Shape and size optimization of functionally graded sandwich plates using isogeometric analysis and adaptive hybrid evolutionary firefly algorithm

The paper presents an effective methodology for modeling and simultaneously optimizing the layer thicknesses (shape) and the ceramic volume fraction distribution (size) of functionally graded (FG) sandwich plates under free vibration in the framework of isogeometric analysis (IGA). The multi-patch B-spline basis functions separately defined in each of the layer thicknesses are used to represent the ceramic volume fraction distribution. Accordingly, the C0− continuity at layer interfaces can be naturally satisfied without any additional conditions. Furthermore, this multi-patch B-spline representation still ensures the continuously and smoothly varying material properties across each layer thickness. The effective material properties are then estimated by either the rule of mixture or the Mori-Tanaka scheme. A non-uniform rational B-splines (NURBS)-based isogeometric finite element model associated with the third-order shear deformation theory (TSDT) is utilized for the plate free vibration analysis. A recently developed adaptive hybrid evolutionary firefly algorithm (AHEFA) with the improvement on the convergence speed and the solution accuracy is employed as an optimizer. Design variables are the layer thicknesses and the ceramic volume fractions at control points located in the thickness direction. Several numerical examples of two types of optimization problems of the FG sandwich plates, including (i) the first natural frequency maximization with volume constraints, and (ii) mass minimization with frequency constraints, are presented to illustrate the effectiveness and reliability of the proposed method.