Accuracy of finite element approximations to structural problems
Finite element approximation accuracy and extent of errors in structural problems
Cyrus, N. J.↗
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Calculation of temperature distributions in thin shells of revolution by the finite element method
Computer program using finite element method for computing temperature distributions in thin shells of revolution
Adelman, H. M.↗
Small scale yielding near a crack in plane strain - A finite element analysis
Elastic-plastic finite element analysis of near crack tip stress and strain field structure
Levy, N.↗
Fluid-structure finite-element vibrational analysis
A fluid finite element has been developed for a quasi-compressible fluid. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that the fluid can possess gravitational potential, and the constitutive equations for fluid contain no shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse-matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.
Feng, G. C.↗
A new formulation of hybrid/mixed finite element
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.
Pian, T. H. H.↗
Recent advances in hybrid/mixed finite elements
In formulations of Hybrid/Mixed finite element methods respectively by the Hellinger-Reissner principle and the Hu-Washizu principle, the stress equilibrium equations are brought in as conditions of constraint through the introduction of additional internal displacement parameters. These two approaches are more flexible and have better computing efficiencies. A procedure for the choice of assumed stress terms for 3-D solids is suggested. Example solutions are given for plates and shells using the present formulations and the idea of semiloof elements.
Pian, T. H. H.↗
Specialty three-dimensional finite element analysis codes
General purpose finite element computer codes that can model inelastic material behavior have been available for more than a decade. However, these codes have not been accurate enough for use in analyzing hot section engine components. To correct this problem, General Electric developed a series of nine new stand-alone computer codes for NASA. Because of the large temperature excursions associated with hot section engine components, these codes have been designed to accommodate broad variations in material behavior, including plasticity and creep. The capabilities of these computer codes are summarized.
Lackney, Joseph J.↗
Kuhn-Tucker optimization based reliability analysis for probabilistic finite elements
The fusion of probability finite element method (PFEM) and reliability analysis for fracture mechanics is considered. Reliability analysis with specific application to fracture mechanics is presented, and computational procedures are discussed. Explicit expressions for the optimization procedure with regard to fracture mechanics are given. The results show the PFEM is a very powerful tool in determining the second-moment statistics. The method can determine the probability of failure or fracture subject to randomness in load, material properties and crack length, orientation, and location.
Liu, W. K.↗
Towards parallel I/O in finite element simulations
I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.
Farhat, Charbel↗
Adaptive remeshing method for finite-element thermal analysis
A finite-element remeshing approach that makes use of quadrilateral and triangular elements is described. The approach uses the solution on a previous mesh to create a new mesh. Meshes are completely unstructured with highly refined elements in regions of steep gradients and larger elements where gradients are smaller. Studies of convergence rates for heat conduction problems with exact solutions show that for problems with highly localized solution variations, the remeshing approach gives smaller solution errors with fewer unknowns than refinement of uniform, structured meshes.
Thornton, Earl A.↗
A multidimensional finite element method for CFD
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.
Pepper, Darrell W.↗
Finite element analysis of high speed compressible flows using mesh refinement/movement procedures
An adaptive mesh refinement procedure for analyzing high-speed inviscid and viscous compressible flows is described. The adaptation procedure which uses both quadrilateral and triangular elements is implemented with an explicit finite element formulation. Elements in regions of strong and weak gradients are refined or coarsened based on inviscid and viscous indicators. Nodal locations are also adaptively moved to better resolve flow features. The effectiveness of the finite element procedure is demonstrated by modeling flows with complex shock structure and viscous-inviscid interactions. Numerical results are compared with experimental data.
Ramakrishnan, R.↗
Adaptive p-version based finite element formulations for thermal modeling/analysis of structural configurations
Adaptive p-version based hierarchical finite element formulations in conjunction with a posteriori error estimation concepts are described with emphasis on applicability for thermal modeling/analysis of structural configurations. The basic concepts and formulations of hierarchical p-versiion finite element for thermal analysis are first described. A posteriori error estimation features are utililzed to steer the process of adaptive refinement. Several configurations comprised of one-dimensional structures are evaluated to validate the applicability of the proposed formulations and to demonstrate the potential of the p-version adaptive formulations for thermal modeling/analysis. The methodology offers potential and promises to be an attractive alternative to conventional finite element thermal modeling/analysis approaches.
Tamma, Kumar K.↗
A Galerkin type finite element method for rotary-wing aeroelasticity in hover and forward flight
A Galerkin finite element method for the spatial discretization of the nonlinear, nonselfadjoint, partial differential equations governing rotary-wing aeroelasticity is presented. This method reduces algebraic manipulative labor significantly when compared to the global Galerkin method based on assumed modes. Furthermore, the Galerkin finite element method is ideally suited to treat rotor blades with discontinuous mass and stiffness distribution and structurally redundant configurations as they appear in bearingless rotors. Implementation of the method is illustrated for the coupled flap-lag aeroelastic problem of hingeless rotor blades in hover and forward flight. Numerical results for stability and response illustrate the numerical properties and convergence behavior of the method. It is concluded that the Galerkin finite element method is a practical tool for solving rotary-wing aeroelastic stability and response problems.
Straub, F. K.↗
Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
Wu, R. W.↗
A mixed shear flexible finite element for the analysis of laminated plates
A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.
Putcha, N. S.↗
COMGEN: A computer program for generating finite element models of composite materials at the micro level
COMGEN (Composite Model Generator) is an interactive FORTRAN program which can be used to create a wide variety of finite element models of continuous fiber composite materials at the micro level. It quickly generates batch or session files to be submitted to the finite element pre- and postprocessor PATRAN based on a few simple user inputs such as fiber diameter and percent fiber volume fraction of the composite to be analyzed. In addition, various mesh densities, boundary conditions, and loads can be assigned easily to the models within COMGEN. PATRAN uses a session file to generate finite element models and their associated loads which can then be translated to virtually any finite element analysis code such as NASTRAN or MARC.
Melis, Matthew E.↗
Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms
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.
Kurdila, Andrew J.↗