Evolutionary Structural Optimization Based on Vibration Criteria

A simple evolutionary procedure is proposed for shape and layout optimization of structures with frequency constraints. The structure is modelled with a fine mesh of finite elements plus boundary conditions. It is considered the following hypothesis: small displacements and strains, homogenous and isotropic material. After each eigenvalue solution, a sensitivity number is determined for each element of the structure, so based in this parameter, a number of the elements are removed from the structure. The frequencies of the resulting structure will be shifted towards a desired direction. Several examples are presented to illustrate the options of changing structural frequencies such as: maximizing one or more frequencies simultaneously, maximizing the gap of arbitrary two frequencies