An isogeometric multimesh design approach for size and shape optimization of multidirectional functionally graded plates

This article firstly presents a novel numerical methodology to concurrently optimize material distribution (size) and thickness variation (shape) of multidirectional functionally graded (MFG) plates under free vibration within the isogeometric analysis (IGA) framework. An isogeometric multimesh design (IMD) approach is proposed to generate two distinct non-uniform rational B-spline (NURBS) surfaces via the k-refinement strategy. A finer analysis one relied upon a combination of the IGA and a generalized shear deformation theory (GSDT) is utilized for the unknown solution approximation in finite element analyses (FEAs). Whilst the other coarser design one is employed for the exact geometry representation as well as the optimal material and thickness depiction. Size and shape design variables are in turn the ceramic volume fraction and z-axis coordinate of the top side of the MFG plate coincidentally assigned to each of control points on this surface. Flexibly utilizing such two surfaces helps diminish a large number of design variables and considerably save the computational cost in optimization problems, yet still appropriately manifesting optimal material and thickness profiles. Additionally, this definition accurately simulates mechanical behavior of MFG plates in analysis ones as well. A recently developed derivative-free adaptive hybrid evolutionary firefly algorithm (AHEFA) is used to solve constrained frequency maximization problems. Several numerical examples are executed to verify the effectiveness and robustness of the present paradigm. (C) 2018 Published by Elsevier B.V.