Topology optimization employing a condensation method for nonlinear structural frames with supplemental mass

A topology optimization schema employing a condensation method for nonlinear frame structures with supplemental mass subjected to time-varying excitation is presented. In the context of the design of structural frames, in certain applications, the supplemental mass can be order(s) of magnitude larger than the mass of the system itself. Thus, condensing the system of governing equations to only those associated with the supplemental mass, reduces the complexity and computational cost of the dynamic analysis and thus the optimization process. In addition to considering material nonlinearity, distributed plasticity, and multiaxial interactions, the hysteretic beam finite element (FE) model employed in this study has constant elastic stiffness and hysteretic matrices facilitating a Guyan-type condensation of the nonlinear dynamic equations. Furthermore, the nonlinear dynamic equations and element evolution equations of hysteretic FE modeling are concisely presented as a system of first-order nonlinear ordinary differential equations (ODEs) that can be solved using general ODE solvers. The schema is demonstrated on various design problems considering different arrangements of supplemental mass, where the objective is to minimize the volume of the structure subject to maximum displacement constraint using a single p-norm.