Shape Optimization of 2D Elastic Structures Using Adaptne Grids
The paper deals with an effective adaptive method for 2D shape optimization of linear elastic structures. The design objective is to find the shape of the kinematically unconstrained boundary assuring minimum volume of the structural material with constraints imposed on equivalent stresses. The geometrical shape parameters are the design variables. The method is based on a special kind of finite element automatically adaptive grids. The original iterative algorithm for solving the nonlinear system of equations and inequalities arising from the Kuhn-Tucker conditions is presented. The proposed approach is successfully tested on two classical examples.
W. GUTKOWSKI and J. ZAWIDZKA, Shape optimization using regular adaptive grid, Proc. of the Seiken - IASS Symposium on Nonlinear Analysis and Design for Shell and Spatial Structures, 17-24, Tokyo, October 1993.
K. YAMAZAKI, J. SAKAMOTO and M. KITANO, An efficient shape optimization technique of a two-dimensional body based on the boundary element method, Comput. Struct., 48, 6, 1073-1081, 1993.
N. KIKUCHI, K.Y. CHUNG, TORIGAKI and J.E. TAYLOR, Adaptive finite element method for shape optimization of linearly elastic structures. The optimum shape - automated structural design, Plenum Press, 139-169, New York 1986.
V.B. VENKAYYA, Optimality criteria: a basis for multidisciplinary design optimization, Computational Mech., 5, 1, 1-21, 1989.
M. KLEIBER, Introduction to the FEM [in Polish], PWN, Warszawa-Poznań 1989.
Y.-T. HWANG and C. FLEURY, A mesh-shape sensitivity synthesis for boundary - formulated shape optimal design, AIAA Paper 1532-CP, 1993.