ALGORITHM AND NUMERICAL ANALYSIS METHOD FOR NONLINEAR CONTACT PROBLEMS IN UNDERGROUND ENGINEERING
ZHOU Mozhen1，QIAN Xiaoxiang1，2，ZHANG Bingyin1
(1. State Key Laboratory of Hydroscience and Engineering，Tsinghua University，Beijing 100084，China；2. Beijing Rail and Transit Design and Research Institute Company Limited，Beijing 100089，China)
Abstract：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.
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2014, Vol. 33 
