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

本研究的主要目的是发展利用边界元方法(BEM)分析各向异性固体在热机械载荷作用下的三维应力的有效方法。这些材料的性能随取向而变化，在工程和科学应用中的应用越来越多。虽然边界元被公认为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式(BIE)中使用的格林函数的数学复杂性。真正涉及三维边界元各向异性热应力分析的出版物也很少。在边界元的基本形式中，热效应通过格林函数表现出来，这种附加的体积积分必须转换为表面积分，以恢复边界元作为一种边界求解技术的独特特征。为此，在为数不多的现有出版物中报告的方案中采用了简化近似；存在裂纹或内角的情况需要区别对待。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施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施和计算。这项拟议的研究旨在将其扩展到处理热效应。由于这种代数形式，包含这些格林函数和温度项的相关联的体积积分在原则上可以精确地转换为表面积分。因此，热弹性的边界元公式可以用相同的算法同时适用于裂纹和非裂纹问题，而不需要进一步的近似。一旦完成这项工作，将实现热载荷作用下裂隙各向异性固体断裂力学分析的双参数方法。还将研究一些具有实际意义的重要的无裂纹和裂纹问题。

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.