Non-smooth Nonlinear Equations Methods for Solving 3D Elastoplastic Frictional Contact Problems

Hu, Zhiqiang; Soh, Ai‐Kah; Chen, W. J.; Li, X. W.; Lin, Gao

doi:10.1007/s00466-006-0074-5

Cited by 10 publications

(4 citation statements)

References 13 publications

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“…Based on the discretization of the contact system using the SBFEM, the frictional contact conditions ( 6)-( 10) can be expressed as B-differentiable equations [2,3].…”

Section: The B-differentiable Equations 41 the Frictional Contact Con...mentioning

confidence: 99%

“…Thus, numerical methods have been widely used to analyze contact problems. The finite-element method [1][2][3][4][5], as the most commonly used numerical method, has been widely employed to solve contact problems. The FEM needs to discretize the full domain of the contact problem, which will increase the calculation amount.…”

Section: Introductionmentioning

confidence: 99%

“…Another key problem in contact analysis is how to enforce the contact constraint conditions. The penalty function method [1,27], Lagrange multiplier method [5,24,28], augmented Lagrange multiplier method [29] and mathematical programming method [3,4,22,30] are often used to treat contact constraint conditions. The penalty function method is an approximate method, which allows the contact bodies to embed with each other.…”

Section: Introductionmentioning

confidence: 99%

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A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems

Xue

Wang

et al. 2022

Fractal Fract

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Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact problems with small deformation in elastostatics. Only the boundaries of the contact system are discretized into surface elements by the scaled boundary finite-element method. The dimension of the contact system is reduced by one. The frictional contact conditions are formulated as B-differentiable equations. The B-differentiable Newton method is used to solve the governing equation of 3D frictional contact problems. The convergence of the B-differentiable Newton method is proven by the theory of mathematical programming. The two-block contact problem and the multiblock contact problem verify the effectiveness of the proposed method for 3D frictional contact problems. The arch-dam transverse joint contact problem shows that the proposed method can solve practical engineering problems. Numerical examples show that the proposed method is a feasible and effective solution for frictional contact problems.

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“…Based on the discretization of the contact system using the SBFEM, the frictional contact conditions ( 6)-( 10) can be expressed as B-differentiable equations [2,3].…”

Section: The B-differentiable Equations 41 the Frictional Contact Con...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems

Xue

Wang

et al. 2022

Fractal Fract

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“…Mathematical programming approaches for incremental state update are closely related to semi-smooth Newton methods [41][42][43][44][45][46][47][48][49][50][51] and to Newton-Schur methods [52][53][54] as illustrated in section 5.2.…”

Section: Introductionmentioning

confidence: 99%

A projected Newton algorithm for the dual convex program of elastoplasticity

Lotfian

Sivaselvan

2014

Numerical Meth Engineering

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SUMMARYIn this paper, we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems. The mathematical programming approach stems from energy-based descriptions of constitutive models. We describe a projected Newton algorithm to solve the dual optimization problem. This algorithm requires solution of an unconstrained optimization problem at the integration point level, rather than a constrained one as carried out by classical return-mapping schemes. Especially, implementation of multi-surface plasticity models is no more involved than that of single-surface models. We explore characteristics and performance of the projected Newton algorithm through numerical examples. Insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non-convex problems such as non-associated flow models.

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Research About Slider Nonlinear Contact Analysis of the Telescopic Boom with Cylinder Supporting

Shi-lin

Zhong-peng

2014

Lecture Notes in Electrical Engineering

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Non-smooth Nonlinear Equations Methods for Solving 3D Elastoplastic Frictional Contact Problems

Cited by 10 publications

References 13 publications

A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems

A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems

A projected Newton algorithm for the dual convex program of elastoplasticity

Research About Slider Nonlinear Contact Analysis of the Telescopic Boom with Cylinder Supporting

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