Nonlinear dynamic response topology optimization using the equivalent static loads method

Abstract

Many structures in the real world show nonlinear responses under dynamic loads. Although nonlinear dynamic response optimization is required, it is difficult to consider the nonlinearities and dynamic effect simultaneously in topology optimization. In the conventional element density based topology optimization considering nonlinearities, low-density elements cause numerical problems due to extreme mesh distortion. And the responses in the time domain must be considered as an objective or constraint function. A method is proposed for nonlinear dynamic response topology optimization using the equivalent static loads method for non linear static response structural optimization (ESLSO). Equivalent static loads are linear static loads which generate the same displacement field by nonlinear dynamic analysis. The paradigm of the method was originally developed for size and shape optimization. In this research, a new algorithm is proposed for topology optimization considering nonlinear dynamic behavior by modifying the existing ESLSO. The new ESLSO can overcome the difficulty which may occur in topology optimization considering nonlinearities. A new objective function is defined for topology optimization in the time domain. The developed method is verified by solving some problems and the results are discussed. © 2012 by the American Institute of Aeronautics and Astronautics, Inc.