地下工程中的非线性接触算法研究及数值实现

ALGORITHM AND NUMERICAL ANALYSIS METHOD FOR NONLINEAR CONTACT PROBLEMS IN UNDERGROUND ENGINEERING

基于罚函数法的点对面形式因其具有显著的简便性而在工程领域内应用广泛。针对罚因子可能引起矩阵病态的缺陷,采用局部坐标系下的相对位移作为与接触相关的广义自由度,大幅提高了罚因子的取值上限,且无需使用专门的矩阵预处理子即可用于求解大规模接触问题。针对点对面存在投影奇异性及结果振荡的风险,发展采用径向基点插值法的三维曲面光滑方法,其优势在于网格适应性极强且不损失曲面精度。将双向链接边表作为三维接触面的数据结构,有效地降低了接触邻接搜索的计算代价。基于以上改进,开发大型非线性接触分析有限元计算程序,数值算例的结果表明,该计算程序具有较强地描述位移不连续现象的能力,能有效求解接触非线性方程,可用于模拟大规模地下工程中的复杂多体接触问题。

The node-to-segment approach using penalty method was widely applied in engineering field due to its great simplicity. To deal with the problem in which a large penalty factor may cause ill-condition,the degree of freedom relevant to contact is described by relative displacement in local coordinate system,which enlarges significantly the upper-limit of penalty factor and provides an efficient solution for large-scale contact problem without using any special preconditions. A general 3D contact smoothing method based on radial point interpolation is proposed to avoid probable projecting singularity and jump of contact force in node-to-segment. This method reproduces smooth surfaces which passes exactly through the surface nodes even for coarse or hybrid meshes. The doubly connected edge list is applied to the local searching for contact information and effectively reduces the computing cost. A nonlinear contact analysis program is written and the results of numerical examples indicate that the program effectively describes the phenomenon of displacement discontinuity,solve the contact nonlinear equation,and tackle the large-scale contact problems in underground engineering.