An efficient design sensitivity analysis using element energies for topology optimization of a frequency response problem

In this study, an efficient design sensitivity analysis (DSA) method is proposed for topology optimization of a frequency response problem. DSA of frequency response is an essential procedure for gradient-based topology optimization, which is used for noise and vibration control of structures. Traditionally, DSA of frequency response requires internal information concerning the finite element analysis (FEA) codes, such as stiffness and mass matrices, element formulation, and coordinate transformation. However, to obtain internal information on the general commercial FEA codes (e.g., MSC.NASTRAN, ANSYS, and ABAQUS), a substantial understanding of the codes and additional post-processing work is required. Furthermore, to handle modeling options (e.g., warping and offset) of complex three-dimensional (3D) built-up structures (e.g., automobile, ship, or airplane), a complicated coordinate transformation is additionally needed. In this paper, to overcome these difficulties, element energy-based DSA of a frequency response is developed using the polarization identity. In comparison with traditional DSA, the developed method is easy and efficient in terms of implementation effort because it requires only simple algebraic computations of element energies provided by commercial FEA codes. To demonstrate the validity and efficiency of the developed method, several numerical examples are solved with the commercial FEA code MSC.NASTRAN.