Strutural Shape Optimization Using Gradient-Based Method

Abstract

The consolidation of the link among four fields in computational mathematics and mechanics is the main objective of this work. Surfaces based on non-uniform rational B-spline (NURBS), mathematical optimization, the finite element method in structural analysis and automatic differentiation are applied to shape optimization of shells. This problem is performed taking into account the fact that the material mechanical characteristics influence both, the structural shape and the thickness variation, in order to obtain the best performance with respect to a specific criterium. These two variables, shape and thickness variation, have an essential role considering that the minimum material cost, a specific frequency and a pure membrane stress state are typical design objectives. Suitable shapes and thickness variation are intrinsic concepts of shell optimization. Therefore, some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation. The shape modification is taken by an optimization code and it is based in the data obtained by a finite element analysis and gradients evaluation. Some examples are analyzed and discussed. As a consequence of the shape optimization, shells with high structural performance and esthetically beautiful shapes can be obtained.