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An interactive method of interface boundary elements and partitioned finite elements for local continuous/discontinuous deformation problems. (English) Zbl 1352.74466
Summary: The interactive method of interface boundary elements (IBEs) and partitioned finite elements (PFEs) is proposed for solving such problems as local continuous/discontinuous deformation (i.e., landslide, concrete cracking, rock mass joints, and internal contraction joints) in concrete dams. The system is divided into continuous displacement bodies and continuous stress joints. The continuous displacement bodies are solved using PFE with the nodal displacements treated as variables, and the rigid displacements in each body and the constraining internal forces on the boundary interface are solved using IBE based on the continuous stress condition and the static force equilibrium condition in each body. Each IBE consists of all interface boundary nodes in a body, and the flexibility matrix is formed using PFE or theoretical analysis. Using this method, a nonlinear iteration procedure is carried out only on the possible discontinuous interface, an approach that greatly improves the computational efficiency. Three numerical examples are used to verify the correctness and validity of the proposed method.
MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
Software:
DEMPack
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[1] Goodman, A model for the mechanics of jointed rock, Journal of Soil Mechanics and Foundation Engineering Division ASCE 94 (3) pp 637– (1968)
[2] Clough, Finite element analysis of retaining wall behavior, Journal of Soil Mechanics and Foundation Engineering Division ASCE 97 (12) pp 1657– (1971)
[3] Desai, Thin layer element for interfaces and joints, International Journal for Numerical and Analytical Methods in Geomechanics 8 (1) pp 19– (1984) · doi:10.1002/nag.1610080103
[4] Boulon, Modeling of soil structure interface behavior: a comparison between elastoplastic and rate-type laws, Computers and Geotechnics 17 (9) pp 21– (1990) · doi:10.1016/0266-352X(90)90027-S
[5] Simo, A perturbed Lagrangian formulation for the finite element solution of contact problems, Computer Methods in Applied Mechanics and Engineering 50 pp 163– (1985) · Zbl 0552.73097 · doi:10.1016/0045-7825(85)90088-X
[6] Kikuhci, A smoothing technique for reduced integration penalty methods in contact problems, International Journal for Numerical Methods in Engineering 18 pp 343– (1982) · Zbl 0479.73086 · doi:10.1002/nme.1620180303
[7] Peric, Computational model for 3-D contact problems with friction based on the penalty method, International Journal for Numerical Methods in Engineering 35 pp 1289– (1992) · Zbl 0768.73100 · doi:10.1002/nme.1620350609
[8] Haug, Frictionless contact of elastic bodies by finite element method and mathematical programming technique, Computers Structures 11 pp 55– (1980) · Zbl 0433.73097 · doi:10.1016/0045-7949(80)90146-7
[9] Francavilla, A note on numerical computation of elastic contact problems, International Journal for Numerical Methods in Engineering 9 pp 913– (1975) · doi:10.1002/nme.1620090410
[10] Sachdeva, A finite element solution for the two-dimensional elastic contact problems with friction, International Journal for Numerical Methods in Engineering 17 pp 1257– (1981) · Zbl 0461.73064 · doi:10.1002/nme.1620170809
[11] Cundall, A discrete numerical model for granular assemblies, Geotechnique 29 (1) pp 47– (1979) · doi:10.1680/geot.1979.29.1.47
[12] Shi GH Goodman RE Discontinuous deformation analysis New York 1984 269 277
[13] Shi, Two dimensional discontinuous deformation analysis, International Journal for Numerical and Analytical Methods in Geomechanics 9 pp 541– (1985) · Zbl 0573.73106 · doi:10.1002/nag.1610090604
[14] Shi, Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures, Engineering With Computers 9 pp 157– (1992) · doi:10.1108/eb023855
[15] AndrĂ©, Discrete element method to simulate continuous material by using the cohesive beam model, Computer Methods in Applied Mechanics and Engineering 213-216 pp 113– (2012) · Zbl 1243.74197 · doi:10.1016/j.cma.2011.12.002
[16] Bobet, Numerical models in discontinuous media: review of advances for rock mechanics applications, Journal of Geotechnical and Geoenvironmental Engineering 11 pp 1547– (2009) · doi:10.1061/(ASCE)GT.1943-5606.0000133
[17] Xu, Combined discrete finite element multiscale numerical method and its application, Chinese Journal of Computation Physics 6 pp 477– (2003)
[18] Azevedo, Hybrid discrete element/finite element method for fracture analysis, Computer Methods in Applied Mechanics and Engineering 195 pp 4579– (2006) · Zbl 1123.74049 · doi:10.1016/j.cma.2005.10.005
[19] Onate, Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems, Computer Methods in Applied Mechanics and Engineering 193 pp 3087– (2004) · Zbl 1079.74646 · doi:10.1016/j.cma.2003.12.056
[20] Munjiza, The Combined Finite-discrete Element Method (2004) · Zbl 1194.74452 · doi:10.1002/0470020180
[21] Munjiza, The combined finite discrete element method for structural failure and collapse, Engineering Fracture Mechanics 71 pp 469– (2004) · doi:10.1016/S0013-7944(03)00044-4
[22] Johnson, Contact Mechanics pp 1– (1985) · doi:10.1017/CBO9781139171731.002
[23] Timoshenko, Theory of Elasticity (1951)
[24] Petersson PE Crack growth and development of fracture zones in plain concrete and similar materials 1981
[25] Hillerborg, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research 6 pp 773– (1976) · doi:10.1016/0008-8846(76)90007-7
[26] Donald IB Giam P The ACADS slope stability program review Proc 6 t h International Symposium on Landslides 1992 3 1665 1670
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