多体接触问题面面接触算法研究

本文重点研究了面面接触算法:(1)将主从面算法与位码算法相结合,定义了共享实常数组用以标识"接触面对"的主面单元和从面单元,借鉴了位码方法的编码思想,将三维空间潜在接触面按一维数组分类排序,实现接触面的全局搜索;(2)点面算法与内外算法相结合,判断主节点沿平均法线方向的投影点是在目标面单元的内部或外部,并通过单元的面积坐标确定接触点局部坐标,进而得到接触关联矩阵,完成接触局部搜索定位,从而避免了求解局部接触点坐标的非线性方程;(3)本文算法将每一个接触块体作为子区域,每个子域可以独立地进行有限元剖分,并采用了拟高斯迭代法隐式求解位移增量和接触力,按照所提出的接触算法策略编制了FORTRAN源代码程序;(4)由数值算例得到了与赫兹接触问题的理论解几乎完全吻合的计算结果,同时借助于商业软件的类似接触计算功能对本文算法的计算结果进行了比较验证,结果几乎完全一致。本文算法的另一优点在于在接触搜索预处理过程中已考虑了接触区域的分解,可以方便地进行高混凝土坝和岩体高边坡静动力稳定的并行计算处理。

Algorithm research on surface-to-surface contact for multibody contact problem

The surface-to-surface contact algorithm is focused on in this paper. (1) Combining the mas-ter-slave surface algorithm with the bit-code algorithm, a shared real constant array is defined to identify the master-surface element and the slave-surface element of the "contact-face couples". Refering to the cod-ing ideas of the bit-code method, the potential contact surfaces in three-dimensional space are sorted as a one-dimensional array to realize global search of contact surface. (2) The combination of the point-surface algorithm and the inside-outside contact search algorithms is used to judge whether the projection point of the master node along the average normal direction is internal or external in the target surface element, and determines the local coordinates of the contact point by the area coordinates of the element, and then obtains the contact association matrix to complete local contact search,thus avoiding solving nonlinear equa-tions of local contact point coordinates. (3) The algorithm preposed treats each contact body as a sub-re-gion,and each sub-region can be independently divided by finite elements. The quasi-Gauss iterative meth-od is used to implicitly solve the displacement increment and contact force. The FORTRAN source code pro-gram is compiled in accordance with the proposed contact algorithm strategy. (4) Calculation results ob-tained from the numerical examples are almost completely matched the theoretical solution of the classic contact problem. At the same time, the contact algorithm presented has been verified by using similar con-tact calculation functions provided by ANSYS commercial software because their calculation results are al-most identical. Another advantage of the algorithm proposed in this paper that the contact area decomposi-tion has been taken into account during the pre-processing of contact search, which can conveniently per-form parallel computional processing for high concrete dams and high slope stability of rock masses.