以無網格法進行壓電材料梁之模擬與分析

ANALYSIS AND SIMULATION OF THE PIEZOELECTRIC CANTILEVER BEAM USIMG MESHFREE METHODS

10.6652/JoCICHE.202406_36(4).0001

楊益(Yi Yang)；林冠中(Kuan-Chung Lin)

無網格法 ； 壓電材料 ； 節點積分法 ； 精確性 ； meshfree method ； piezoelectric material ； direct nodal integration ； accuracy

中國土木水利工程學刊

36卷4期（2024 / 06 / 01）

319 - 327

繁體中文;英文

本研究將以有限元素法（Finite element method, FEM）與無網格法之再生核質點法（Reproducing kernel particle method, RKPM）模擬壓電材料梁僅受電場作用下的位移及電場變化。在無網格法中將使用不同的積分方法，如高斯積分法（Gauss integration, GI）、直接節點積分法（Direct nodal integration, DNI）和穩定一致節點積分法（Stable conforming nodal integration, SCNI）得到穩定且精確之數值結果。並將三種方法求出的數值解與解析解做比較，找出無網格法中的最佳近似解。研究結果顯示無網格法使用上述三種數值積分方法其數值解均穩定且收斂，而且計算效率優於有限元素法，未來可用於模擬降噪協助精密產業製程。

In this research, two numerical methods, the finite element method (FEM) and the reproducing kernel particle method (RKPM), are used to simulate the displacement and electric field action of the piezoelectric cantilever beam under the change of the electric field. Different integration methods in the RKPM, such as gauss integration, direct nodal integration (DNI), and stable conforming nodal integration (SCNI) are used to analyze stable and accurate numerical issues. The numerical solutions obtained by the three methods and FEM are compared with the analytical solutions. The research results show that the numerical solutions of the RKPM are stable and accurate obtained from these three numerical integration methods, and the computational efficiency is better than that of the finite element method. It can be used for noise reduction simulation in the precision industry in the future.