zbMATH — the first resource for mathematics

A contact algorithm for 3D discrete and finite element contact problems based on penalty function method. (English) Zbl 1384.74048
Summary: A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved.

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
Full Text: DOI
[1] Nakashima H, Oida A (2004) Algorithm and implementation of soil-tire contact analysis code based on dynamic FE-DE method. J Terramech 41(2–3): 127–137 · doi:10.1016/j.jterra.2004.02.002
[2] Oñate E, Rojek J (2004) Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems. Comput Methods Appl Mech Eng 193(27–29): 3087–3128 · Zbl 1079.74646 · doi:10.1016/j.cma.2003.12.056
[3] Rojek J, Zarate F, De Saracibar CA, Gilbourne C, Verdot P (2005) Discrete element modelling and simulation of sand mould manufacture for the lost foam process. Int J Numer Methods Eng 62(11): 1421–1441 · Zbl 1078.74681 · doi:10.1002/nme.1221
[4] Lei Z, Zang MY (2010) An approach to combining 3D discrete and finite element methods based on penalty function method. Comput Mech 46(4): 609–619 · Zbl 1358.74060 · doi:10.1007/s00466-010-0502-4
[5] Zhong ZH, Nilsson L (1989) A contact searching algorithm for general contact problems. Comput Struct 33(1): 197–209 · Zbl 0708.73063 · doi:10.1016/0045-7949(89)90141-7
[6] Oldenburg M, Nilsson L (1994) The position code algorithm for contact searching. Int J Numer Methods Eng 37(3): 359–386 · Zbl 0788.73071 · doi:10.1002/nme.1620370302
[7] Benson DJ, Hallquist JO (1990) A single surface contact algorithm for the post-buckling analysis of shell structures. Comput Meth Appl Mech Eng 78(2): 141–163 · Zbl 0708.73079 · doi:10.1016/0045-7825(90)90098-7
[8] Belytschko T, Neal MO (1991) Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int J Numer Methods Eng 31(3): 547–572 · Zbl 0825.73984 · doi:10.1002/nme.1620310309
[9] Wang SP, Nakamachi E (1991) The inside-outside contact search algorithm for finite element analysis. Int J Numer Methods Eng 31(3): 547–572 · Zbl 0825.73984 · doi:10.1002/nme.1620310309
[10] Chaudhary BC, Bathe KJ (1986) A solution method for static and dynamic analysis of three-dimensional contact problems with friction. Comput Struct 24(6): 855–873 · Zbl 0604.73116 · doi:10.1016/0045-7949(86)90294-4
[11] Doghri I, Muller A, Taylor RL (1998) A general three-dimensional contact procedure for implicit finite element codes. Eng Comput 15: 233–259 · Zbl 0935.74064 · doi:10.1108/02644409810202639
[12] Hallquist JO, GoudreauGL Benson DJ (1985) Sliding interfaces with contact-impact in large-scale Lagrangian computations. Comput Meth Appl Mech Eng 51(1–3): 107–137 · Zbl 0567.73120 · doi:10.1016/0045-7825(85)90030-1
[13] Wang FJ, Cheng JG, Yao ZH (2000) A contact searching algorithm for contact-impact problems. Acta Mech Sin 16(4): 374–382 · doi:10.1007/BF02487690
[14] Munjiza A, Andrews KRF (1998) NBS contact detection algorithm for bodies of similar size. Int J Numer Methods Eng 43(1): 131–149 · Zbl 0937.74079 · doi:10.1002/(SICI)1097-0207(19980915)43:1<131::AID-NME447>3.0.CO;2-S
[15] Hallquist JO (2006) LS-DYNA Theory Manual. Livermore Software Technology, California
[16] Moré JJ, Cosnard MY (1979) Numerical solution of nonlinear equations. ACM Trans Math Softw 5(1): 64–85 · Zbl 0393.65019 · doi:10.1145/355815.355820
[17] Brent RP (1973) Some efficient algorithms for solving systems of nonlinear equations. SIAM J Numer Anal 10(2): 327–343 · Zbl 0258.65051 · doi:10.1137/0710031
[18] Han K, Perić D, Owen DJR (2000) A combined finite/discrete element simulation of shot peening processes Part II: 3D interaction laws. Eng Comput 17: 680–702 · Zbl 1112.74516 · doi:10.1108/02644400010340615
[19] Zhong ZH (1993) Finite Element Procedures for Contact-impact Problems. Oxford University Press, Oxford
[20] Liu K, Gao L (2003) The application of discrete element method in solving three dimensional impact dynamics problems. Acta Mech Solida Sin 16(3): 256–261
[21] Yu JB, Liu XK, Zang MY (2010) Analysis of impact responses of front windshield using combined DEM/FEM method. J Hunan Univ(Natural Sciences) 37(2): 126–129
[22] Cheng M, Liu W, Liu K (2009) New discrete element models for elastoplastic problems. Acta Mech Sin 25: 629–637 · Zbl 1269.74208 · doi:10.1007/s10409-009-0271-5
[23] Liu K, Liu W (2006) Application of discrete element method for continuum dynamic problems. Arch Appl Mech 76: 229–243 · Zbl 1161.74522 · doi:10.1007/s00419-006-0018-8
[24] Akin ED (2003) Object-Oriented programming via Fortran 90/95. Cambridge University Press, Cambridge
[25] Hu N (1997) A solution method for dynamic contact problems. Comput Struct 63(6): 1053–1063 · Zbl 0899.73565 · doi:10.1016/S0045-7949(96)00408-7
[26] Wong SV, Hamouda AMS, Hashmi MJC (2000) Kinematic Contact-Impact Algorithm with Friction. Int J Crashworthiness 6(1): 65–82 · doi:10.1533/cras.2001.0163
[27] Curnier A (1984) A theory of friction. Int J Solids Struct 20(7): 637–647 · Zbl 0543.73138 · doi:10.1016/0020-7683(84)90021-0
[28] Wriggers P, Van TV, Stein E (1990) Finite element formulation of large deformation impact-contact problems with friction. Comput Struct 37(3): 319–331 · Zbl 0727.73080 · doi:10.1016/0045-7949(90)90324-U
[29] Perić D, Owen DJR (1992) Computational model for 3-D contact problems with friction based on the penalty method. Int J Numer Methods Eng 35(6): 1289–1309 · Zbl 0768.73100 · doi:10.1002/nme.1620350609
[30] Laursen TA, Simo JC (1993) Algorithmic symmetrization of coulomb frictional problems using augmented lagrangians.. Comput Meth Appl Mech Eng 108(1–2): 133–146 · Zbl 0782.73076 · doi:10.1016/0045-7825(93)90157-S
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.