A Two-Level Strategy For Topology And Orientation Optimization Of Laminated Shell Structures.

Abstract

This article presents different approaches for solving problems of topology and
orientation optimization of laminated shell structures. The objective of the design is the
minimization of volume under compliance constraints. The design variables are the relative
densities and the principal material direction orientation of each layer in an element. A twolevel
strategy is used, optimizing sequentially the orientation and then the density, aiming
reducing the computational effort during each iteration. Sequential Linear Programming
method is used to solve both optimization problems. Mathematical algorithms were derived
for the solution of the problem. These algorithms were coded for single and multiple loading
cases. The topology optimization can be considered as an extension for laminated shell
structures of Cardoso6 and Sant’Anna25 works. An eight node degenerated shell finite element
with explicit integration on the thickness direction, as in Kumar et al., is used to solve the
equilibrium equations for laminated composites. Some illustrative examples are presented
and discussed to show the applicability of the proposed optimization approaches.