三维弹塑性摩擦接触多极边界元法

三维弹塑性摩擦接触问题是多重非线性问题，对接触区表面和塑变区的离散，须划分大量单元进行大规模运算才能获得接触位移、面力及应力场的准确信息。传统边界元法由于离散自由度所需内存大，CPU计算时间冗长，完整解题运算规模受到限制。本文在三维弹性多极留数边界元法的基础上，开发研制三维弹性数学规划型摩擦接触多极边界元法及源程序，建立三维弹塑性摩擦接触多极边界元法并研制其源程序，更新了课题组开发的原传统的三维弹塑性摩擦接触边界元法。数值试验表明，本法使计算机内存量减少近百倍，从而使细划分单元的大规模运算成为可能，并提高了计算精度。

Multipole BEM for Three-dimensional Elasto-plastic Contact with Friction

It is a highly nonlinear problem of 3-D elastoplastic contact with friction. To obtain the key information about the real size, displacement and traction in contact zone, the elements in contact and plastic zone should be subdivided. However, the increase of degrees of freedom is limited by the problem-solving scale when traditional BEM is used, for a larger memory size is required and the solution procedure costs too long CPU time. In this paper, based on 3-D Elastic Multipole Residual BEM, we developed 3-D Elastic contact Multipole BEM adopting Mathematical Programming, 3-D Elastoplastic contact Multipole BEM and source programs. The computing structure of traditional 3-D Elastoplastic contact BEM with friction is updated. Numerical experiment shows that with this new method, the need of computer memory size is only one hundredth of the traditional one, which makes the large-scale computing of subdivided elements possible and improves the computational precision.