The second part of the paper includes numerical tests verifying equations of motion of flexible bodies in absolute coordinates with rectangle and isosceles trapezoid finite elements. The equations are formulated in the first part of the paper. The verification is based on three types of problems: calculation of natural frequencies and modes, evaluation of buckling, and computation of large static and dynamic deflections of flexible bodies. Tests show good agreement with the theoretical results and the results obtained by other authors.
Equations of motion of a finite element in absolute coordinates including mass matrix, generalized inertia and internal forces are derived. A trapezoidal element for dynamic models of flexible shells in the shape of surface of revolution is considered. The element can be used for modeling dynamics of automotive tire and air spring bellows and some other flexible elements of transport systems undergoing large elastic deflections.
The second part of the paper continues a discussion on the topic of paralel computations in railway dynamics. The algorithms described in the first part of the paper are applied to parallel simulation on computers with multicore processors of six different models of rail vehicles and trains with the number of degrees of freedom from about one hundred to more than 20 thousands. A considerable simulation speedup is reported. In addition, an example of evaluation of wheel profile wear on multicore processors and comparison of different approaches to multi-variant computations are considered.
Parallel computations speed up simulation of multibody system dynamics, in particular, dynamics of railway vehicles and trains. It is important for reduction of required time at the stage of new railway vehicle design, for increase of complexity of studied problems and for real-time applications. We consider realization of paralel computations in Universal Mechanism software in three different areas: simulation of rail vehicle and train dynamics, evaluation of wheel profile wear and multi-variant computations. The use of clusters for parallel running of multi-variant computations is illustrated. Co-simulation based on the interface between Universal Mechanism and Matlab/Simulink and other software tools is discussed.
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