Topology design optimization of structures at high frequencies using power flow analysis

A density–based topology optimization method is developed for power flow problems in steady state using an adjoint design sensitivity analysis (DSA) method. Design variables such as Young's modulus, density, and damping factor are parameterized using a bulk material density function. A generalized compliance of structures, defined as the inner product of prescribed loading and response function, is selected as an objective function. The objective is to minimize the generalized compliance within allowable material volume. Since already factorized system matrix obtained from the power flow analysis is utilized to evaluate the adjoint response and sensitivity, computational cost for the DSA is trivial. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity, requiring only 0.15% of CPU cost for finite difference sensitivity. Also, it turns out that the developed method can yield an optimal structural layout to transmit the vibrational power effectively.