Efficient Strategies for Shape Optimization of Structures

A structural model oriented toward design is devised. It is based on a hierarchical geometric description starting with master points. The latters define curves such as B-Splines or Rational Parametric curves and three-and four-sided areas (patches). The process of mesh generation and the definition of design variables proceed from this model.

Second a general sensitivity analysis formulation is recalled. Sensitivity analysis is an essential aspect which consists of computing derivatives of the functions which define the optimization problem. Attention is restricted on static linear problems involving shape variables.

The optimization strategy is also described. It uses approximation concepts and exhibits excellent convergence properties: the overall optimization process usually requires less than ten finite element analyses.

Examples of application to real life structures are offered. They demonstrate the generality and efficiency of the proposed formulation. Optimization of axisymetric structures with three-dimensional loading is also considered by using Fourier analyses.