Estudo da maximização da frequência de treliças com massa não estrutural

Abstract

This work study the problem of maximizing the fundamental frequency of trusses and the effect of including a non structural mass. The problem of maximizing the natural frequencies of structures is important for mechanical engineering applications, however, the optimization model has difficult technical issues when some structural element is removed (topology optimization). Fortunately, there exists theoretical results that transforms the original problem in a semidefinite optimization model. In this sense, the present work shows the mathematics to define the semidefinite model for the maximum eigenfrequency problem. To solve that problem numerically, the Feasible Arc Interior Point Algorithm (FAIPA-SDP) is employed. Some numerical examples are solve with this algorithm. Those numerical examples shows that FAIPA-SDP solve the optimization problems. Those results also confirm all the theoretical properties presented in this work.