Maximization of structural natural frequency with optimal support layout

The optimal layout of supports is one of the key factors that dominates static and dynamic performances of the structure. In this work, supports are considered as elastic springs. The purpose is to carry out layout optimization of supports by means of topology optimization method. The technique of pseudo-density variables that transforms a discrete-variable problem into a continuous one is used in order that the problem is easily formulated and solved numerically. In this formulation, a power law of the so-called solid isotropic material with penalty model is employed to approximate the relation between the element stiffness matrix and density variable. Such a relation makes it easy to establish the computing scheme and sensitivity analysis of natural frequency. Support layout design that corresponds to optimization of boundary conditions is studied to maximize the natural frequency of structures. Numerical results show that reasonable distributions of supports can be generated effectively.