本文應用微分再生核(DRKP)方法於簡支承多層疊合彈性與壓電材料板之靜力分析。有別於傳統文獻中之再生核方法，直接以近似形狀函數進行微分運算來獲得導函數相應之形狀函數；DRKP方法則以基底函數微分再生條件來決定高階導函數之形狀函數。本文應用廣義Hellinger-Reissner能量穩值原理，經由變分推衍程序獲得三維電彈力學Euler-Lagrange方程式和可能的邊界條件。依據DRKP適點方法，求解簡支承多層疊合彈性或壓電材料板受電場和彈性場外載重作用下的靜力行為。結果顯示DRKP方法是一種十分精準並且快速收歛的無網格方法。

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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