Layout Optimization of Structures with Finite-size Features using Multiresolution Analysis

A scheme for layout optimization in structures with multiple finite-sized heterogeneities is presented. Multiresolution analysis is used to compute reduced operators (stiffness matrices) representing the elastic behavior of material distributions with heterogeneities of sizes that are comparable to the size of the structure. Two approaches for computing the reduced operators are presented: one based on a multiresolution analysis of displacements and the other based on a multiresolution analysis of a function representing the material distribution. Numerical examples using the mean compliance as the objective function are presented to illustrate the method.