Qualitative analysis of solutions to discrete static contact problems with Coulomb friction

Haslinger, Jaroslav; Janovský, Vladimír; Ligurský, Tomáš

doi:10.1016/j.cma.2010.09.010

Cited by 9 publications

(8 citation statements)

References 9 publications

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“…After finding a new tangent direction t, one restarts the predictor-corrector with (y k , t) and continues tracing a solution curve. A similar restarted predictor-corrector method has already been successfully tested on simple contact problems in [7,8], where computation of a suitable tangent for restart relies on precise expressions for sub-domains of smooth behaviour. The test examples presented at the end of the next section show that the predictor-corrector works well also with the tangent switch proposed here.…”

Section: Numerical Continuationmentioning

confidence: 97%

“…The principal idea of the present continuation strategy is the same as the one proposed in [7,8], namely, to continue smooth pieces of solution curves by a predictor-corrector method and to join the smooth pieces continuously.…”

Section: Numerical Continuationmentioning

confidence: 98%

“…A similar algorithm has already been tested on static contact problems in [7,8], but only on finite-element models with very small number of degrees of freedom. Here we show results for more realistic models.…”

Section: Introductionmentioning

confidence: 93%

“…Our approach is close to the continuation from [3] for normal maps with polyhedral convex sets, to the ones from [5,6] for frictionless contact problems or to the ones from [7][8][9] for plane contact problems with Coulomb friction. The main contrast to all those papers is that the present algorithm does not obey precise expressions of sub-domains of smooth behaviour of the PC 1 -function involved, which require quite detailed specification of the function during implementation.…”

Section: Introductionmentioning

confidence: 99%

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A continuation problem for computing solutions of discretised evolution problems with application to plane quasi-static contact problems with friction

Ligurský

Renard²

2014

Computer Methods in Applied Mechanics and Engineering

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A continuation problem for finding successive solutions of discretised abstract first-order evolution problems is proposed and a general piecewise C 1 continuation problem is studied. A condition ensuring local existence and uniqueness of its solution curves is given. An analogy of the first-order system of smooth problems is derived and results of existence and uniqueness of its solutions are stated. Possibility of continuation of a solution curve along directions solving the first-order system is discussed. A technique for numerical continuation of the solution curves is developed. Furthermore, an application of the abstract continuation problem is presented for plane quasi-static contact problems with friction. Various formulations of the first-order system are derived for this case so that the analysis from the abstract frame can be developed and supplemented. Finally, the proposed numerical continuation is tested on model examples.

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Section: Numerical Continuationmentioning

confidence: 97%

Section: Numerical Continuationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A continuation problem for computing solutions of discretised evolution problems with application to plane quasi-static contact problems with friction

Ligurský

Renard²

2014

Computer Methods in Applied Mechanics and Engineering

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“…Bifurcations can potentially occur and some mathematical studies have related the possible non-uniqueness of the solution to the size of the mesh and to the values of the friction coefficient (Hild and Renard, 2005;Haslinger et al, 2012). While a rigorous mathematical analysis aiming to investigate the existence of bifurcations and, if they do exist, their nature, is outside the scope of this paper, potential non-uniqueness can result in different solutions when segments of pipes whose lengths are different multiples of L N / p are considered.…”

Section: Fully Nested Multiscale Analysis Of Risersmentioning

confidence: 99%

An accurate and computationally efficient small-scale nonlinear FEA of flexible risers

2016

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a b s t r a c tThis paper presents a highly efficient small-scale, detailed finite-element modelling method for flexible risers which can be effectively implemented in a fully-nested (FE 2 ) multiscale analysis based on computational homogenisation. By exploiting cyclic symmetry and applying periodic boundary conditions, only a small fraction of a flexible pipe is used for a detailed nonlinear finite-element analysis at the small scale. In this model, using three-dimensional elements, all layer components are individually modelled and a surface-to-surface frictional contact model is used to simulate their interaction. The approach is applied on a 5-layered pipe made of inner, outer and intermediate polymer layers and two intermediate armour layers, each made of 40 steel tendons. The capability of the method in capturing the detailed nonlinear effects and the great advantage in terms of significant CPU time saving are demonstrated by comparing the results obtained on elements of pipe of different lengths, equal to one pitch length L p as

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A method of piecewise‐smooth numerical branching

Ligurský

Renard

2017

Z Angew Math Mech

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A method of numerical branching is proposed for piecewise-smooth steady-state problems when any analytical expressions are not known for the regions of smoothness of the function involved. The performance of the method is shown for model bifurcations in discretised contact problems with Coulomb friction. First, different parameter settings in its input are tested so that the optimum one can be proposed. Then, the method is used to investigate the behaviour of the bifurcations for different meshes. All solution branches seem to be discovered reliably if the parameters are set up properly.where . w denotes a suitable weighted norm [11, pp. 86 and 87]. Our branching method consists of two steps: an approximation of the end pointȳ and a subsequent location of new branches from a neighbourhood of the approximate end point.

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Qualitative analysis of solutions to discrete static contact problems with Coulomb friction

Cited by 9 publications

References 9 publications

A continuation problem for computing solutions of discretised evolution problems with application to plane quasi-static contact problems with friction

A continuation problem for computing solutions of discretised evolution problems with application to plane quasi-static contact problems with friction

An accurate and computationally efficient small-scale nonlinear FEA of flexible risers

A method of piecewise‐smooth numerical branching

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