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

本研究的主要目的是开发有效的技术，使用边界元法（BEM）的三维（3D）应力分析的各向异性固体热机械载荷下。 这些具有随取向而变化的性质的材料越来越多地用于工程和科学应用中。虽然边界元法是一种有效的处理各向同性弹性固体的工具，但对于三维各向异性的情况却不能这样说。这是由于在边界积分方程（BIE）中使用的绿色函数的数学复杂性。也有很少的出版物确实处理三维边界元各向异性热应力分析。在基本形式的BIE，热效应表现出自己的绿色的功能，在一个额外的体积积分，必须转化为表面的恢复边界元法作为一个边界解决方案技术的显着特点。为此，简化近似已被通过在几个可用的出版物中报告的计划，裂纹或内角的情况下，目前需要区别对待。作为该领域中BEM发展的一个进步，申请人及其同事最近实施了一种基于绿色函数的精确、明确、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，包含这些绿色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，热弹性力学的边界元公式可以应用于裂纹和非裂纹问题，具有相同的算法，而无需进一步的近似。一旦这已经完成，双参数方法的断裂力学分析的各向异性固体在热负荷下将被实施。一些重要的非裂纹和裂纹问题的实际利益将被调查。

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.