In the field of multibody dynamics, structural components, such as beams or plates, have been discretized in different ways, according to special requirements of certain problem configurations. In literature, models, which follow the same mechanical theories but a different numerical discretization technique, such as the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF), have been calculated for comparison. In existing examples, the solutions of these calculations do not always coincide very accurately. Therefore, in the present contribution, which is an extension of a former work of the authors, standard static and dynamic problems in the large deformation regime are treated. Special emphasis is laid on converged solutions, using an analytical reference value in the static case. For dynamic examples a reference value based on the strain energy is provided, in order to simplify the comparison of the different formulations and to provide a reference value, similar to the static case, for future studies. For both formulations planar finite elements based on the Bernoulli Euler theory are utilized. In case of the ANCF the finite element consists of two position and two slope coordinates in each node only. In the FFRF beam finite element, as usual, two sets of coordinates are used to describe the actual configuration. The first set of coordinates defines the location and orientation of the body reference frame. The second set of coordinates describes small superimposed transverse and axial deflections relative to the body frame. The transverse deflections are approximated by means of two static modes for the rotation at the boundary and a user-defined number of eigen-modes of the clamped-clamped beam. The axial deflection is represented by a linear approach. In numerical studies, the accuracy of the two formulations is compared for two example problems, a cantilever beam with a singular force at the free end and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the results coincide in the converged case.

In extension to a former work, a detailed comparison of the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF) is performed for standard static and dynamic problems, both in the small and large deformation regimes. Special emphasis is laid on converged solutions and on a comparison to analytical and numerical solutions from the literature. In addition to the work of previous authors, the computational performance of both formulations is studied for the dynamic case, where detailed information is provided, concerning the different effects influencing the single parts of the computation time. In case of the ANCF finite element, a planar formulation based on the Bernoulli–Euler theory is utilized, consisting of two position and two slope coordinates in each node only. In the FFRF beam finite element, the displacements are described by the rigid body motion and a small superimposed transverse deflection. The latter is described by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. In numerical studies, the accuracy and computational costs of the two formulations are compared for a cantilever beam, a pendulum, and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the choice of the optimal formulation depends on the problem configuration. Recent claims in literature that the ANCF would have deficiencies compared with the FFRF thus can be refuted.

A 3D finite element model is developed to simulate the load noise in order to understand the acoustic and mechanical behavior of power transformers. As we can show, a 3D model is required to get a good correlation between the simulation and measurements, because some resonant modes are not axisymmetric and the phases influence each other. To reduce the complexity of the model we investigated different simplifications of the windings and their effect on the vibration results.

In the present paper, a comparison of the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF) is performed for standard static and dynamic problems, both in the small and large deformation regime. Special emphasis is laid on the converged solutions and a comparison to analytical and numerical solutions from the literature. In addition to the work of previous authors, the computational performance of both formulations is studied for the dynamic case, where detailed information is provided concerning the different effects influencing the single parts of the computation time. In case of the ANCF finite element, a planar formulation based on the Bernoulli-Euler theory is utilized, consisting of two position and two slope coordinates in each node only. In the FFRF beam finite element, the displacements are described by the rigid body motion and a small superimposed transverse deflection. The latter is described by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. In numerical studies, the accuracy and computational costs of the two formulations are compared for a cantilever beam, a pendulum and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the choice of the optimal formulation depends on the problem configuration. Recent claims in the literature that the ANCF would have deficiencies compared to the FFRF thus can be refuted.

AbstractNumerous contributions have been made concerning multibody systems, hydraulic actuators or the design of feedback controllers. A system that combines these fields has been studied rarely. In the present work the systematic simulation of an entire machine, which consists of structural mechanical elements where single masses are transported, hydraulic actuation systems and a closed loop controller is studied. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

hydraulic actuators. The computer-aided simulation of the mechanical behaviour of single machine elements is of increasing interest in industrial practice. With the software available at present, however, the simulation of an entire machine is possible only with rough approximations. This paper deals with the systematic simulation of a whole machine, the elements of which perform large movements. In extension of the existing literature, large rigid-body motions and flexible deformations are combined with hydraulic actuators and an appropriate automatic controller.

In the present Lecture, we study the motion of a single elasto-plastic body that represents a moving element of a structure or machine, where we present equations that are applicable to three-dimensional motions and bodies of arbitrary shape. We assume the displacements and strains of the body to be small with respect to a floating reference configuration, and we present the corresponding small-strain clasto-plastic-constitutive relations. We then point out the necessity of refined computational procedures for obtaining the plastic parts of strain in the case of a reversed loading, a problem often to be encountered in practice. In a Rayleigh-Ritz procedure, the flexible coordinates, which are coupled to the rigid-body degrees of freedom via the equations of motion, must be brought into connection with the plastic parts of strain. Often, the influence of the plastic parts of strain upon the motion of the body can not be neglected. We sketch an advantageous iterative numerical procedure for computing the plastic parts of strain, and we eventually discuss their influence upon the equations of motion in more detail.

Die computergestützte Simulation des mechanischen Verhaltens von Maschinenteilen nimmt in der industriellen Entwicklung einen hohen Stellenwert ein. Mit der derzeit zur Verfügung stehenden Software ist jedoch die Simulation einer gesamten Maschine oft nur unter groben Vernachlässigungen möglich. Der vorliegende Beitrag beschäftigt sich mit der systematischen Gesamtsimulation einer Maschine, bei welcher einzelne Teile große Bewegungen durchführen. In Erweiterung der vorliegenden Literatur werden große Starrkörperbewegungen und elastische Verformungen mit hydraulischen Stellgliedern und einem entsprechenden Regler kombiniert.

In the present work, we study biaxial vibrations of elasto-plastic beamswith a prescribed rigid-body motion. Exemplarily, we treat the case of ahinged-hinged beam with a rotation about a fixed hinge. Such a problemis frequently to be encountered in machine dynamics. The deformations ofthe beam are assumed to remain small. In order to describe the beamvibrations, we utilize the Bernoulli–Euler beam theory. Axial vibrationsof the beam are neglected. We study cases, in which the flexuralstiffness of the beam is considerably lowered due to catastrophicenvironmental influences, such that the deformations relative to therigid-body motion, albeit small, reach the plastic regime. In thepresent paper, special emphasis is laid upon including the effect ofgeometric stiffening due to a comparatively fast rigid-body rotation.The equations of motion are derived by Hamilton's principle. The biaxialdeflections are discretized in space by means of Legendre polynomials.The plastic strains are discretized over length, height and width of thebeam by small plastic cells. Galerkin's procedure, together with aproper implicit midpoint rule is used for integration of the equationsof motion. The plastic strains are computed in every time-step by asuitable iterative procedure. Linear elastic/perfectly plastic behavioris exemplarily treated in a numerical study.

Heavily loaded deformable structures performing rigid body motions may exhibit elastic as well as plastic strains, particularly when the elastic stiffness and the yield stress are considerably lowered by catastrophic environmental influences. The dynamic equations are derived from the Newton‐Euler equations. Plastic strains are included by an additive split of the total strains. Exemplarily we study the movement of a spherical pendulum.