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In industrial applications of multibody dynamics the standard time integration methods are implicit. They are tailored to small and medium-sized nonlinear differential-algebraic equations of motion that may contain stiff components resulting from stiff force elements [].

This paper investigates nonlinear vibration in a forced cantilever with a contact boundary. The cantilever is assumed as an Euler-Bernoulli beam, and the contact is specified by the Derjaguin-Müller-Toporov theory. The mathematical model is a linear non-autonomous partial-differential equation with a nonlinear autonomous boundary condition. The method of multiple scales is applied to calculate the steady-state response in principal resonance. The equation of response curves is derived from the solvability condition of eliminating secular terms. Numerical examples are presented to demonstrate the effects of the excitation amplitude, the damping coefficient, and the coefficients related to the contact boundary.

This paper extends the formulation of frictionless impact analysis of planar deformable bodies presented in [] to frictional impact. In the approach presented in that paper, a linear complementarity problem (LCP) on position level based on the Signorini conditions for the impact problem of continua was formulated. For this purpose, the normal gap distance between possible contact points was represented in terms of normal impact forces. Now, in order to consider the friction, this formulation may be appended to the formulation of tangential contact forces developed for continual contact in [, ]. The key issue behind this approach arises from this fact that in the case of deformable bodies, the behavior of impact in the tangential direction is similar to that of the continual contact for a short period of time. However, it is obvious that this assumption is valid only for impact analysis of deformable bodies and in the case of rigid bodies impact analysis, these two events must be distinguished.

We introduce a new approach for control based load-balanced particle simulation, applying a recursive domain decomposition scheme that enables a minimization of communication expense and efficient hierarchical parallel neighborhood search, especially optimized for multiuser clusters of workstations with fluctuating processor loads.

The non-smooth modeling of mechanical and electrical systems allows for ideal unilateral contacts, sprag clutches and dry friction in mechanical systems and for ideal diodes and switches in electrical systems. The formulation of nonsmooth electrical models is demonstrated by the example of the DC-DC buck converter using the flux approach. The non-smooth electrical elements are described with set-valued branch relations in analogy with set-valued force laws in mechanics. With the set-valued branch relations, the dynamics of the circuit are described as measure differential inclusions. The measure differential inclusions obtained for the DC-DC buck converter are related to an analogous mechanical system. For the numerical solution, the measure differential inclusions are formulated as a measure complementarity system and discretised with a difference scheme, known in mechanics as time-stepping. For every time-step a linear complementarity problem is obtained.

The softened rolling contact of two paper machine rolls is considered. A regenerative excitation source can exists in the system due to the finite relaxation time of the roll cover polymer materials. The modeling of the rolls is described by multibody substructuring methodology and the polymer cover layer between the rolls in contact is modeled by contact spring reaction forces calculated according to the stiffness of the layer. The regenerative excitation is introduced to the system as a time delay term and it is calculated from the penetration history of the cover layer. The solution of the system equations is obtained by numerical time integration by utilizing the method of steps time delay equation solution procedure. Some numerical results are illustrated.

The discrete (or distinct) element method (DEM) has been recently recognized as efficient numerical tool for solving many scientific and technological problems in various fields of engineering. The method started in the 70-ies with its first application to simulate the dynamic behaviour of granular material in the work of Cundall and Strack []. Unlike the continuum approach, the DEM presents particulate material as an assemblage of discrete elements. It is based on the Lagrangian approach, according to which particles of granular material are treated as contacting bodies, while the dynamical parameters (i. e. position, velocity, orientation, etc.) of each body are tracked during the simulation. Some variations on the theme of DEM and granular materials may be found in []–[].

In this article a generalized elasto-plastic model for the plane frictional contact of rigid bodies is presented. The basic assumptions for this model are the rigidness of the plane contact area and locally acting friction.

Axially elastic rods are basic machine elements in hydraulic hammers, pilers and percussive drills []. The problem to analyze the motion history of such mechanisms is a very complex one, because the rods are simultaneously in large amplitude axial motion superimposed with a small amplitude elastic wave motion. The wave motion experiences division to reflected and transmitted components at each rod-rod interface depending on the current boundary stiffness []. The wave motion in each rod can be computed by finite elements or alternatively in space of semidefinite eigenfunctions. The feasibility of these methods in solving wave propagation problems in multi-rod systems with nonlinearly behaving rod-rod interfaces has been investigated and evaluated. The object of the experimental case study is a classical Hopkinson split bar apparatus [] used in experimental analysis of material response to shock pulses. Another example representing a pile hammering system [] evaluates the computational performance of the proposed approaches in long-term simulation of a complete work process.

Regularization methods based on the penalization of the tangent displacements are among the most exploited techniques in combination with finite element methods to model frictional interactions. Usually the global tangent displacements are described via convective coordinates which are e.g. used in a finite element discretization of the contact surface. These displacements serve to compute the tangent tractions in the case of sticking via a regularization procedure as well as in the case of sliding via a return-mapping scheme. The convective coordinates of the contact point as well as the corresponding tangent tractions are considered as history variables and have to be stored for each load step. In this contribution, we discuss the particular issue of continuous transfer for history variables in the case of large deformation problems adapted for the covariant contact description developed in Konyukhov and Schweizerhof []. Some specific examples are chosen to illustrate the effect of incorrect transfer for both non-frictional and frictional problems and, therefore, the necessity of the proposed techniques.