臺灣博碩士論文加值系統

本文主要是應用大變形理論，提出具有「大變形、大轉角」條件下之薄板幾何非線性理論，本文首先建立平板在大轉角變形的位移表示式，依力學的合理性，得到板在變形狀態沿板厚方向的彎矩及力平衡方程式。與此同時，由大變形理論著手，直接建立截面力(彎矩)的組成律，此組成律可分成二部分，第一類截面力(基於第一類P.K.應力張量) 與剛體位移(轉角)有關、第二類截面力(基於第二類P.K.應力張量)則與平板中面應變(曲率)有關，接著在處裡平面外問題時，在邊界上增設了轉角自由度，使在分析兩面板接合問題時，可使交界處確實接合，在非線性分析上，則採用了U.L.法預測位移，有效降低了由T.L.法預測位移的困難度，並藉T.L.法迭代修正，最後則應用無網格法進行實例分析。

This study intends to develop a geometric nonlinear plate theory with consideration of finite deformations and rotations. The displacement components of a plate element under finite rotations can be formulated and then the equations of equilibrium along edge forces and moments at deformed state based on the rationality of mechanics will be expressed. Meanwhile, the cross sectional forces of the plate can be represented in terms of constitutive law considering finite deformations, in which the first kind of cross sectional forces (in terms of the first kind P.K. stress tensor) are related to rigid body motions, and the second kind cross sectional forces (in terms of the second kind P.K. stress tensor) are expressed by the mid-plane strains (curvatures) of the plate. Finally, the degree of freedom for rotation is introduced to deal with the continuity on the boundary between two plates. The updated Lagrange (U.L.) method is adopted to improve the efficiency of displacement prediction, and, the total Lagrange (T.L.) method is selected to correct the accuracy of displacement prediction. Whole case study will be analyzed through meshless method.

謝誌 I
中文摘要 II
ABSTRACT III
目 次 IV
圖目次 VI
表目次 VIII
第一章 導論 1
1-1 文獻回顧 1
1-2 研究方法 2
1-3 研究內容 3
第二章 平板幾何非線性理論推導-採用T.L.法 4
2-1 前言 4
2-2 基本物理量—建立變形狀態的截面彎矩 5
2-3 應變表示式 7
2-4 第一類及第二類截面力(彎矩)組成律—剛體運動 8
2-5 力平衡方程式 10
2-6 U.L.推演法的表示式 12
第三章 無網格數值分析方法概述 20
3-1 前言 20
3-2 無網格分析方法介紹 20
3-3 平面外的線性問題-考慮邊界轉角自由度 24
第四章 幾何非線性數值分析方法探討 29
4-1 前言 29
4-2 預測階段-應用U.L.增量表示式 29
4-3 修正階段-應用T.L.增量表示式 35
4-4 數值分析方法-弧長法 37
4-5 分析流程 40
第五章 實例分析 43
5-1 前言 43
5-2 線性分析-面內問題 43
5-3 線性分析-面外問題 51
5-4 幾何非線性分析-面內問題 56
第六章 結論 66
6-1 結論 66
6-2 展望 67
參考文獻 68

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