A Time‐Stepping Algorithm for Stiff Mechanical Systems with Unilateral Constraints

Funk, Kilian; Pfeiffer, Friedrich

doi:10.1002/pamm.200310099

Cited by 8 publications

(8 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We refer to the works of Murty and Yu and Acary and Brogliato for details on linear complementarity problems and their numerical treatment. As a modification of Lemke's algorithm, a mechanically feasible pivoting strategy was proposed in the work of Funk and Pfeiffer . Typically, Moreau's time‐stepping scheme is assumed to have a possible impact, and therefore a velocity jump at the midpoint of the considered integration step, see for example other works.…”

Section: Moreau‐type Integratorsmentioning

confidence: 99%

Time finite element based Moreau‐type integrators

Capobianco

Eugster

2018

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary With the postulation of the principle of virtual action, we propose, in this paper, a variational framework for describing the dynamics of finite dimensional mechanical systems, which contain frictional contact interactions. Together with the contact and impact laws formulated as normal cone inclusions, the principle of virtual action directly leads to the measure differential inclusions commonly used in the dynamics of nonsmooth mechanical systems. The discretization of the principle of virtual action in its strong and weak variational form by local finite elements in time provides a structured way to derive various time‐stepping schemes. The constitutive laws for the impulsive and nonimpulsive contact forces, ie, the contact and impact laws, are treated on velocity‐level by using a discrete contact law for the percussion increments in the sense of Moreau. Using linear shape functions and different quadrature rules, we obtain three different stepping schemes. Besides the well‐established Moreau time‐stepping scheme, we can present two alternative integrators referred to as symmetric and variational Moreau‐type stepping schemes. A suitable benchmark example shows the superiority of the newly proposed integrators in terms of energy conservation properties, accuracy, and convergence.

show abstract

Section: Moreau‐type Integratorsmentioning

confidence: 99%

Time finite element based Moreau‐type integrators

Capobianco

Eugster

2018

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…The problem is similar to the one connected with the analysis of frictional contact problems solved via complementarity methods [28] …”

Section: Algebraic Descriptionmentioning

confidence: 99%

Formulation of the tangential velocity slip problem in terms of variational inequalities

Strozzi

Giacopini

Bertocchi

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part J:

View full text Add to dashboard Cite

This contribution deals with a modelling of the tangential velocity slip problem in terms of variational inequalities. In particular, various technical situations for which the slippage problem appears to play an important role are first reviewed. Then, a mathematical formulation in terms of variational inequalities is developed where the critical shear stress criterion is considered. The theoretical conditions under which a unique solution exists are also discussed and an algebraic description based upon a complementarity approach is presented. Preliminary numerical results end the paper and a validation versus an analytical solution is proposed.

show abstract

“…Klarbring and Björkman (1988) used this strategy to reduce the problem to a generalized linear complementarity problem (LCP). A more elegant algorithm is briefly described by Funk and Pfeiffer (2003) and has been implemented and explained in more detail by Bertocchi (2008).…”

Section: Evolution Of the Systemmentioning

confidence: 99%