Otimização Paramétrica De Estruturas Treliçadas Sob a Ação De Cargas Dinâmicas Utilizando O Método Do Carregamento Estático Equivalente

Abstract

Structural optimization subject to dynamic loading is a challenging problem in many aspects, starting with the large number of constraints that must be respected at all instants of time. Furthermore, the computational cost to evaluate the gradients of these constraints is significantly high and requires a large storage space. In the literature, some methods reduce the number of constraints evaluating at selected instants of time, such as the worst case. Alternatively, a single equivalent functional is constructed to eliminate the time dependence by integrating the violated constraints over time. In this work, the Equivalent Static Load (ESL) method is used, in which the original dynamic problem is reduced into a number of static linear optimization problems with multiple load cases. An attractive feature of this method is the possibility of solving non-linear problems, avoiding the high cost due to repeated structural analyzes and constraint calculations. Classical problems of plane trusses subjected to dynamic loads are solved using the ESL method. The function to be minimized is the truss mass, which is subjected to stress and displacement constraints, where the design variables are the cross-sectional areas of the members. In addition, an interface using ANSYS ® and MATLAB ® was developed for a modular approach, in which finite element analysis and optimization can be performed separately. This process makes possible the optimization of structures that present non-linear behavior from the use of most structural analysis software packages available on the market.