A surface-to-surface scheme for 3D contact problems by boundary face method. (English) Zbl 1403.74063
Summary: The surface-to-surface contact algorithm has been proposed to overcome the drawbacks of node-to-surface algorithm in finite element method implementations. In the surface-to-surface algorithm, contact constraints are imposed between sub-elements rather than between nodes, and an auxiliary plane for each element is introduced to perform overlapping area detection. This work presents a combination of the surface-to-surface algorithm and the boundary face method (BFM) for solving contact problems in three dimensions. The BFM is based on boundary integral equation and is a truly isogeometric method, as it makes direct use of the geometric information of the bounding surface of a body. Apparently, the BFM is more suitable for solving contact problems. In our implementation, the auxiliary plane is no more necessary, but replaced by the boundary faces themselves which already exist in the BFM data structure. Our implementation is natural and can more precisely match the contact conditions between faces, and therefore, higher level of accuracy can be expected. Numerical examples presented have demonstrated the advantages of the combined method.
MSC:
| 74M15 | Contact in solid mechanics |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
References:
| [1] | Hertz, H., Study on the contact of elastic solids, J Reine Angew Math, 92, 156-171, (1882) · JFM 14.0807.01 |
| [2] | Gladwell, G. M.L., Contact problems in the classical theory of elasticity, (1980), Sijthoff and Noordhoof Netherlands · Zbl 0431.73094 |
| [3] | Johnson, K. L., Contact mechanics, (1985), Cambridge University Press Cambridge · Zbl 0599.73108 |
| [4] | Francavilla, A.; Zienkiewicz, O. C., A note on numerical computation of elastic contact problems, Int J Numer Methods Eng, 9, 4, 913-924, (1975) |
| [5] | Fredriksson, B., Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems, Comput Struct, 6, 4, 281-290, (1976) · Zbl 0349.73036 |
| [6] | Andersson, T.; Fredriksson, B.; Allan Persson, B. G., The boundary element method applied to two-dimensional contact problems, (Brebbia, C. A., Proceedings of the Second International Seminar on Recent Advances in BEM, (1980), Southampton: CML Publications), 247-263 · Zbl 0466.73105 |
| [7] | Paris, F.; Garrido, J. A., On the use of discontinuous elements in two dimensional contact problems, (Brebbia, C. A., Boundary Elements VII, (1985), Springer Berlin), 1327-1330 |
| [8] | Blázquez, A.; París, F., On the necessity of non-conforming algorithms for ‘small displacement’ contact problems and conforming discretizations by BEM, Eng Anal Bound Elem, 33, 2, 184-190, (2009) · Zbl 1244.74140 |
| [9] | Bathe, K. J.; Chaudhary, A., A solution method for planar and axisymmetric contact problems, Int J Numer Methods Eng, 21, 65-88, (1985) · Zbl 0551.73099 |
| [10] | Klarbring, A.; Bjöourkman, G., Solution of large displacement contact problems with friction using Newton’s method for generalized equations, Int J Numer Methods Eng, 34, 1, 249-269, (1992) · Zbl 0761.73105 |
| [11] | Wriggers, P., Computational contact mechanics, (2006), Springer Berlin · Zbl 1104.74002 |
| [12] | Olukoko, O. A.; Becker, A. A.; Fenner, R. T., A new boundary element approach for contact problems with friction, Int J Numer Methods Eng, 36, 2625-2642, (1993) · Zbl 0780.73095 |
| [13] | París, F.; Blázquez, A.; Canas, J., Contact problems with nonconforming discretizations using boundary element method, Comput Struct, 57, 5, 829-839, (1995) · Zbl 0900.73903 |
