A Study of Two-Dimensional Plane Elasticity Finite Elements for Optimal Design

ABSTRACT Design of structures using a variety of two-dimensional finite elements is considered in this paper. An efficient technique of computing first-order derivatives of pointwise stress constraints for simple and higher-order two-dimensional (membrane) finite elements is presented. Computational aspects of design sensitivity vector calculation, using a semi-analytical method versus traditional methods are presented. Implementation of a fully-stressed design approach to find a suitable initial estimate leads to increased computational efficiency. These aspects of the design procedure are illustrated through analysis of numerical examples. Experience indicates that a suitable mix of low and higher-order elements yields the most efficient and accurate design model.

[1]  Edward J. Haug,et al.  Methods of Design Sensitivity Analysis in Structural Optimization , 1979 .

[2]  Biren Prasad,et al.  A GENERAL CAPABILITY OF DESIGN SENSITIVITY FOR FINITE ELEMENT SYSTEMS , 1982 .

[3]  M. E. Botkin,et al.  Structural shape optimization with geometric description and adaptive mesh refinement , 1985 .

[4]  Kyung K. Choi,et al.  Accuracy of Finite Element Based Shape Design Sensitivity Analysis , 1985 .

[5]  Subramaniam Rajan,et al.  SADDLE: A computer-aided structural analysis and dynamic design language—Part I. design system , 1986 .

[6]  S. Rajan.  A hybrid nonlinear programming method for design optimization , 1986 .

[7]  Philip E. Gill,et al.  Practical optimization , 1981 .

[8]  G. L. Giles,et al.  Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system , 1982 .

[9]  B. Esping,et al.  Minimum weight design of membrane structures using eight node isoparametric elements and numerical derivatives , 1984 .

[10]  Garret N. Vanderplaats,et al.  Comment on "Methods of Design Sensitivity Analysis in Structural Optimization" , 1980 .

[11]  Kyung K. Choi,et al.  Shape Optimal Design of an Engine Connecting Rod , 1984 .

[12]  M. E. Botkin,et al.  Shape Optimization of Plate and Shell Structures , 1981 .

[13]  Raphael T. Haftka,et al.  Preliminary design of composite wings for buckling, strength and displacement constraints , 1979 .

[14]  Edward J. Haug,et al.  Design sensitivity analysis of elastic mechanical systems , 1978 .

[15]  Garret N. Vanderplaats,et al.  CONMIN: A FORTRAN program for constrained function minimization: User's manual , 1973 .

[16]  Raphael T. Haftka,et al.  Optimum Structural Design with Plate Bending Elements—A Survey , 1981 .