Topology Optimization of Frame Bracing System for Natural Frequency

Abstract

A method to optimize the topology of frame bracing system is presented. Firstly frame is filled by truss-like continuum uniformly. The truss-like continuum simulates the distributive bracing system. The frame combined with truss-like continuum is analyzed by finite element method. The densities and orientations of bracing system at nodes are taken as design variables. The distribution field of bracing system is optimized by the method of moving asymptotes (MMA) and the method of steepest descent. The frame bracing system is established according to the optimal distribution field of bracing system. The natural frequency of optimal braced frame increases to more than two times while material increases only 5%. For no intermediate densities being suppressed, there is no numerical instability, such as checkerboard patterns and one-node connected hinges. The expression of natural frequency and its sensitivities of truss-like continuum are derived.