelmingly large and complex structures. These models allow the accurate determination of natural frequencies and mode shapes. However, adequate methods for modeling highly damped and high frequency dependent structures did not exist until recently. The most commonly used method, Modal Strain Energy, does not correctly predict complex mode shapes since it is based on the assumption that the mode shapes of a structure are real. Recently, many techniques have been developed which allow the modeling of frequency dependent damping properties of materials in a finite element compatible form. Two of these methods, the Golla-Hughes-McTavish method and the Lesieutre-Mingori method, model the frequency dependent effects by adding coordinates to the existing system thus maintaining the linearity of the model. The third model, proposed by Bagley and Torvik, is based on the Fractional Calculus method and requires fewer empirical parameters to model the frequency dependence at the expense of linearity of the governing equations. This work examines the Modal Strain Energy, Golla-Hughes-McTavish and Bagley and Torvik models and compares them to determine the plausibility of using them for modeling viscoelastic damping in large structures.

Slater, Joseph C.↗

NASA NTRS2007

Compatibility Condition in Theory of Solid Mechanics (Elasticity, Structures, and Design Optimization)

The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.

Patnaik, Surya N.↗

NASA NTRS1988

Improved method for stress and compatibility analysis of multicomponent rotating systems

An improved method of analyzing multicomponent rotating assemblies for the determination of operating stresses and component compatibility has been developed. In this method, a single finite element model is developed which contains all of the separate components in the rotating assembly. This is made possible by using gap elements to simulate the contact surfaces between components. The MARC finite element computer program is then used to perform the analysis. This improved method is less time consuming and more reliable than the conventional method of analyzing such systems. Results are presented for two different stress-compatibility analyses of a six-component axial flow compressor rotor. The results for the previously used flexibility analysis method are compared with those for the improved analysis method. The stresses predicted by each method compare quite well with each other. The predictions of the component compatibility, as well as the magnitude of the forces at the contact surfaces, also compare well for these two analysis procedures. It is therefore recommended that the improved analysis method be used to determine the stress-compatibility characterstics of multicomponent rotating systems.

Carek, Gerald A.↗

NASA NTRS1996

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Kaljevic, Igor↗

NASA NTRS1972

Nonlinear behavior of shells of revolution under cyclic loading

A large deflection elastic-plastic analysis is presented, applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed. The monotonic results are compared with other theoretical solutions.

Levine, H. S.↗

NASA NTRS1973

Nonlinear behavior of shells of revolution under cyclic loading.

A large deflection elastic-plastic analysis is presented applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed.

Levine, H. S.↗

NASA NTRS1990

General purpose program to generate compatibility matrix for the integrated force method

An efficient procedure for obtaining the compatibility conditions of finite-element models involves the generation of both field and compatibility conditions from deformation-displacement relations, using (1) the compatibility bandwidth, and (2) the node-determinacy concept. A computer program thus structured will generate sparse and banded compatibility conditions for a structure that is idealized by the finite elements.

Nagabhusanam, J.↗

DOE OSTI2024

Diffusion Limit–Preserving Lumped DFEMs on AMR Meshes

Here, we present sweep-compatible, novel upwinding recipes for the bilinear discontinuous (BLD) finite element method (FEM) that allows lumped BLD to be used on adaptive mesh refinement (AMR) meshes for thick transport applications without adding additional degrees of freedom at hanging nodes that exist on refinement boundaries. We analyze the properties of the upwinding and lumping that are needed for BLD to get the thick diffusion limit on such meshes, present results demonstrating locking with the wrong recipe, and present results showing error convergence and robustness properties for two diffusive problems on a variety of AMR meshes.

42 ENGINEERING↗

NASA NTRS2001

Modeling and Analysis of Wrinkled Membranes: An Overview

Thin-film membranes are basic elements of a variety of space inflatable/deployable structures. Wrinkling degrades the performance and reliability of these membrane structures, and hence has been a topic of continued interest. Wrinkling analysis of membranes for general geometry and arbitrary boundary conditions is quite challenging. The objective of this presentation is two-fold. Firstly, the existing models of wrinkled membranes and related numerical solution methods are reviewed. The important issues to be discussed are the capability of a membrane model to characterize taut, wrinkled and slack states of membranes in a consistent and physically reasonable manner; the ability of a wrinkling analysis method to predict the formation and growth of wrinkled regions, and to determine out-of-plane deformation and wrinkled waves; the convergence of a numerical solution method for wrinkling analysis; and the compatibility of a wrinkling analysis with general-purpose finite element codes. According to this review, several opening issues in modeling and analysis of wrinkled membranes that are to be addressed in future research are summarized, The second objective of this presentation is to discuss a newly developed membrane model of two viable parameters (2-VP model) and associated parametric finite element method (PFEM) for wrinkling analysis are introduced. The innovations and advantages of the proposed membrane model and PFEM-based wrinkling analysis are: (1) Via a unified stress-strain relation; the 2-VP model treat the taut, wrinkled, and slack states of membranes consistently; (2) The PFEM-based wrinkling analysis has guaranteed convergence; (3) The 2-VP model along with PFEM is capable of predicting membrane out-of-plane deformations; and (4) The PFEM can be integrated into any existing finite element code. Preliminary numerical examples are also included in this presentation to demonstrate the 2-VP model and PFEM-based wrinkling analysis approach.

Yang, B.↗

NASA NTRS1991

Compatible thermal and structural elements for the analysis of beam and plate structures

Energy methods are used to formulate steady-state thermal elements which are compatible with structural beam and plate elements. Comparisons of energy method results with finite element results indicate that the energy methods achieve similar accuracy with fewer degrees of freedom. Limitations of energy methods with regard to discontinuous functions and computational overflow are noted. Thermal stress calculations are simplified by the use of similar formulations for the thermal and structural elements. The advantages that these energy-based elements offer to high-temperature structural optimization are discussed.

Vause, R. F.↗

NASA NTRS1992

A piecewise continuous Timoshenko beam model for the dynamic analysis of tapered beam-like structures

Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.

Shen, Ji Yao↗

NASA NTRS1987

A probabilistic Hu-Washizu variational principle

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Liu, W. K.↗