| 孙芳玲,张耀明,高效伟,董丽.热弹性平面问题的规则化边界积分方程[J].计算力学学报,2015,32(4):485~489 |
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| 热弹性平面问题的规则化边界积分方程 |
| Regularized boundary integral equations for thermoelastic problems |
| 投稿时间：2014-02-04 修订日期：2014-10-03 |
| DOI：10.7511/jslx201504007 |
| 中文关键词: 边界元法 热弹性问题 热应力 间接变量边界积分方程 |
| 英文关键词:BEM thermoelastic problem thermal stress indirect boundary integral equation |
| 基金项目:山东省自然科学基金(ZR2010AZ003);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ1307)资助项目. |
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| 中文摘要: |
| 对于热弹性平面问题,过去广泛集中在直接变量边界元法研究,本文研究间接变量规则化边界元法,建立了间接变量规则化边界积分方程.和直接边界元法相比,间接法具有降低密度函数的连续性要求、位移梯度方程中的热载荷体积分具有较弱奇异性等优点.数值实施中,用精确单元描述边界几何,不连续插值函数逼近边界量.算例表明,本文方法效率高,所得数值结果与精确解相当吻合. |
| 英文摘要: |
| This paper is mainly devoted to the research on the regularization of indirect BEM for two-dimensional thermoelastic problems.The regularized boundary integral equations (BIEs) with indirect unknowns,which don't involve the direct calculation of singular integrals,are established.Up to now,the universal researches for thermoelastic problems are focused on the direct BEM.Compared with these existing methods,the proposed algorithm has many advantages: (1) the C1,α continuity requirement for density function in the direct formulation can be relaxed to the C0,α continuity in the presented formulation; (2) the proposed method is easy to implement and more suitable for solving the thin body problems because the solution process doesn't involve the HFP integrals and nearly HFP integrals,so regularized algorithms of integrals are generally more effective and implementary; (3) the proposed regularized BIEs can be used for the calculation of the displacement gradients and stresses on the boun-dary,and but not limited to the tractions.Furthermore,they are independent of the displacement BIEs; (4) the domain integrals for thermal loads in the displacement gradient equations only involve the weak singularity.A systematic approach for implementing numerical solutions is presented by adopting the exact elements to depict the boundary geometry and discontinuous interpolating function to approximate the boundary quantities.Some benchmark examples show that a good precision and high computational efficiency can be achieved by the present method. |
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