| 功能梯度材料及复合材料平面断裂中的一系列偏微分方程边值问题 |
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| 引用本文： | 高廷凯.功能梯度材料及复合材料平面断裂中的一系列偏微分方程边值问题[J].山西师范大学学报,2005,19(3):52-56. |
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| 作者姓名： | 高廷凯 |
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| 作者单位： | 太原科技大学应用科学学院,山西太原030024 |
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| 摘 要： | 本文首先推导了弹性模量以任意函数形式连续变化时，各向异性功能梯度材料平面断裂问题的基本方程，在此基础上又进一步考虑了各向同性、正交异性功能梯度材料以及各向同性、正交异性、各向异性复合材料平面断裂问题的情况，再结合Ⅰ型、Ⅱ型、Ⅰ＋Ⅱ型裂纹的边界条件，共得出六类（18个）偏微分方程边值问题．同时从方程的角度揭示了各向同性、正交异性、各向异性的密切联系以及功能梯度材料和复合材料的有机统一性．
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| 关 键 词： | 偏微分方程 边值问题 功能梯度材料 复合材料 断裂 |
| 文章编号： | 1009-4490（2005）03-0052-05 |
| 收稿时间： | 2005-07-21 |
| 修稿时间： | 2005年7月21日 |
A Series of Boundary Value Problem of Partial Differential Equation on Functionally Graded Materials and Composite Materials Plane Fracture |
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| Gao TingKai.A Series of Boundary Value Problem of Partial Differential Equation on Functionally Graded Materials and Composite Materials Plane Fracture[J].Journal of Shanxi Teachers University,2005,19(3):52-56. |
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| Authors: | Gao TingKai |
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| Abstract: | The search for plane fracture problems of anisotropic functionally graded materials with the elastic modulus variation represented in the arbitrary function form can be classified as solving a class of boundary value problem of partial differential equation. As a base, The search for plane fracture problems of isotropic, orthotropic functionally graded materials and three kinds of composite materials can be classified as solving five classes of boundary value problems of partial differential equation. |
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| Keywords: | Partial differential equation Boundary value problem Functionally graded materials Composite materials Fracture |
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