The Refined Theory of Thermoelastic Plane Problems
The Refined Theory of Thermoelastic Plane Problems
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DOI：
10.1080/01495730701519615
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发表时间：
2007-10
影响因子：
2.8
通讯作者：
Yang Gao;B. Zhao
中科院分区：
文献类型：
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作者：
Yang Gao;B. Zhao
基于热弹性理论，在没有特殊假设的情况下，利用Biot解和Lur‘e方法，从厚板理论出发，系统地、直接地推导了平面问题的各种二维方程和解。这些方程和解可以用来构造平面问题的精化理论。在齐次边界条件下，得到了板的精确控制方程和解，它由四个控制方程组成。值得注意的是，精化理论与Gregory的分解定理是一致的。在非齐次边界条件下，板的近似控制方程和解的精度可达二阶项。修正了经典平面应力问题中应力假设的正确性。
Based on thermoelastic theory, various two-dimensional equations and solutions for plane problems have been deduced systematically and directly from thick plate theory by using Biot's solution and Lur'e method without ad hoc assumptions. These equations and solutions can be used to construct the refined theory for the plane problems. In the case of homogeneous boundary conditions, the exact governing differential equations and solutions for the plate are derived, which consist of four governing differential equations. It is important note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order terms. The correctness of the stress assumptions in the classic plane stress problems is revised.