Numerical integration for the inverse dynamics of a large class of cranes

Multibody System Dynamics - A recently developed index reduction method is applied to comparatively complicated underactuated mechanical systems in the context of inverse dynamics. The inverse...     

An energy–momentum consistent method for transient simulations with mixed finite elements developed in the framework of geometrically exact shells

In this paper, a mixed variational formulation for the development of energy–momentum consistent (EMC) time‐stepping schemes is proposed. The approach accommodates mixed finite elements based on a Hu–Washizu‐type variational formulation in terms of displacements, Green–Lagrangian strains, and conjugated stresses. The proposed discretization in time of the mixed variational formulation under consideration yields an EMC scheme in a natural way. The newly developed methodology is applied to a high‐performance mixed shell finite element. The previously observed robustness of the mixed finite element formulation in equilibrium iterations extends to the transient regime because of the EMC discretization in time. Copyright © 2016 John Wiley & Sons, Ltd.     

Energy-momentum-entropy consistent numerical methods for large-strain thermoelasticity relying on the GENERIC formalism

In the present paper, structure-preserving numerical methods for finite strain thermoelastodynamics are proposed. The underlying variational formulation is based on the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) formalism and makes possible the free choice of the thermodynamic state variable. The notion “GENERIC consistent space discretization” is introduced, which facilitates the design of Energy-Momentum-Entropy (EME) consistent schemes. In particular, three alternative EME schemes result from the present approach. These schemes are directly linked to the respective choice of the thermodynamic variable. Numerical examples confirm the structure-preserving properties of the newly developed EME schemes, which exhibit superior numerical stability.     

On transformations and shape functions for enhanced assumed strain elements

We summarize several previously published geometrically nonlinear EAS elements and compare their behavior. Various transformations for the compatible and enhanced deformation gradient are examined. Their effect on the patch test is one main concern of the work, and it is shown numerically and with a novel analytic proof that the improved EAS element proposed by Simo et al in 1993 does not fulfill the patch test. We propose a modification to overcome that drawback without losing the favorable locking-free behavior of that element. Furthermore, a new transformation for the enhanced field is proposed and motivated in a curvilinear coordinate frame. It is shown in numerical tests that this novel approach outperforms all previously introduced transformations.     

Extension of the enhanced assumed strain method based on the structure of polyconvex strain-energy functions

In this work, two well-known approaches for mixed finite elements are combined to render three novel classes of elements. First, the widely used enhanced assumed strain (EAS) method is considered. Its key idea is to enhance a compatible kinematic field with an incompatible part. The second concept is a framework for mixed elements inspired by polyconvex strain-energy functions, in which the deformation gradient, its cofactor and determinant are three principal kinematic fields. The key idea for the novel elements is to treat enhancement of those three fields separately. This approach leads to a plethora of novel enhancement strategies and promising mixed finite elements. Some key properties of the newly proposed mixed approaches are that they are based on a Hu-Washizu type variational functional, fulfill the patch test, are frame-invariant, can be constructed completely locking free and show no spurious hourglassing in elasticity. Furthermore, they give additional insight into the mechanisms of standard EAS elements. Extensive numerical investigations are performed to assess the elements' behavior in elastic and elasto-plastic simulations.     

Conservation of generalized momentum maps in mechanical optimal control problems with symmetry

In this paper, a structure‐preserving direct method for the optimal control of mechanical systems is developed. The new method accommodates a large class of one‐step integrators for the underlying state equations. The state equations under consideration govern the motion of affine Hamiltonian control systems. If the optimal control problem has symmetry, associated generalized momentum maps are conserved along an optimal path. This is in accordance with an extension of Noether's theorem to the realm of optimal control problems. In the present work, we focus on optimal control problems with rotational symmetries. The newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem. This is true for a variety of one‐step integrators used for the discretization of the state equations. Examples are the one‐step theta method, a partitioned variant of the theta method, and energy‐momentum (EM) consistent integrators. Numerical investigations confirm the theoretical findings. Copyright © 2016 John Wiley & Sons, Ltd.     

Validation of flexible multibody dynamics beam formulations using benchmark problems

As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.     

Multiple-reason decision making based on automatic processing.

It has been repeatedly shown that in decisions under time constraints, individuals predominantly use noncompensatory strategies rather than complex compensatory ones. The authors argue that these findings might be due not to limitations of cognitive capacity but instead to limitations of information search imposed by the commonly used experimental tool Mouselab (J. W. Payne, J. R. Bettman, & E. J. Johnson, 1988). The authors tested this assumption in 3 experiments. In the 1st experiment, information was openly presented, whereas in the 2nd experiment, the standard Mouselab program was used under different time limits. The results indicate that individuals are able to compute weighted additive decision strategies extremely quickly if information search is not restricted by the experimental procedure. In a 3rd experiment, these results were replicated using more complex decision tasks, and the major alternative explanations that individuals use more complex heuristics or that they merely encode the constellation of cues were ruled out. In sum, the findings challenge the fundaments of bounded rationality and highlight the importance of automatic processes in decision making. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Transient 3d contact problems—NTS method: mixed methods and conserving integration

The present work deals with a new formulation for transient large deformation contact problems. It is well known, that one-step implicit time integration schemes for highly non-linear systems fail to conserve the total energy of the system. To deal with this drawback, a mixed method is newly proposed in conjunction with the concept of a discrete gradient. In particular, we reformulate the well known and widely-used node-to-segment methods and establish an energy-momentum scheme. The advocated approach ensures robustness and enhanced numerical stability, demonstrated in several three-dimensional applications of the proposed algorithm.