Title

移動Trefftz近似法在二維彈性力學問題分析之應用

Translated Titles

Analysis of Two Dimensional Elasticity by the Moving Trefftz Method

Authors

楊立禎

Key Words

無元素法 ; Trefftz法 ; H-R變分原理 ; 二維彈性力學 ; Meshless Method ; Trefftz Method ; Hellinger-Reissner Variational principle ; Two-dimensional Elasticity

PublicationName

成功大學土木工程學系學位論文

Volume or Term/Year and Month of Publication

2018年

Academic Degree Category

碩士

Advisor

王永明

Content Language

繁體中文

Chinese Abstract

本文採用移動Trefftz近似法式結合了無元素法之移動近似及邊界積分法中Trefftz法滿足微分方程求解基底。在本文利用H-R變分原理求得平衡方程式及基底函數配合邊界條件計算求得變數。 文中分析懸臂梁受剪力、簡支梁受均部荷重、無限板中央裂縫受拉力及無限板中央開孔受拉力等二維彈性力學問題,並且透過不同的佈點方式及不同的基底階數分析配合解析解分析其結果精度及誤差收斂性,驗證此法的可靠性及可行性。 分析算例後,在利用均勻佈點方式,隨著節點數越多,可有良好的精確性及收斂性,若有應力集中現象,會隨著佈點間距越小,越明顯。均勻佈點與隨機佈點兩者經度相差不大,驗證了本文所使用的方法受到佈點方式之影響不大,並且從誤差表中可發現位移及應力之精確度相近,與一般數值方法中位移精確度往往大於應力精度相比較,本文之數值方法在應力分析上更為精準。 總結以上幾點結論,本文之移動Trefftz 近似法,在分析二維彈性力學之問題上皆能得到良好的結果精度,為穩定及具有實用性之數值模擬方法。

English Abstract

In this thesis, we use the moving Trefftz method to analyze the two dimensional elasticity problems. The method is combined with the meshless method and the Trefftz method in the boundary integral equation to satisfy the differential equation. In this paper, the modified H-R variational principle is used to obtain the integral equation relative to the boundary conditions. Using the bases that satisfy the equilibrium equation and by the moving approximation techniques, the numerical solution can be obtained. Using this method, we simulate a cantilever beam loaded by the shear force, a simply support beam loaded by the uniform load, an infinite plate with a crack in the middle loaded by the tensile force and an infinite plate with a hole loaded by the tensile force, and we use different point distribution and different order of base function. By analyzing the numerical results with the exact solution and comparing the accuracy and error convergence of the results, we can verify the reliability and feasibility of this method.

Topic Category 工學院 > 土木工程學系
工程學 > 土木與建築工程
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