SIMP-Based Dynamic Topological Optimum depending on Maximum Eigenfrequency for Reinforcement of Concrete Beams

Abstract

Computer aided topology optimization design is a relatively new but rapidly expanding area of structural mechanics. Topology optimization design is used in an increasing rate by for example building and bridge engineering as well as the car, machine and aerospace industries. The reason for this is that it often achieves great savings and design improvements by solving the basic engineering problem of distributing a limited amount of material in a design space, in which a certain objective function has to be optimized. In static problems a common objective is to minimize the compliance such as strain energy and in dynamic problems the first natural eigenfrequency is often maximized in order to evaluate the stiffest structures. The goal of this study is to get a wide use for structural designs in the topology optimization. Therefore with respect to SIMP dynamic topology optimization problems are treated in comparisons with static problems in this research. For the topology optimization problems implemented algorithms can be the optimality criteria method and the method of moving asymptotes (MMA). Numerical applications topologically maximizing the first natural eigenfrequency or minimizing strain energy of plates verify the generality and wide use of topology optimization with respect to structural designs.