Material optimization of tri-directional functionally graded plates by using deep neural network and isogeometric multimesh design approach

• Published in: Applied Mathematical Modelling Vol. 87; pp. 501 - 533
• Main Authors: Do, Dieu T.T., Nguyen-Xuan, H., Lee, Jaehong
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.11.2020; Elsevier BV
• Subjects: Algorithms; Artificial neural networks; Basis functions; Computational efficiency; Computing costs; Cost analysis; Deep neural network; Design optimization; Eigenvalue problem; Finite element method; Free vibration; Functionally gradient materials; Isogeometric analysis; Modified symbiotic organisms search; Multi-directional functionally graded plates; Neural networks; Plates; Shear deformation; Two dimensional analysis; Isogeometric analysis; Deep neural network; Eigenvalue problem; Multi-directional functionally graded plates; Modified symbiotic organisms search
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.06.002

•2D behaviors of multi-directional FG plates are analyzed by using GSDT and IGA.•NURBS function describes material distribution in all three directions of FG plates.•Deep neural network is utilized to directly predict behaviors of the FG plates.•Optimal material distributions of tri-directional FG plates are found.•An isogeometric multimesh design is used to save significant computational cost. The paper is aimed at enhancing computational performance for optimizing the material distribution of tri-directional functionally graded (FG) plates. We exploit advantages of using a non-uniform rational B-spline (NURBS) basis function for describing material distribution varying through all three directions of functionally graded (FG) plates. Two-dimensional free vibration and buckling behaviors of multi-directional (1D, 2D and 3D) FG plates analyzed by using a combination of generalized shear deformation theory (GSDT) and isogeometric analysis (IGA) is first proposed. This approach can help to save a significant amount of computational cost while still ensure the accuracy of the solutions. The effectiveness and reliability of the present method are demonstrated by comparing it to other methods in the literature. The obtained results are in excellent agreement with the reference ones. More importantly, data sets consisting of input-output pairs are randomly generated from the analysis process through iterations for the training process in deep neural networks (DNN). DNN is utilized as an analysis tool to supplant finite element analysis to reduce computational cost. By using DNN, behaviors of the multi-directional FG plates are directly predicted from those material distributions. Optimal material distributions of tri-directional FG plates under free vibration or compression in various volume fraction constraints are found by using modified symbiotic organisms search (mSOS) algorithm for the first time. Moreover, an isogeometric multimesh design technique is also used to diminish a large number of design variables in optimization. Optimal results obtained by DNN are compared with those of IGA to verify the effectiveness of the proposed method.