為了解決在物理問題中面臨偏微分控制方程式之求解，各式計算方法於焉產生。本文引用王永明研究群提出之微分再生核節點法，進行樑、板結構力學行為之應用研究。該法提出新穎的概念來推衍再生核節點法中導函數相應之形狀函數。有別於傳統再生核節點法中對於形狀函數需直接由微分程序求得，本方法建立一組微分再生條件去計算再生核節點法中導函數相應之形狀函數。
文中將根據微分再生核適點法，應用在樑與板的動、靜態分析中，對於該相關一維度及二維度之物理問題，將本法逐點代入其物理域內部之無因次化控制方程與邊界之邊界條件中，進行聯立代數方程式之求解。本分析法所得之數值結果，除與文獻中之解析解進行綜合比較外，對本法應用時適當之影響半徑(a)及基底函數最高階次(n)亦將進一步探討。

A differential reproducing kernel particle (DRKP) method is developed for solving partial differential equations governing a certain physical problem. A novel idea is proposed for determining the shape functions for derivatives of the reproducing kernel (RK) approximants. Contrary to the manipulation in the reproducing kernel particle (RKP) method where the differential operation toward the shape functions of the RK approximants is directly taken, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A point collocation approach based on the present DRKP approximations for multi-dimensional problems is formulated. It is shown from the illustrative examples that the present method indeed is a fully meshless approach with excellent accuracy and fast rate of convergence.

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