Optimal design of MR sandwich plates using a level set based topology optimization method

Abstract

This paper proposes a level set based topology optimization method for finding optimal layout of the magneto-rheological (MR) fluid layer in an MR sandwich plate such that the vibration characteristics of the plate be improved. For this purpose, we consider the eigenfrequency and the loss factor as objective functions that should be maximized. The storage and loss modulus of the MR fluid are assumed to be magnetic field and frequency dependent. A finite element model utilizing the Mindlin plate theory is developed to derive the governing equations of motion. The topological derivative of the Lagrangian is computed at a certain point by measuring the influence of removing element on the Lagrangian and then applied to an evolutionary equation to update the level set function. In this study, we employ a density filter to regularize the continuity of the resulting level set function and consequently the complexity of the optimal configuration. Finally, several examples are presented to confirm the validity and efficiency of the method.