Smoothing Newton method for solving two- and three-dimensional frictional contact problems

Leung, A.Y.T.; Chen, Guoqing; Wanji, Chen

doi:10.1002/(sici)1097-0207(19980330)41:6<1001::aid-nme319>3.0.co;2-a

Cited by 32 publications

(17 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(39), P ni ,P τ i ,θ i , dλ j (i = 1, 2, ..NC, j = 1, 2, ..NumGausP) are taken as unknowns, and the yield function f j and the incremental displacement du j , which should satisfy the equilibrium Eqs. (12) or (13), are the functions of these unknowns. The dimension of H is NumGaus P + 3 × N C. Note that Eqs.…”

Section: A Complete Non-smooth Nonlinear Equations Methods (Nnem2)mentioning

confidence: 99%

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

Soh

Chen

et al. 2006

Comput Mech

View full text Add to dashboard Cite

Based on the non-smooth nonlinear equations method for modeling three-dimensional elastic frictional contact problems (hereafter called NNEM), the extension to elastoplastic case in which the material nonlinearity is also involved is presented in this paper. Two approaches which combine two methods for solving elastoplastic problem with NNEM are proposed. A Numerical example is given to demonstrate the validation of the approaches.

show abstract

Section: A Complete Non-smooth Nonlinear Equations Methods (Nnem2)mentioning

confidence: 99%

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

Soh

Chen

et al. 2006

Comput Mech

View full text Add to dashboard Cite

show abstract

“…Techniques to deal with the discontinuities that inequalities invariably imply were adopted in the finite element context. Reference [11] presents a strategy for 'smoothing' the Newton-Raphson method for dealing with contact constraints and Bathe and Bouzinov [12] propose regularizations that allow differentiability at the expenses of accuracy. Recently, Areias and César de Sá [13] proposed a new second-order algorithm which allows a smoother transition between active and non-active contact constraints without modifying the constraint satisfaction accuracy.…”

Section: General Considerationsmentioning

confidence: 99%

“…3. Reduced-gradient methods, described in References [11,24,25], for example. Variants that use second-order information are based on a reduced Hessian matrix (e.g.…”

Section: Inequality Constraints Arising From the Non-penetration Condmentioning

confidence: 99%

Algorithms for the analysis of 3D finite strain contact problems

Areias

Sá

Curnis

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYFrom the constraint imposition aspects in 3D to friction regularization, various ideas are exposed in this paper. A variation of the Rockafellar Lagrangian is proposed which results in continuous second-order derivatives if Lagrange multiplier estimates are greater or equal than one. This fact allows the adoption of a full second-order (i.e. Lagrange-Newton) method avoiding sequential unconstrained minimization techniques. An algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods. A modified constraint definition to deal with non-smooth situations is presented. Aspects of friction implementation, including a regularization scheme which ensures stepwise objectivity, are detailed. Finally, several illustrative examples are carried out with success.

show abstract

“…First, one may treat the discretized system directly; we refer to [1,6,7,25,28] for Newtontype methods. A drawback of this approach is that it only applies in finite dimensions and that convergence results are difficult to obtain.…”

Section: Introductionmentioning

confidence: 99%

Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

Kunisch¹,

Stadler²

2005

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract. The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinitedimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an infinite-dimensional semi-smooth Newton method for the solution of the problem with given friction. The resulting algorithm is locally superlinearly convergent and can be interpreted as active set strategy. Combining the method with an augmented Lagrangian method leads to convergence of the iterates to the solution of the original problem. Comprehensive numerical tests discuss, among others, the dependence of the algorithm's performance on material and regularization parameters and on the mesh. The remarkable efficiency of the method carries over to the Signorini problem with Coulomb friction by means of fixed point ideas.Mathematics Subject Classification. 49M05, 49M29, 74M10, 74M15, 74B05.

show abstract

Smoothing Newton method for solving two- and three-dimensional frictional contact problems

Cited by 32 publications

References 20 publications

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

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

Algorithms for the analysis of 3D finite strain contact problems

Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

Contact Info

Product

Resources

About