Topology optimization of nonlinear structures with damping under arbitrary dynamic loading

This study presents an extended unit load method in which the displacement of a chosen degree of freedom (DOF) in a nonlinear structure under arbitrary dynamic loading is expressed as an integration of mutual strain energy density over a continuum domain. This new integral formulation for the displacement of a chosen DOF is developed by using the virtual work principle and can be used for linear or nonlinear structural behaviours. The integral form of the displacement is then used to develop new formulations for structural topology optimization involving arbitrary dynamic loading using the moving iso-surface threshold (MIST) method. Presented are two specific topology optimization problems with two objective functions: (a) to minimize the peak of a chosen displacement; or (b) to minimize the average power spectral density (PSD) of the chosen displacement over a finite time interval. New MIST formulations and algorithms are developed for solving two damping topology optimization problems of a structure under arbitrary dynamic loading, with or without large displacements, and having cellular damping materials with multi-volume fractions. Several numerical examples are presented to demonstrate the validity and efficiency of the presented unit load method and the MIST formulations and algorithms.