This article investigates topology optimization of multi-layer multi-material composite structures under static loading. A moving iso-surface threshold optimization method, previously well defined for single or cellular materials, is extended to multi-layer multi-material structures using a physical response function discrepancy scheme. It is also integrated with an alternating active-phase algorithm as an alternative procedure. The proposed methods are applied to three types of objective functions, namely, minimizing compliance, maximizing mutual strain energy and minimizing full-stress designs. The corresponding response functions relevant to each optimization problem according to the proposed topology optimization methods are strain energy density, mutual strain energy density and von Mises stress, respectively. Examples are presented and compared with those available in the literature to verify the derived formulations on topology optimization for multi-layer multi-material structures. Highlights

Topology optimization is an effective method in the design of acoustic media. This article presents optimization for graded damping materials to minimize sound pressure at a reference point or sound power radiation under harmonic excitation. The Helmholtz integral equation is used to calculate an acoustic field to satisfy the Sommerfeld conditions. The equation of motion is solved using a unit dynamic load method. Formulations for the sound pressure or sound power radiation in an integral form are derived in terms of mutual kinetic and strain energy densities. These integrals lead to novel physical response functions for solving the proposed optimization problem to design graded damping materials. The response function derived for individual frequency is utilized to solve the multi-objective optimization problem of minimizing sound pressure at the reference point for excitations with a range of frequencies. Numerical examples are presented to verify the efficiency of the present formulations.