Mixed linear complementarity formulation of discontinuous deformation analysis

Zheng, Hong; Li, Xiaokai

doi:10.1016/j.ijrmms.2015.01.010

Cited by 51 publications

(21 citation statements)

References 27 publications

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“…Usually, system G (u, v) = 0 represents the equilibrium condition; while the complementarity relationship in system (2) represents the constraints [32,33].…”

Section: Nonlinear Complementarity Problemsmentioning

confidence: 99%

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Zheng

Liu

2015

Computer Methods in Applied Mechanics and Engineering

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144

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“…Usually, system G (u, v) = 0 represents the equilibrium condition; while the complementarity relationship in system (2) represents the constraints [32,33].…”

Section: Nonlinear Complementarity Problemsmentioning

confidence: 99%

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Zheng

Liu

2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

144

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“…[24]. Here, g is the positive vector formed by collecting g   and g   of all the contact pairs; the second system…”

Section: Mixed Complementarity Formulations For Ddamentioning

confidence: 99%

“…In the formulation, however, the complementarity equations representing the tangential contact condition are nonlinear, which compromises the convergence and accuracy of this formulation. Recently, Zheng and Li [24] expressed all the contact conditions in terms of linear complementarity equations, and the nonlinearity is weakened greatly. Meanwhile, the discrete momentum conservation equations together with the contact equations in the linear complementarity form constitute the primal form of DDA.…”

Section: Introductionmentioning

confidence: 99%

Condensed form of complementarity formulation for discontinuous deformation analysis

Zheng

2015

Sci. China Technol. Sci.

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While the classical discontinuous deformation analysis (DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem (MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible. discontinuous deformation analysis, contact and impact, complementarity theory, non-smooth analysis, open-close iteration Citation:Li X K, Zheng H. Condensed form of complementarity formulation for discontinuous deformation analysis. Sci China Tech Sci, 2015, 58: 1509 1519,

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“…This scheme, with a strong numerical damping effect, is not only of high importance for the numerical stability of the DRBEM, but also to allow the oscillations caused by contact forces to dissipate rapidly if the modified DRBEM is coupled with the DDA method with iterative procedures for accurate contact force calculations. It should be mentioned that the DDA method has been reformulated by Zheng and Li [30] as a mixed complementarity problem, where the contact conditions are expressed by the complementarity equations and no artificial springs are needed. This advance of the DDA method avoids the introduction of the artificial parameters and the open-close iteration.…”

Section: Stepwise Updating Based Drbemmentioning

confidence: 99%

Dual reciprocity boundary element based block model for discontinuous deformation analysis

Guo

2015

Sci. China Technol. Sci.

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This paper presents a further development of the dual reciprocity boundary element method (DRBEM) with stepwise updating to pave the way for the introduction of boundary element mesh into the discontinuous deformation analysis (DDA). The advantage of the proposed method lies in its adoption of static fundamental solutions and reduction in the size of the governing equations by transforming the inertial term domain integrals to boundary integrals in the dynamic large displacement analysis. The unconditionally stable Newmark-β time integration method involving numerical damping to enhance the numerical stability is implemented for the dynamic analysis. In order to be coupled with the DDA to improve the deformability of the DDA block domains, a stepwise updating algorithm of the system variables is introduced. The stress updating in the analysis involved in the calculation of a domain integral and internal cells are used for the integration of the initial stress term. Several examples are used to verify the geometry-updated DRBEM model and satisfactory results have been obtained. boundary element method, stepwise updating, initial stress, large displacement Citation:Fu G Y, Ma G W, Qu X L. Dual reciprocity boundary element based block model for discontinuous deformation analysis.

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Mixed linear complementarity formulation of discontinuous deformation analysis

Cited by 51 publications

References 27 publications

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Condensed form of complementarity formulation for discontinuous deformation analysis

Dual reciprocity boundary element based block model for discontinuous deformation analysis

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