热弹性问题直接边界元法中的边界层效应

The boundary layer effect in the BEM of thermo elasticity problems with direct formulation

在热弹性问题的直接变量边界元分析中,求解近边界点处的热应力时,会涉及几乎强奇异和几乎超奇异积分的处理问题,特别是几乎超奇异积分的处理会更加困难.为此采用一种非线性变量替换法,有效地改善了被积函数的震荡特性,从而消除了核积分的几乎奇异性.数值实验表明,本算法稳定,效率高,并可达到很高的计算精度,即使场点非常靠近边界,仍可避免边界层效应现象.

For the direct boundary element analysis of thermo elastic problem,the nearly strongly singular and hyper-singular integrals occur when the thermal stress at interior points close to the boundary needs to be calculated,and especially,the hyper-singular integrals are harder to treat.In this paper,an efficient non-linear transformation is adopted and applied to calculate the thermal stress at interior points very close to the boundary.It can remove or damp out the nearly singularity efficiently by smoothing out the rapid variations of the integrand of nearly singular integrals,and improve the accuracy of numerical results greatly.Numerical examples of thermo elasticity problems are given with satisfactory results,showing the high efficiency and stability of the suggested approach,and the boundary layer effect can be avoided successfully even when the internal points are very close to the boundary.