Maximum Eigenfrequency-Based Dynamic Optimization Design for Topologically Reinforcing Concrete Deep Beams

Abstract

The goal of this study is to numerically compare solutions and algorithms determined by element- and node-wise topology optimization designs for dynamic free vibration-resistance structures. As another version in the fields of topology optimization methods, the study supports the node-based optimization rather than the classical element-based optimization comparing two methods. The terms element-and node-wise denote the usage of element and node density as design parameter, respectively. For static problems solution comparisons of the two types for SIMP topology optimization designs have already been introduced by the author⁽¹⁾. For dynamic topology optimization problems the objective is in general related to maximum eigenfrequency optimization subject to a given material limit since structures with a high fundamental frequency tends to be reasonable stiff for static loads. For dynamic problems SIMP material is used in this study and an implemented optimization method is the method of moving asymptotes (MMA). Numerical applications topologically maximizing the first natural eigenfrequency for dynamic concrete deep beam designs depending on element or node density verify differences of solutions and algorithms between dynamic element- and node-wise topology optimum designs.