Optimization Concepts and Applications in Engineering

Introduction

Finite elements is a well known tool for analysis of structures. If we are given a structure, such as an airplane wing, a building frame, a machine component, etc., together with loads and boundary conditions, then finite elements can be used to determine the deformations and stresses in the structure. Finite elements can also be applied to analyze dynamic response, heat conduction, fluid flow, and other phenomena. Mathematically, it may be viewed as a numerical tool to analyze problems governed by partial differential equations describing the behavior of the system. Lucien Schmit in 1960 recognized the potential for combining optimization techniques in structural design [Schmit 1960]. Today, various commercial finite element packages have started to include some optimization capability in their codes. In the aircraft community, where weight and performance is a premium, special codes combining analysis and optimization have been developed. Some of the commercial codes are listed at the end of Chapter 1. The methodology discussed in this chapter assumes that a discretized finite element (or a boundary element) model exists. This is in contrast with classical approaches to optimization of structures that directly work with the differential equations governing equilibrium and aim for an analytical solution to the optimization problem.