Optimal design of FG sandwich nanoplates using size-dependent isogeometric analysis

In this study, an effectively computational optimization approach for size-dependent isogeometric analysis of functionally graded (FG) sandwich nanoplates is proposed. The multi-patch B-spline basis functions through the thickness direction are employed to approximate distributions of ceramic volume fraction. This approach smoothly and continuously ensures the distributions of ceramic volume fraction across each layer, and automatically satisfies the C0-continuity at each layer interface. The material properties based on both Mori-Tanaka scheme and the rule of mixture are implemented. To capture the size effects, the Eringen's nonlocal elasticity is used. Governing equations are then derived and a combination of the NURBS formulation and four variables refined plate theory (RPT) are employed to analyze natural frequencies of the FG sandwich nanoplates. Thanks to continuous higher-order derivatives of NURBS basis functions, the present approximation is easy to satisfy the requirement of C2-continuity of the FG sandwich nanoplates. An adaptive hybrid evolutionary firefly algorithm with fast convergence speed and less computational cost is used as an optimizer. The ceramic volume fraction across the z-direction at control points and the thickness of each layer are considered as continuous design variables. Numerical examples for free vibration and optimization analyses of the FG sandwich nanoplates are examined. Several new results are obtained and considered as benchmark problems for further studies on the FG sandwich nanoplates.