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张耀明, 温卫东, 王利民, 赵熙强. 弹性力学平面问题中一类无奇异边界积分方程[J]. 力学学报, 2004, 36(3): 311-321. DOI: 10.6052/0459-1879-2004-3-2003-153
引用本文: 张耀明, 温卫东, 王利民, 赵熙强. 弹性力学平面问题中一类无奇异边界积分方程[J]. 力学学报, 2004, 36(3): 311-321. DOI: 10.6052/0459-1879-2004-3-2003-153
A Kind Of New Nonsingular Boundary Integral Equations For Elastic Plane Problem[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(3): 311-321. DOI: 10.6052/0459-1879-2004-3-2003-153
Citation: A Kind Of New Nonsingular Boundary Integral Equations For Elastic Plane Problem[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(3): 311-321. DOI: 10.6052/0459-1879-2004-3-2003-153

弹性力学平面问题中一类无奇异边界积分方程

A Kind Of New Nonsingular Boundary Integral Equations For Elastic Plane Problem

  • 摘要: 从理论上提出一种新的方法,归化出间接变量无奇异边界积分方程. 采用Lagrange二次单元,建立一个数值求解框架系统. 此外,基于问题的计算区域的特殊性,给出一种边界近似方法. 数值算例表明该方法所取得的数值结果与精确解相当接近,特别是边界量的数值结果. 此外,该方法容易被推广到三维问题.和已有的直接变量的情形相比较,具有优点:1)无需处理HFP积分. 大大降低处理问题的复杂性,并提高了计算效率和解的精度;2)摆脱了问题的具体形式,进入纯代数操作.这样做的好处是从理论上建立一种普遍适用的方法,不仅适用于弹性力学问题,同样可应用于其它问题,如位势问题, Stokes问题等. 3)提供了一种计算CPV积分的方法.

     

    Abstract: A new approach is presented, in which thenonsingular IBIE is established. A numerically systematic scheme isestablished by adopting quadratic Lagrange's elements.A new geometry boundary approximatetechnique is presented. Some numerical examples will be applied to validate the current scheme. It is shown that a betterprecision and high computational efficiency can be derived by thepresentation, especially the numerical results of boundary quantities match theexact solutions very well. Besides, it can be easily extended to the threedimensional problems.Compared with the direct unknown's situation, the present approach has manyadvantages:1) it is not necessary to deal with the HFP so that it is simpler,and with better precision and high computational efficiency. 2) The presentation only requires algebraic manipulations so that it can easilybe extended to the other problems, such as potential problems and Stokesproblems. 3) This paper establishes a technique applicable for thecalculation of CPV integrals.

     

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