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Internal variables and their sensitivities in three- dimensional linear elasticity by the boundary contour method

机译：边界轮廓法在三维线性弹性中的内部变量及其敏感性

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摘要

A variant of the usual boundary element method (BEM), called the boundary contour method (BCM), has been presented in the literature in recent years. In the BCM in three-dimensions, surface integrals on boundary elements of the usual BEM are transformed, through an application of Stokes' theorem, into line integrals on the bounding contours of these elements. A new formulation for design sensitivities in three-dimensional linear elasticity, based on the BCM, has been recently presented in Ref [12]. This challenging derivation is carried out by first taking the material derivative of the regularized boundary integral equation (BIE) with respect to a shape design variable, and then converting the resulting equation into its boundary contour version. The focus of [12] is the boundary problem, i.e., evaluation of displacements, stresses and their sensitivities on the bounding surface of a body. The focus of the present paper is the corresponding internal problem, i.e., analogous calculations at points inside a body. Numerical results for internal variables and their sensitivities are presented here for selected examples.
机译：近年来，文献中已经介绍了通常的边界元法（BEM）的一种变体，称为边界轮廓法（BCM）。在三维BCM中，通过应用斯托克斯定理，通常BEM边界元素上的表面积分被转换为这些元素的边界轮廓上的线积分。参考文献[12]最近提出了一种基于BCM的三维线性弹性中设计灵敏度的新公式。通过首先获取正则化边界积分方程（BIE）相对于形状设计变量的材料导数，然后将所得方程转换为其边界轮廓版本，可以实现这一具有挑战性的推导。 [12]的焦点是边界问题，即，在物体的边界表面上的位移，应力及其敏感性的评估。本文的重点是相应的内部问题，即在人体内部各点的类似计算。对于选定的示例，此处提供了内部变量及其灵敏度的数值结果。

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