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| The complementary model and smoothing algorithm for 3D contact problems |
| LI Cuihua1，2，ZHENG Hong1，3，JIANG Qinghui4，ZHOU Chuangbing4 |
| (1. State Key Laboratory of Geomechanics and Geotechnical Engineering，Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，Wuhan，Hubei 430071，China；2. Hubei Water Resources Technical College，Wuhan，Hubei 430072，China；3. College of Architecture and Civil Engineering，Beijing University of Technology，Beijing 100124，China；4. School of Civil and Architectural Engineering，Wuhan University，Wuhan，Hubei 430072，China) |
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Abstract The contact problem is one of the key mechanical problems in the discontinuous medium such as rock. Based on the physical meaning of 3D contact problem，the equivalent complementary models were established in normal and tangential directions，respectively. A new approximating smooth function was proposed for the nonlinear property of the complementary model. The approximating function is equivalent to the complementary model when the parameter tends to 0+. Since the approximation function is C1 continuous，the corresponding Jacobian matrix is nonsingular under any condition which enables the successful solution for the conventional Newton algorithm. By introducing the direction vector，the constraint function method proposed in 2D frictional contact problems was extended to 3D ones. Hence the stability problem caused by the periodicity of the direction angle in 3D contact problems was resolved. Then，the 3D point-surface contact for finite element model was established. At last，the validity of the proposed method was verified with several classical cases.
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余德浩. 有限元、自然边界元与辛几何算法[J]. 高等数学研究，2001，4(4)：5-10.(YU Dehao. Finite element methods，natural boundary element method and Symplectic geometry algorithms[J]. Studies in College Mathematics，2001，4(4)：5-10.(in Chinese))
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2016, Vol. 35 
