Variational Methods in Structural Optimization

Synonyms

Optimization of structures

Definitions

In structural optimization, the variational methods play a unique role. They enable formulation of a large class of problems in which structural design variables, state variables, and local and global constraints imposed to them are considered and the extremum of a functional representing a quality of considered structure is searched for. The constraints are usually attached to the objective functional by means of Lagrange multipliers. This approach enables consideration of problems of different nature and multidisciplinary optimization. In this entry, the fundamental idea of variational formulation is explained and illustrated by the classic example of beam shape optimization.

Introduction

Optimization has existed since human consciousness emerged and in a sense even longer because one can expect that nature somehow optimizes its actions. But contemporary concept of structural and multidisciplinary optimization has gained a lasting place...