Optimal material distribution for heat conduction of FGM based on meshless weighted least-square method

A numerical procedure is presented to determine the optimal material distribution of functionally graded material (FGM) for heat conduction problem. The material volume fractions are used as primary design variables and material properties are assumed to be temperature independent. The purpose is to minimize the difference between the actual values of a field variable and a desired target field with given initial and boundary conditions for transient problem. Examples are solved numerically for given boundary conditions and objective functions using meshless weighted least-square (MWLS) method. A discrete function is employed in the MWLS method to construct a set of linear equation, which avoids the burdensome task of numerical integration and leads to a pure meshless analysis for FGM. The presented optimization method, through the numerical experiments, is found to provide optimal volume fraction distributions that minimize objective function, as well as the rapid and stable convergence.