A parametric quadratic programming approach to elastic contact problems with friction

Zhong, Wanxie; Sun, Shulin

doi:10.1016/0045-7949(89)90066-7

Cited by 36 publications

(15 citation statements)

References 13 publications

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“…Substitution of (26), (27) (33) are known at the instant t o . Inequality (32) is a combination of all the constitutive relations From the point of view of optimum programming theory, the boundary value problem described in equations (1)- (6) and (26)- (29) may be regarded as an optimum control problem of the system.…”

Section: Parametric Variational Principle For Elastic-plastic Problemsmentioning

confidence: 99%

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Zhang

1995

Num Anal Meth Geomechanics

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SUMMARYFinite element procedures for numerical solution of various engineering problems are often based on variational formulations. In this paper, a parametric variational principle applicable to elastic-plastic coupled field problems in consolidation analysis of saturated porous media is presented. This principle can be used to solve problems where materials are inconsistent with Drucker's postulate of stability, such as in non-associated plasticity flow or softening problems. The finite element formulation was given, and it can be solved by either the conventional method or a parametric quadratic programming method.

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Section: Parametric Variational Principle For Elastic-plastic Problemsmentioning

confidence: 99%

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Zhang

1995

Num Anal Meth Geomechanics

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“…The numerical treatment of the unilateral contact with dry friction is certainly one of the non-smooth mechanics topics for which many efforts have been made in the past. In the literature, many attempts have been developed to deal with such problems using the finite element method, these include the penalty function method (Chan and Tuba, 1971;Parisch, 1989;Wriggers et al, 1990), the flexibility method (Francavilla and Zienkiewicz, 1975), the mathematical programming method (Klarbring and Björkman, 1988;Zhong and Sun, 1989;Zhang et al, 1998;Kim and Kwak, 1996), the Lagrange multiplier method (Chaudhary and Bathe, 1986) and the augmented Lagrangian method (Simo and Laursen, 1992;Feng, 1995;de Saxcé and Feng, 1998). A large number of algorithms for the modeling of contact problems by the finite element method have been presented in the literature.…”

Section: Introductionmentioning

confidence: 99%

A finite element finite-strain formulation for modeling colliding blocks of Gent materials

Feng¹,

Renaud²,

Cros³

et al. 2010

International Journal of Solids and Structures

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a b s t r a c tThe present paper is devoted to the analysis of the contact/impact problems with Coulomb friction and large deformation between two hyperelastic bodies of Gent model. The total Lagrangian formulation is adopted to describe the geometrically non-linear behavior. For the finite element implementation, the explicit expression of the incremental law of Gent model is derived. A first order algorithm is applied for the numerical integration of the time-discretized equation of motion. Efficiency and accuracy of the resulting method is illustrated on a two-dimensional static contact problem and a three-dimensional dynamic contact problem as compared with ANSYS simulations.

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“…The minimization is formulated as a mathematical programming problem and the solution can be obtained by using either linear programming or quadratic programming techniques (Chand et al 1976;Fischer and Melosh 1987;Hung and Saxce 1980;Klarbring 1986;Kikuchi and Oden 1988;Lee 1994). Zhong and Zhang (1988) and Zhong and Sun (1989) developed a parametric variational principle (PVP) for the analyses of plane contact problems and elastic plastic structures. The corresponding theories are further summarized in Zhong et al (1997).…”

Section: Introductionmentioning

confidence: 99%

A finite element model for contact analysis of multiple Cosserat bodies

et al. 2005

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The objective of this paper is to develop a finite element model for multi-body contact analysis of Cosserat materials. Based on the parametric virtual work principle, a quadratic programming method is developed for finite element analysis of contact problems. The contact problem with friction between two Cosserat bodies is treated in the same way as in plastic analysis. The penalty factors, that are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of contact problems of Cosserat materials, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. Compared with the conventional work on Cosserat elasticity, the newly developed model is on the contact analysis of the Cosserat materials and is seldom found in the existing literatures. Four examples are computed to illustrate the validity and importance of the model develope

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A parametric quadratic programming approach to elastic contact problems with friction

Cited by 36 publications

References 13 publications

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

A finite element finite-strain formulation for modeling colliding blocks of Gent materials

A finite element model for contact analysis of multiple Cosserat bodies

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