本研究應用無網格節點積分方法，對智慧材料壓電材料及電磁彈性體，進行靜態載重分析。研究中使用再生核質點法(Reproducing Kernel Particle Method, RKPM)建構形狀函數，並採用穩定一致節點積分法(Stabilized conforming nodal integration, SCNI)進行數值積分，若結果產生震盪或誤差，則使用自然穩定節點積分法(Naturally stabilized nodal integration, NSNI)進行修正。本研究專注於壓電材料和電磁彈性體，兩種材料皆屬於智慧材料，具有物理場相互轉換的耦合特性，分析智慧材料主要由能量形式出發，並利用最小勢能原理做推導，最後成功使用無網格法進行數值分析。經數值例題測試，從壓電材料與電磁彈性體的數值分析結果可知，NSNI修正方法均能有效改善SCNI方法的計算結果，使其更接近有限元素法的數值，並改善震盪的情況。在固定梁與集中載重條件下，該方法表現尤為出色。本研究成功將無網格法節點積分法應用於物理多重耦合問題的有效分析，為相關領域提供了一個新的解決方案。

This study applies meshfree nodal integration methods to perform static load analysis on smart materials, including piezoelectric materials and magneto-elastic materials. The Reproducing Kernel Particle Method (RKPM) is used to construct shape functions, and Stabilized Conforming Nodal Integration (SCNI) is employed for numerical integration. If oscillations or errors occur in the results, Naturally Stabilized Nodal Integration (NSNI) is applied for correction. This research focuses on piezoelectric materials and magnetoelastic materials, both of which are smart materials with coupling characteristics enabling conversion between physical fields. The analysis of smart materials is primarily based on energy forms and derived using the minimum potential energy principle, successfully utilizing meshfree methods for numerical analysis.
Through numerical example tests, the results of the numerical analysis of piezoelectric materials and magneto-elastic materials show that the NSNI correction method can effectively improve the calculation results of the SCNI method, making them closer to the values obtained using the Finite Element Method and improving oscillations. The method performs exceptionally well under fixed beam and concentrated load conditions. This study successfully applies meshfree nodal integration methods to eectively analyze multi-physics coupling problems, providing a new solution for related fields.

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