Based on Reissner’s mixed variational theorem (RMVT), the authors develop a finite annular prism method (FAPM) for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to either uniformly or trigonometrically distributed loads. In this formulation, the toroidal shell is divided into a number of finite annular prisms with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridian-radial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAPMs shows that their solutions converge rapidly, and the convergent FAPM solutions closely agree with the 3D elasticity solutions available in the literature.
摘要 I
Extended Abstract II
誌謝 VI
目錄 VII
表目錄 VIII
圖目錄 IX
符號對照表 Ⅹ
第一章 緒論 1
第二章 材料係數 6
2.1. 單層均質同心圓環殼 6
2.2. 正交性疊層同心圓環殼 6
2.3. 雙向FG材料同心圓環殼 6
2.3.1. 混合法則(the rule of mixtures) 7
2.3.2 Mori-Tanaka微觀力學法則 8
第三章 理論推衍 9
3.1. 同心圓環殼的幾何座標 9
3.2. 橫向應力與位移變量之假設 10
3.3. Reissner混合變分理論 12
3.4. Euler-Lagrange方程式以及邊界條件 14
第四章 數值範例 19
4.1. 無限長，均質均向性材料封閉式同心圓環殼 19
4.2. 正交性材料同心圓環層殼 20
4.3. 單向及雙向FG材料同心圓環殼 21
第五章 結論 26
參考文獻 27
附錄A. 工程常數與彈性係數間關係式 48
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