Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach

A new isogeometrical procedure for optimization of material composition of functionally graded structures in thermo-mechanical processes is introduced. The proposed method employs a generalized form of the standard isogeometric analysis method, allowing for gradation of material properties through patches. The variations of material properties are captured in a fully isogeometric formulation using the same NURBS basis functions employed for construction of the geometry and approximation of the solution. Subsequently, the applicates of control points that define the surfaces of volume fractions of the constituents are considered as the design variables and obtained by solving the optimization problem using a mathematical programming algorithm. Some numerical examples under thermal and mechanical loadings are considered to demonstrate the performance and applicability of the proposed method. Comparison of the obtained results with those of the other existing approaches such as finite elements and meshfree methods verifies the presented results. It will be seen that the proposed procedure considerably removes the difficulties of the existing methods and provides a promising tool for material design of functionally graded structures.