Structural Shape Optimisation by using Multi-direction Boundary Points Movement Method

Abstract

Structural shape optimisation is a process of changing the structural boundary to reach to an optimum design (i.e. minimum weight, low cost, etc.) while satisfying the structural geometry (i.e. height, radius, etc.) and behaviour (i.e. stress, natural frequency, etc.) constraints. These problems can be solved by either calculus or heuristic-based methods. Although the calculus based methods are by far the best in terms of computational efficiency, however, they may not reach to the global optimum. A Heuristic-based methods with the distinctive feature of local and global search is more robust to obtain the global optimum. There are several heuristic-based methods in existence, however the most common, robust and reliable one is the Genetic Algorithms (GA). It works by mimicking the evolution process found in natural to obtain the optimum solution [1]. The aim of this research is to apply GA to the problem of shape optimisation. Past research has concentrated in applying binary GA to shape optimisation by carrying out step-wise movements of the boundary of the structure in a specific direction in 2D space [2],[3]. The research presented here extends the method by allowing the movements of boundary in any direction. For all of the methods mentioned, the structural boundary under design condition is represented by a finite number of segments with two boundary points (BP) connected at each segment ends. In fact, the change of the structural boundary is governed by the movement of these points. This study looks at what effect multi-directional movement of these points have on the optimum design. Several examples with different movement cases including the stepwise, recursive step-wise and multi-direction were considered. The results obtained by the latter two methods indicated an improvement over the step-wise method, thus allowing the structure to adapt itself closer to the global optimum.