Three dimensional thermoelastic stress analysis of anisotropic solids by the boundary element method

本研究的主要目的是开发利用边界元法（BEM）对各向异性固体在热机械载荷下的三维（3D）应力分析的有效技术。这些具有随取向变化而变化的性能的材料越来越多地用于工程和科学应用。虽然边界元法是处理各向同性弹性固体的有效工具，但对于三维各向异性的情况却并非如此。这是由于边界积分方程（BIE）中使用的格林函数的数学复杂性。关于三维边界元各向异性热应力分析的文献也很少。在BIE的基本形式中，热效应与格林函数在一个额外的体积积分中表现出来，这个体积积分必须转化为表面积分，以恢复边界元作为边界解技术的独特特征。为此目的，在为数不多的现有出版物中报告的办法中采用了简化的近似方法；如果存在裂纹或内角，则需要进行不同的处理。作为边界元在这一领域发展的一个进步，申请人和他的同事最近实现了一种基于格林函数的精确、显式、代数形式的方法。与以前的公式相比，它们可以以相对有效的方式实现和计算。拟议的研究旨在将其扩展到处理热效应。由于代数形式的关系，包含格林函数和温度项的相关体积积分原则上可以精确地转化为表面积分。因此，热弹性的边界元公式可以用相同的算法应用于裂纹和非裂纹问题，而无需进一步的近似。一旦完成，热载荷作用下各向异性固体裂纹断裂力学分析的双参数方法将得以实现。本课程将探讨一些重要的非裂纹和裂纹问题。

The main objective of this research is to develop efficient techniques using the Boundary Element Method (BEM) for three-dimensional (3D) stress analysis of anisotropic solids under thermo-mechanical loads. These materials which have properties that vary with orientation are increasing being used in engineering and scientific applications. Although the BEM is very well established as an efficient tool for treating isotropic elastic solids, the same cannot be said for the case of 3D anisotropy. This is due to the mathematical complexity of the Green's functions that were used in the boundary integral equation (BIE). There is also paucity of publications indeed dealing with 3D BEM anisotropic thermal stress analysis. In the basic form of the BIE, thermal effects manifest themselves with the Green's functions in an additional volume integral which has to be transformed into surface ones to restore the distinctive feature of the BEM as a boundary solution technique. To this end, simplifying approximations have been adopted in the schemes reported in the few available publications; cases where cracks or internal corners are present need to be treated differently. As an advance in the development of the BEM in this area, the applicant and his co-workers have recently implemented an approach based on an exact, explicit, algebraic form of the Green's functions. They can be implemented and computed in a relatively efficient manner compared to previous formulations. The proposed research aims to extend it to handle thermal effects. Because of the algebraic form, the associated volume integral containing these Green's functions and the temperature terms can, in principle, be transformed exactly into surface ones. The BEM formulation for thermoelasticity can thus be applied to both crack and non-crack problems with the same algorithm without further approximations. Once this has been accomplished, the two-parameter approach for fracture mechanics analysis of cracked anisotropic solids under thermal loads will be implemented. Some important non-crack and crack problems of practical interest will be investigated.