A Differential Reproducing Kernel Particle Method for the Analysis of Multilayered Elastic and Piezoelectric Plates
Chih-Ping Wu; Kuan-Hao Chiu and Yun-Ming Wang

doi:10.3970/cmes.2008.027.163
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 27, No. 3, pp. 163-186, 2008
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Keywords Meshless methods, Reproducing kernels, Point collocation, Piezoelectric plates, Static, Bending.
Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, the Euler-Lagrange equations of three-dimensional piezoelectricity and the possible boundary conditions are derived. A point collocation method based on the present DRKP approximations is formulated for the static analysis of simply supported, multilayered elastic and piezoelectric plates under electro-mechanical loads. It is shown that the present DRKP method indeed is a fully meshless approach with excellent accuracy and fast convergence rate.
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