Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics

This paper develops a formalism for the design of conserving time-integration schemes for Hamiltonian systems with symmetry. The main result is that, through the introduction of a discrete directional derivative, implicit second-order conserving schemes can be constructed for general systems which preserve the Hamiltonian along with a certain class of other first integrals arising from affine symmetries. Discrete Hamiltonian systems are introduced as formal abstractions of conserving schemes and are analyzed within the context of discrete dynamical systems; in particular, various symmetry and stability properties are investigated.

Time Integration and Discrete Hamiltonian Systems

The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#

https://hosting.umons.ac.be/html/mecara/grasmech/PaperWasfyNoor.pdf

Computational strategies for flexible multibody systems

A generalized formulation of the Energy-Momentum Methodwill be developed within the framework of the GeneralizedMethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response. Furthermore, the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the Constraint Energy-Momentum Algorithm. The goal of this general approach of implicit energyconserving and decaying time integration schemes is, to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties. Numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non-linear structural dynamics. Among the methods considered will be the Newmark Method, the classical -methods, the Energy-Momentum Methodwith and without numerical dissipation, the Constraint EnergyMomentum Algorithm and the Constraint Energy Method. Copyright ? 1999 John Wiley & Sons, Ltd.

Energy‐conserving and decaying Algorithms in non‐linear structural dynamics

Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics

New procedures are proposed for implicit dynamic analysis using the finite element method. The main aim is to give stable solutions with significant rigid-body motions, in particular rotations. In contrast to most conventional approaches, the time-integration strategy is closely linked to the ‘element technologies’ with the latter involving a form of co-rotational procedure. For the undamped situation, one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied (i.e. with gravity loading).

J. Shi

Papers

A co‐rotational element/time‐integration strategy for non‐linear dynamics