薄体结构热弹性力学分析的边界元法

The Boundary Element Method of the Thermoelasticity Analysis for Structures with Thin Bodies

针对边界元法分析薄体结构和求解近边界物理参量时遇到的几乎奇异积分难以处理的困难,将几乎奇异积分划分为两种类型,分别通过分部积分把引起积分几乎奇异的参量变换至积分号之外,从而建立了一个新的正则化算法,成功计算了几乎强奇异和超奇异积分。文中用该算法分析了二维热弹性力学薄体问题,算例证明了本法的有效性。

The nearly singular integrals occur in boundary element method when it is applied to analyzing structures with thin bodies or calculating the physical quantities very close to the boundary. A regularization algorithm is given to calculate the nearly singular integrals, which are classified into two forms.The singular factor is separated from the integrands of these nearly singular integrals by using integration by parts, so that the nearly strongly singular and hyper-singular integrals are successfully evaluated. The algorithm is used to analyze the structures with thin bodies for two-dimensional thermoelasticity problems. Numerical example demonstrates the algorithm is effective.