Multi-material and Shape Optimization using Meshfree Methods

Heterogeneous objects have shown their high potential in many areas. Appliances, machines, and parts can be seen as a mixture of materials in a continuous or discrete way. The material distribution affects the properties of the objects, so the combination and the density presence of the materials can be designed to achieve high performance of parts at lower costs. Nowadays, manufacturing technologies provide the capability to tailor materials and virtually control the composition locally. For the best results in the optimization process both the material distribution and the shape must be suited for the objectives. Meshfree methods are useful in shape optimization processes because neither the boundary conditions nor the geometry has the restriction of such a mesh process in each optimization step. A Mesh free method such us the R-function method (RFM) does not use a costly discretization process and incorporates the boundary conditions of the problem in an analytical form.  We use a geometric representation constructed with R-functions to model the material distribution.  In this way the material distribution can be viewed as a shape optimization problem. We study a heat sink fin made of aluminum and copper to optimize the shape of the fin itself and the geometry that represents the material distribution. In our work, the shape optimization process effectively optimizes the geometry that controls the material distribution and the proper geometry of the part itself in order to maximize the performance at the lowest cost.