Date: Friday, December 5, 2003
Time: 3:30 p.m.
Place: W129 Nebraska Hall
We study numerical methods for generating optimal shapes for thermal systems working under conductive and convective conditions. The focus is on problems that require large shape changes from a simple geometry to a complex 2D shape. FEM when applied to problems involving large shape changes requires re-meshing for every new domain. Re-meshing the domain results in loss of accuracy and therefore, meshfree methods are used for solving shape optimization problems. Previous attempts on shape optimization problems using meshfree methods treated node motion in one direction. There are difficulties when the general 2D motion of nodes is considered.
A meshfree method that allows general motion of nodes for shape optimization of thermal systems is investigated. Initially, a meshfree method based on nodal integration is used to solve the PDE’s in the shape optimization problem. We develop the formulation of nodal integration for thermal problem under steady state conditions. This meshfree method needs a representative domain to calculate the domain integration of the weak form. We discuss the complications involved in building a representative domain for highly non-convex shapes. Gradient-based methods are used to solve the optimization problem. Shape sensitivity analysis is crucial in solving the optimization problem when using the gradient-based methods. The Material Derivative Approach and the Fixed Grid method are the methods used to formulate the shape sensitivity problem. We next present the Fixed Grid method in the Element-Free Galerkin (EFG) method for shape optimization.
The Fixed Grid method is used to formulate the shape optimization problem. We consider node-motion of design variables in one-direction and compare the results of the Fixed Grid method with the Material Derivative approach. We show how the Fixed Grid method in the EFG method can be used to produce shapes that improve the objective function value.
