Shape preserving design with topology optimization for structures under harmonic resonance responses

For a structural system composed of functional components in a vibration environment, it is of great importance to suppress the dynamic warping deformation of these local regions to ensure the performance and functionality of the system. Especially for a vibrating structure under a resonance response with critical deformations, such dynamic shape preserving design (SPD) problem is addressed to maintain local performances using topology optimization in this paper. The structure is assumed to be linear and elastic, with Rayleigh damping, and subjected to a time-harmonic external excitation with a resonant frequency. The elastic work describing the maximum strain energy in a vibration period is defined to quantitatively measure the extreme warping deformation of local functional components. A normalized constraint on local elastic work is further introduced into a dynamical topology optimization model while maximizing the first-order eigenfrequency. Moreover, to preserve the outlines of void regions (e.g., openings), a dynamic artificial weak element (AWE^dyn) technique is proposed to help measure and suppress the local deformation of voids. Numerical tests show that the dynamic elastic work could accurately describe the deformations of resonance structures. The effects of shape preservation are successfully achieved through topology optimization by suppressing warping deformations in subdomains.