A Mesh-Free DRK-Based Collocation Method for the Coupled Analysis of Functionally Graded Magneto-Electro-Elastic Shells and Plates
Chih-Ping Wu; Kuan-Hao Chiu; and Yung-Ming Wang

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 35, No. 3, pp. 181-214, 2008
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Keywords Mesh-free methods, Collocation methods, DRK approximants, Coupled magneto-electro-elastic effects, FG material, Static, Shells, Plates.
Abstract A mesh-free collocation method based on differential reproducing kernel (DRK) approximations is developed for the three-dimensional (3D) analysis of simply-supported, doubly curved functionally graded (FG) magneto-electro-elastic shells under the mechanical load, electric displacement and magnetic flux. The material properties of FG shells are firstly regarded as heterogeneous through the thickness coordinate and then specified to obey an identical power-law distribution of the volume fractions of the constituents. The novelty of the present DRK-based collocation method is that the shape functions of derivatives of reproducing kernel (RK) approximants are determined using a set of differential reproducing conditions without directly taking the differentiation towards the RK approximants. That prevents from the complicated calculations on the determination of the derivatives of RK approximants in the conventional RK methods. The present formulation is derived using the orthogonal curvilinear coordinates of doubly curved shells and can be reduced to the formulation of plates by letting the curvature radii be an infinite value. In the implementation of the present DRK-based collocation method, several crucial parameters such as the optimal support size and highest-order of the basis functions are discussed. The influence of the power-law exponent on the magnetic, electric and mechanical variables induced in the FG shells is studied.
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