| [14] | Aliabadi MH, Brebbia CA. Computational methods in contact mechanics. Southampton Boston: Computational Mechanics Publications/Elsevier Applied Science; 1993. · Zbl 0790.73004 |
| [15] | De Lorenzis, L.; Wriggers, P.; Hughes, T. J.R., Isogeometric contact: a review, GAMM-Mitteilungen, 37, 1, 85-123, (2014) · Zbl 1308.74114 |
| [16] | Simo, J. C.; Wriggers, P.; Taylor, R. L., A perturbed Lagrangian formulation for the finite element solution of contact problems, Comput Methods Appl Mech Eng, 50, 2, 163-180, (1985) · Zbl 0552.73097 |
| [17] | Papadopoulos, P.; Taylor, R. L., A mixed formulation for the finite element solution of contact problems, Comput Methods Appl Mech Eng, 94, 3, 373-389, (1992) · Zbl 0743.73029 |
| [18] | Yang, B.; Laursen, T. A.; Meng, X., Two dimensional mortar contact methods for large deformation frictional sliding, Int J Numer Methods Eng, 62, 9, 1183-1225, (2005) · Zbl 1161.74497 |
| [19] | Puso, M. A.; Laursen, T. A., A mortar segment-to-segment contact method for large deformation solid mechanics, Comput Methods Appl Mech Eng, 193, 6, 601-629, (2004) · Zbl 1060.74636 |
| [20] | Farah, P.; Popp, A.; Wall, W. A., Segment-based vs. element-based integration for mortar methods in computational contact mechanics, Comput Mech, 55, 1, 209-228, (2015) · Zbl 1311.74120 |
| [21] | Laursen, T. A.; Puso, M. A.; Sanders, J., Mortar contact formulations for deformable-deformable contact: past contributions and new extensions for enriched and embedded interface formulations, Comput Methods Appl Mech Eng, 205, 3-15, (2012) · Zbl 1239.74070 |
| [22] | Blazquez, A.; Paris, F.; Canas, J., Interpretation of the problems found in applying contact conditions in node-to-point schemes with boundary element non-conforming discretizations, Eng Anal Bound Elem, 21, 4, 361-375, (1998) · Zbl 0957.74065 |
| [23] | Blazquez, A.; Paris, F.; Mantic, V., BEM solution of two dimensional contact problems by weak application of contact conditions with non-conforming discretizations, Int J Solids Struct, 35, 3259-3278, (1998) · Zbl 0973.74652 |
| [24] | Zhang, J. M.; Qin, X. Y.; Han, X.; Li, G. Y., A boundary face method for potential problems in three dimensions, Int J Numer Methods Eng, 80, 3, 320-337, (2009) · Zbl 1176.74212 |
| [25] | Yastrebov, V. A., Numerical methods in contact mechanics, (2013), ISTE/Wiley London · Zbl 1268.74003 |
| [26] | Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput Methods Appl Mech Eng, 194, 39, 4135-4195, (2005) · Zbl 1151.74419 |
| [27] | Zhou, F. L.; Zhang, J. M.; Sheng, X. M.; Li, G. Y., Shape variable radial basis function and its application in dual reciprocity boundary face method, Eng Anal Bound Elem, 35, 2, 244-252, (2011) · Zbl 1259.65188 |
| [28] | Qin, X. Y.; Zhang, J. M.; Li, G. Y.; Sheng, X. M., An element implementation of the boundary face method for 3D potential problems, Eng Anal Bound Elem, 34, 11, 934-943, (2010) · Zbl 1244.74182 |
| [29] | Gu, J. L.; Zhang, J. M.; Sheng, X. M., B-spline approximation in boundary face method for three-dimensional linear elasticity, Eng Anal Bound Elem, 35, 11, 1159-1167, (2011) · Zbl 1259.74083 |
| [30] | Zhou, F. L.; Zhang, J. M.; Sheng, X. M.; Li, G. Y., A dual reciprocity boundary face method for 3D non-homogeneous elasticity problems, Eng Anal Bound Elem, 36, 9, 1301-1310, (2012) · Zbl 1351.74088 |
| [31] | Foley, J. D.; VanDam, A.; Feiner, S. K.; Hughes, J. F., Computer graphics: principles and practice, (1997), Addison-Wesley Reading |
| [32] | Zheng, X. S.; Zhang, J. M.; Xiong, K.; Shu, X. M., Boundary face method for 3D contact problems with non-conforming contact discretization, Eng Anal Bound Elem, 63, 40-48, (2016) · Zbl 1403.74269 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
