Otimização topológica simultânea à localização de atuadores em estruturas

Abstract

This work develops a general and integrative methodology to the simultaneous project for topology optimization and actuators placement in structures. Two problems are addressed: one considers proportional actuators and the other considers piezoelectric actuators. The topology optimization considers three material phases: two made of solid materials while the other is empty. A project variable is considered for each solid phase. One of these solid materials is reserved for the purely structural part while the other is intended to represent the most favorable regions of the structure for actuators placement. In both problems, the control is static and the topology optimization is intended to minimize the compliance. The sensitivity analysis is developed to obtain the equilibrium equations and the derivatives of the objective function with respect to the project variables to each problem. To obtain numerical results, the structural models were discretized in finite elements and an appropriate algorithm was implemented in Matlabr. The numerical simulations show that the methodology used in this work can produce a well-defined structural topology indicating the best position for actuators. Finally, it is worth emphasizing the results obtained perfectly agree with other ones obtained through simpler procedures, which perform topology optimization and control in a non-simultaneous process.