Análise de Sensibilidade na Optimização Topológica

Abstract

The Topogical Gradient is a function which provides the sensibility of the problem defined in a certain domain when a small hole in a given position is created. This concept is a powerful tool to obtain the optimal topology for a big class of engineering problems. The most important limitation in this methodology is that, when a hole is created, it is impossible to establish a homeomorfism between the involved spaces.
Then, it is necessary to develop some specific mathematical tools to obtain the gradients.
In this work we introduce an alternative form to get the Topological Gradient based on Sensibility Analisis concepts. With this methodology we can use the mathematical procedures developed in the context of shape optimization to calculate the Topological Gradient. In this way, the optimal topology is obtained, which is a much simpler and constructive method than the ones existing in the literature.