Computational optimization for porosity-dependent isogeometric analysis of functionally graded sandwich nanoplates

Abstract

A simply and effectively computational optimization for porosity-dependent isogeometric analysis of functionally graded (FG) sandwich nanoplates is proposed for the first time. Porosity-dependent material properties are defined via the modified power law function. The distribution of ceramic volume fraction is approximated by using the multi-patch B-spline basis functions through the thickness direction. This approach ensures smoothly and continuously vary material properties across each layer, and automatically satisfies the C0-continuity at each layer interfaces. To consider length scale effects, the Eringen’s nonlocal elasticity theory is used to model porous FG sandwich nanoplates. Based on a combination of NURBS formulations and four variables refined plate theory, governing equations of the nanoplates are derived and employed to obtain natural frequencies of the porous FG sandwich nanoplates. The present approximation is easy to satisfy the requirement of at least third order derivatives of basis functions in approximate formulations of nanoplates. To save computational costs, an adaptive hybrid evolutionary firefly algorithm is used. Continuous design variables including the thickness of each layer and the ceramic volume fraction at control points are considered for constraint optimization problems. New results are performed and considered as benchmark results for further studies on the porous FG sandwich nanoplates.