Mass redistribution method for finite element contact problems in elastodynamics

Khenous, Houari B.; Laborde, P.; Renard, Yves

doi:10.1016/j.euromechsol.2008.01.001

Cited by 74 publications

(117 citation statements)

References 18 publications

(29 reference statements)

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“…In this case, it is advisable to change the time discretization of (37) like, e.g., described in [27,55]. But even then, the additional problem occurs that the computed contact stresses show spurious oscillations in time [30]. In order to avoid this, we employ a local modification of the mass matrix such that its entries associated with the potential contact nodes vanish.…”

Section: Frictional Contactmentioning

confidence: 99%

“…In this subsection, we exemplify the formation of the nonlinear semismooth operators K m H used in (30) for the cases of a nonlinear displacement stress relationship and frictional contact. For the for mer effect, the derivation of the function K m H proceeds along the lines of Section 2.1, but with the Cauchy stress tensor r in (1) being replaced by the first Piola Kirchhoff stress tensor P(u).…”

Section: Frictional Contactmentioning

confidence: 99%

“…We refer to [21] and the references therein for an overview of Newton methods and to [15,50] for the definition of semismoothness. The residuals of (31), (32) In the following, we transfer the idea of Algorithm 1 to (30). Be cause of the nonlinearity, we have to combine two iterative pro cesses, namely the semismooth Newton loop for the nonlinear effects and the subdomain iteration presented in Section 3.…”

Section: Iterative Solution Schemementioning

confidence: 99%

“…Be cause of the nonlinearity, we have to combine two iterative pro cesses, namely the semismooth Newton loop for the nonlinear effects and the subdomain iteration presented in Section 3. The natural way of doing so is to use Algorithm 1 to solve the tangential systems of the semismooth Newton iteration applied to (30). The corresponding scheme is summarized in Algorithm 2, using the notationẑ introduced in (17) …”

Section: Iterative Solution Schemementioning

confidence: 99%

“…In Sub section 5.2, we state the conditions of frictional contact as an exam ple for a nonlinear problem with inequality constraints and sketch how these conditions can equivalently be reformulated as a set of semismooth equations. Hence, we assume in the following that (30) can be solved by a generalized form of the Newton method for semismooth systems. We refer to [21] and the references therein for an overview of Newton methods and to [15,50] for the definition of semismoothness.…”

Section: Iterative Solution Schemementioning

confidence: 99%

See 4 more Smart Citations

Solving dynamic contact problems with local refinement in space and time

Hager

Hauret

Tallec

et al. 2012

Computer Methods in Applied Mechanics and Engineering

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International audienceFrictional dynamic contact problems with complex geometries are a challenging task from the compu tational as well as from the analytical point of view since they generally involve space and time multi scale aspects. To be able to reduce the complexity of this kind of contact problem, we employ a non conforming domain decomposition method in space, consisting of a coarse global mesh not resolving the local struc ture and an overlapping fine patch for the contact computation. This leads to several benefits: First, we resolve the details of the surface only where it is needed, i.e., in the vicinity of the actual contact zone. Second, the subproblems can be discretized independently of each other which enables us to choose a much finer time scale on the contact zone than on the coarse domain. Here, we propose a set of interface conditions that yield optimal a priori error estimates on the fine meshed subdomain without any artificial dissipation. Further, we develop an efficient iterative solution scheme for the coupled problem that is robust with respect to jumps in the material parameters. Several complex numerical examples illustrate the performance of the new scheme

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Section: Frictional Contactmentioning

confidence: 99%

Section: Frictional Contactmentioning

confidence: 99%

Section: Iterative Solution Schemementioning

confidence: 99%

Section: Iterative Solution Schemementioning

confidence: 99%

Section: Iterative Solution Schemementioning

confidence: 99%

See 3 more Smart Citations

Solving dynamic contact problems with local refinement in space and time

Hager

Hauret

Tallec

et al. 2012

Computer Methods in Applied Mechanics and Engineering

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Hybrid‐mixed discretization of elasto‐dynamic contact problems using consistent singular mass matrices

Tkachuk

Wohlmuth

Bischoff

2013

Numerical Meth Engineering

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SUMMARYAn alternative spatial semi-discretization of dynamic contact based on a modified Hamilton's principle is proposed. The modified Hamilton's principle uses displacement, velocity and momentum as variables, which allows their independent spatial discretization. Along with a local static condensation for velocity and momentum, it leads to an approach with a hybrid-mixed consistent mass matrix. An attractive feature of such a formulation is the possibility to construct hybrid singular mass matrices with zero components at those nodes where contact is collocated. This improves numerical stability of the semi-discrete problem: the differential index of the underlying differential-algebraic system is reduced from 3 to 1, and spurious oscillations in the contact pressure, which are commonly reported for formulations with Lagrange multipliers, are significantly reduced. Results of numerical experiments for truss and Timoshenko beam elements are discussed. In addition, the properties of the novel discretization scheme for an unconstrained dynamic problem are assessed by a dispersion analysis.

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A nonsmooth generalized‐ α scheme for flexible multibody systems with unilateral constraints

Chen

Acary

Virlez

et al. 2013

Numerical Meth Engineering

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SUMMARY Mechanical systems are usually subjected not only to bilateral constraints, but also to unilateral constraints. Inspired by the generalized‐ α time integration method for smooth flexible multibody dynamics, this paper presents a nonsmooth generalized‐ α method, which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions. Both the algorithm and the implementation are illustrated in detail. Numerical example tests are given in the scope of both rigid and flexible body models, taking account for both linear and nonlinear systems and comprising both unilateral and bilateral constraints. The extended nonsmooth generalized‐ α method is verified through comparison to the traditional Moreau–Jean method and the fully implicit Newmark method. Results show that the nonsmooth generalized‐ α method benefits from the accuracy and stability property of the classical generalized‐ α method with controllable numerical damping. In particular, when it comes to the analysis of flexible systems, the nonsmooth generalized‐ α method shows much better accuracy property than the other two methods. Copyright © 2013 John Wiley & Sons, Ltd.

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Mass redistribution method for finite element contact problems in elastodynamics

Cited by 74 publications

References 18 publications

Solving dynamic contact problems with local refinement in space and time

Solving dynamic contact problems with local refinement in space and time

Hybrid‐mixed discretization of elasto‐dynamic contact problems using consistent singular mass matrices

A nonsmooth generalized‐ α scheme for flexible multibody systems with unilateral constraints

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