Topology optimization of truss-like continuum structures for natural frequencies

A method to maximize the natural frequencies of vibration of truss-like continua with the constraint of material volume is presented. Truss-like is a kind of particular anisotropic continuum, in which there are finite numbers of members with infinitesimal spaces. Structures are analyzed by finite element method. The densities and orientations of members at nodes are taken as design variables. The densities and orientations of members in elements are interpolated by these values at nodes; therefore they vary continuously in design domain. For no intermediate densities being suppressed, there is no numerical instability, such as checkerboard patterns and one-node connected hinges. The natural frequency and its sensitivities of truss-like continuum are derived. Optimization is achieved by the techniques of moving asymptotes and steepest descent. Several numerical examples are provided to demonstrate this optimization method.