Keywords: finite element methods, hydraulic systems, modelling, simulation, coupled system, non-linear.

In this paper, we present a method for the modelling of a hydraulic driven flexible test system for a fusion reactor maintenance robot using a non-linear finite element method. The mechanical part of the robot test system is assembled by Reissner's geometrically exact beam elements and mass elements [1]. In the example the robot test system movement is caused by the modelling of the hydraulic cylinders as a separate first order differential equations. The hydraulic system is partitioned into elements that can be assembled together likewise in the finite element method [2]. A subsystem that contains the transmission line with orifices or volumes at the ends of transmission line can be considered as an element of hydraulic system. In the finite element analysis, the basic idea is to divide the whole hydraulic system into elements that can be assembled together. This assembling procedure gives the ordinary differential equation system and the Jacobian matrix for whole the hydraulic system. This approach will lead to a coupled three field mixed order ordinary differential equation system [3]. The governing equations of motion in the dynamic case are solved by using an implicit Newmark time integration method.

This paper introduces a new modelling technique for hydraulic systems. The hydraulic system is partitioned into elements that can be assembled together likewise in the finite element method. A subsystem that contains the transmission line with orifices or volumes at the ends of transmission line can be considered as an element of the hydraulic system. In the finite element analysis the basic idea is to divide the whole hydraulic system into elements that can be assembled together. This assembling procedure gives the ordinary differential equation system and the Jacobian matrix for whole the hydraulic system. Our modelling technique can be exploited in finite element codes where elements for the beams and bars already exist.

1

H. Marjamäki, J. Mäkinen, "Modelling a Telescopic Boom - The 3D Case: Part II", Computers & Structures, 84(29-30), 2001-2015, 2006. doi:10.1016/j.compstruc.2006.08.010

2

J. Mäkinen, H. Marjamäki, "Modelling Hydraulic Systems as Finite Elements", The 17th IASTED International Conference on Applied Simulation and Modelling (ASM-2008), Corfu, Greece, 23-25 Jun 2008.

3

H. Marjamäki, J. Mäkinen, "The Raising Movement of a Hydro-Mechanical Lift Frame", In M. Papadrakakis, D. Charmpis, N. Lagaros, Y. Tsompanakis, (Editors), "COMPDYN 2007 First International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2007)", Rethymno, Greece, 13-16 June 2007.

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