Multi-patch isogeometric material optimization of bi-directional functionally graded plates

This study investigates an effective design methodology for the optimal material distribution of bi-directional functionally graded plates (2D-FGPs) with complex shape. In mechanical analysis, a multi-patch isogeometric method is used to analyze the statics of 2D-FGP, which is based on the third-order shear deformation theory and Nitsche’s technology. This method can effectively avoid the use of duplicate nodes in the parameterization of IGA for complex shapes to obtain C1-continuity of 2D-FGPs. In the optimal design problem, we have constructed a rectangular material design mesh (RMDM) based on the shape of 2D-FGPs, which can map the material distribution on the surface of plate to achieve the implementation of the optimization process. This two-dimensional B-spline control points of RMDM are set as the design variable with mass reduction and the first-order natural frequency maximization as optimization objectives, and limited arbitrary deflection as constraint conditions. In addition, an improved multi-objective particle swarm optimization algorithm (IMOPSO) is used to obtain a series of Pareto optimization solutions that meet the needs of the designer. The validity and applicability of this innovative combination of multi-patch isogeometric analysis and IMOPSO are demonstrated through several numerical examples in integrated design. This approach further accomplishes the numerical unified CAD/CAE optimization design of 2D-FGPs across multiple non-smooth boundaries.