STATIC AND VIBRATIONAL SHAPE AND TOPOLOGY OPTIMIZATION USING HOMOGENIZATION AND MATHEMATICAL-PROGRAMMING

The homogenization method together with mathematical optimization conc epts were combined to perform two-dimensional shape and topology optim ization of structures under volume constraint. Static, as well as sing le or multi-eigenvalue vibrational optimization of structures are cons idered. The basic assumption of the method is that the structure under consideration is formed by the spatial repetition of a non-homogeneou s microstructure, composed of solid material and void regions. The met hod, upon convergence, allocates material or voids at different parts of the structure and thus, an optimum shape is achieved. A detailed st udy was made to assess the effect of various microstructural models on the final optimum shape. Good convergence characteristics were obtain ed for all examples considered. Comparison of the algorithm with publi shed results using the optimality criteria method was attempted and si milarities and differences are discussed. The results show that the pr oposed method can perform accurate static and vibrational optimization . Furthermore, its generality allows the implementation of more than o ne constraint in a straightforward manner, a very important feature fo r the design engineer.