Structural shape optimization and convex programming methods

Nowadays, convex programming methods are recognized as an efficient approach to solve a variety of structural optimization problems. Their integration with F.E. computing codes as well as modern CAD systems provides a powerful tool to fulfil realistic engineering design tasks. In this paper, two topics are addressed. The first one is concerned with shape optimization techniques which include automatic selection of design variables based on parametric CAD model, appropriate implementation of semi-analytical sensitivity analysis method and mesh perturbators for velocity field evaluations. The second one is about convex programming methods. A comparative study of different methods will make sure that using general and high-quality approximation schemes are essential to improve the efficiency of the design procedure when considered problems are characterized by different types of constraints (e.g. static, dynamic) and different types of design variables (e.g. sizing, configurational, topological). In this context, the GMMA (Generalized Method of Moving Asymptotes) and DQA (Diagonal Quadratic Approximation) methods are proposed here. Numerical examples are given to illustrate concerned issues and different methods. A discussion will be made about results.