Accuracy of design sensitivity for optimization of structural using small strain theory by finite element method

Bhagate, Kiran A. and Pawar, Prashant and Singh, Arbind Kumar and Ye, Jianqiao (2006) Accuracy of design sensitivity for optimization of structural using small strain theory by finite element method. In: III European Conference on Computational Mechanics : Solids, Structures and Coupled Problems in Engineering: Book of Abstracts. Springer, Berlin, p. 711. ISBN 1402049943

Abstract

Optimization of structures is always a fantasizing area for many researchers from past few decades. Many efforts have been taken in reducing the errors from the optimization process especially after advancement in computer faclities. The resulting structures are more efficient, economical and reliable. In traditional optimization techniques, the most important factor affecting on optimization process is the search direction which is the derivative of change in respose of structure due to change in design variables. This derivative is called as sensitivity derivative.Accuracy of sensitivity analysis is very much dependent on the method of structural analysis, technique of sensitivity calculation, computational efficiency etc. In this work, accuracy of sensitivity derivatives in elastic and plastic analyses are investigated on the basis of small strain theory. Combined with the Finite element method, which provides an excellent tool for the analysis of complex structures, the different techniques used for sensitivity calculations are finite difference method, semianalytical method and analytical method. Detail discussion of formulation and implementation of these methods are presented. Comparative study shows the relative error, cost of computation and efficiency of the above methods.From the results obtained, it can be stated that the finite difference method is the simplest technique that does not require access to the finite elemen analysis code and hence requires less efforts. However, this method is inefficient and less accurate. Analytical method is the most accurate method but its formulation and implementation is difficult as compared to other two metods. Semianalytical method is found to be a compromise of the two that results in more accurate solutions than from the finite diference method and is easy to implement as compared to the analytical method. The comparisons provide useful information for design engineers to decide a suitable method in the calculation of sensitivity erivatives for different structural optimization problems.