Continuous Optimization in Aerospace Structures

In structural design optimization, engineers and designers aim to obtain more efficient designs with regards to measures such as weight, stiffness or frequency, for a given set of design variables. These design variables can be of different type such as material properties or geometric variables. Hence, depending on the design variables that are chosen, different techniques such as topology, shape, and size optimization have been introduced. This section presents a brief introduction to the topic in their continuous and corresponding discrete formulation based on the finite element method (FEM). Basic concepts of the advanced technologies that are involved in a typical structural design progress are also briefly included, such as: modelling analysis using the FEM, mesh generation/adaptivity, and error estimation. Illustrative examples of numerical instabilities in the FE solution, of shape and topology optimization, and of fully integrated engineering design optimization processes are also presented. Keywords: engineering design optimization; topology optimization; shape optimization; size optimization; homogenization; finite element method; mesh generation; adaptivity