Fundamentals on the Topological Derivative concept and its classical applications

Abstract

The concept of the topological derivative has been derived for several engineering problems during the last years. In this chapter, the fundamentals and the resulting closed formulae of topological derivative for some of the most classical problems are addressed. A brief review of the mathematical statements used in the topological derivative concept is given. The programming strategies regarding implementing the main routine for the topology optimization are pointed out. Some numerical examples concerning classical applications are introduced to demonstrate the application of the topological derivative concept for topology problems.