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O. Dmitrochenko, G. Mikheev, D. Pogorelov, R. Gandikota. A nonlinear finite element for simulation of dynamics of beam structures using multibody system approach.

11th World Congress on  Computational Mechanics (WCCM XI), July 20-25, 2014, Barcelona, Spain, pp. 655-666.

Abstract.

Many engineering dynamic problems can be simulated as beam structures. For example, such models are applied in well drilling. Dynamic simulation allows optimizing shape of well bore and operations parameters of the drilling. Calculation speed of simulation of dynamics of a drill string depends on size of matrices of a model and on effectiveness of numerical methods.

The approach to simulation of dynamics of drill strings are suggested by the authors in [1]. The drill string is presented as a set of uniform beams connected via force elements. Flexibility of the beams is simulated using the modal approach. Thus, each beam has at least twelve degrees of freedom: six coordinates define position and orientation of a local frame and six modes are used for modeling flexibility. For simulation of the drilling processes, implicit Park method with Jacobian of stiff forces is used [2]. Analysis of vibration, rock cutting, buckling and post-buckling behaviour and other processes of the drilling can be successfully modeled using the approach. But it has some disadvantages.

Firstly, number of degrees of freedom can be decreased if a single nonlinear finite element model is used instead of the model including great number of beam subsystems. Secondly, simulation of real rotation of the drill string using the modal approach related to the problem with calculation of Jacobians from stiff force elements. The expressions of the modal coordinate derivatives of the stiff forces are variable since each mode is calculated in the local frame of the beam and rotate together with the frame.

[1]       D. Pogorelov, G. Mikheev, N. Lysikov, L. Ring, R. Gandikota and N.  Abedrabbo, A Multibody System Approach to Drill String Dynamics Modeling, 2012 Proceedings of the ASME 11th Biennial Conference on Engineering Systems Design and Analysis (ESDA2012), Volume 4, ISBN No: 978-0-7918-4487-8, pp. 53-62, 2012.
[2]       D. Yu. Pogorelov. Jacobian matrices of the motion equa­tions of a system of bodies. Journal of Computer and Systems Sciences International, 46, Nr. 4, 563–577, 2007.


 
 
 

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