Finite element solutions of optimization problems with stability constraints involving columns and laminated composites.

Abstract

The primary aim of this study is to assess the applicability and performance of the finite element method (FEM) in solving structural optimization problems with stability constraints. In order to reach this goal, several optimization problems are solved using FEM which are briefly described as follows: The strongest column problem is one of the oldest optimization problems for which analytical solutions exist only for some special cases. Here, both unimodal and bimodal optimization of columns under concentrated and/or distributed compressive loads with several different boundary conditions and constraints are performed using an iterative method based on finite elements. The analytical solutions available in the literature for columns under concentrated loads and an analytical solution derived for simply supported columns under distributed loads are used for verification purposes. Optimization results are presented for fibre-reinforced composite rectangular plates under inplane loads. The non-uniformity of the in-plane stresses due to stress diffusion and/or in-plane boundary conditions is taken into account, and its influence on optimal buckling load is investigated. It is shown that the exclusion of the in-plane restraints may lead to errors in stability calculations and consequently in optimal design. The influences of the panel aspect ratio, stacking sequence, panel thickness, and the rotational edge restraints on the optimal axially compressed cylindrical and non-cylindrical curved panels are investigated, where the optimal panel is the one with the highest failure load. The prebuckling and the first-ply failure loads of the panels are calculated and minimum of these two is selected as the failure load. The results show that there are distinct differences between the behaviour of cylindrical and non-cylindrical panels. The formulations of the finite elements which are used throughout the study are given and several verification problems are solved to verify the accuracy of the methodology. The computer codes written in Matlab are also given in the appendix sections accompanied with the selected codes used for optimization purposes.