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A Reduced Basis Approach for Rapid and Reliable Computation of Structural Linear Elasticity Problems Using Mixed Interpolation of Tensorial Components Element

Hunan Univ. - F. Lei, Y. L. Ma, Y. C. Bai, H. B. Yang
  • Journal Article
  • 17-227-5-905
Published 2013-05-01 by SAGE Publications in United Kingdom
As the reduced basis method is well used in some other fields to rapidly solve engineer systems, it is adapted to structural computation here. In this article, a reduced basis approach of computing structural linear elasticity problems is proposed to obtain rapid and reliable outputs using mixed interpolation of tensorial components elements. The procedure is as follows. First, structural computation problems based on finite element formulation should be parameterized. As an example, finite element formulation based on a type of element is analyzed and parameters in the formulation are extracted explicitly. Parameterized structural problem is built by assembling finite element formulation of components with parameters. Then, an approximate subspace of lower dimension based on structural outputs within whole parameter domain is constructed by an adaptive procedure. By projecting the parameterized structural problem onto that subspace, it is reduced to a parameterized lower dimension problem, which can be solved rapidly with random given parameters. The procedure is divided into two phases, naming offline and online procedure. Structures in vehicle design problems are employed to verify the…

A Note on Shear Effects in Progressive Crushing of Prismatic Tubes

Amoco Production Co.-Shankar Bhat
MIT Dept. of Ocean Engineering-Tomasz Wierzbicki
Published 1986-04-22 by SAE International in United States
As opposed to slender columns, tubular members used in the automobile industry are quite “stocky” so that the shear rigidity is comparable to the bending rigidity. It has been conjunctured that appreciable shear forces developed in the process of progressive crushing might be responsible for a loss of stability and a global collapse of compressive members. This problem is studied here using a simple model of the tube undergoing finite rotations and local crushing. It was found that the shear forces are caused by redistribution of stresses at the crushed zones and tube ends and by the associated finite changes of the geometry of the tube. An essential mechanism which triggers these events is the unsymmetric local folding, described by Abramowicz and Jones.A simple estimate is given on the maximum magnitude of shear forces both in the positive and negative direction. At the level of a single compressed member, the global collapse can be prevented by controlling the local folding process. In the case of an integrated front panel, the unsymmetric folding of one member…
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Generic “Stick” Model of a Vehicular Structure

Engineering and Manufacturing Staff, Ford Motor Co.-Choon T. Chon, Homa Mohammadtorab
Numerics Corp., Presently with Engineering Mechanics, Research Corp.-Mohamed El-Essawi
Published 1986-04-22 by SAE International in United States
The paper describes a method of developing generic “stick” models (beam only finite element models) of vehicle structures. The EAL program is used to create two- and four-door generic models through a capability for specifying geometry by assigning dimensions of a vehicle structure. A description is given for elastic analyses, the steps of sensitivity analyses and the test setup for measuring bending and torsional stiffness of a body-in-white structure. The analysis results are shown to be in good agreement with the test data for the overall bending and torsional stiffness. Sensitivity coefficients of the total strain energy are computed using the forward finite diference scheme.
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Structural Behavior of Members Consisting of Curved Elements

Department of Civil Engineering University of Missouri-Rolla-M. B. Parks, C. Santaputra, W. W. Yu
Published 1986-04-22 by SAE International in United States
A series of stub column tests have been performed in order to determine the initial buckling stress of curved elements with three supported edges and one longitudinal edge free. An empirical expression for the prediction of the elastic local buckling of this type of curved element has been developed and is compared to the test data. The tangent modulus concept is employed for the prediction of inelastic buckling. Also studied is the interaction between flat and curved elements when the flat element buckles before the adjoining curved element.
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Future Developments in Structural Analysis

Chrysler Corp.-J. E. Thompson
Published 1974-02-01 by SAE International in United States
The power and generality of the finite element approach to structural analysis is evident from the literature. However, this very generality demands that the user define his problem to the finite element computer program in great detail and with precision. To extend the use of this method within industry and to approach more complex dynamic, nonlinear problems requires new solutions to the problem of generating large, error-free piles of data and improvements in the efficiency of the computer programs and in the flexibility of model description. This paper describes near- and long-term developments aimed at solving these problems.
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