Abstract
In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.
Highlights
The analytical methods of mechanics, clearly stated in Lagrange’s book (1788) [1], were alternative formulations to Newton-Euler’s equations of motion (EoM)
If the system has a large number of bodies, with many constraints, the use of this method becomes problematic in determining the dynamic response of such a system [19,20]
The main step the finite element analysis (FEA) of an elastic multibody system (MBS) is to obtain the equations of motion for the finite elements chosen forindiscretization
Summary
The analytical methods of mechanics, clearly stated in Lagrange’s book (1788) [1], were alternative formulations to Newton-Euler’s equations of motion (EoM). Have rarely been used by researchers to solve practical engineering problems related to the evolution of mechanical systems They have advantages in terms of the number of the equations needed for modeling and computational effort. Lagrange multipliers and reducing the number of computation operations [13] Due to these advantages, it may become a procedure and researchers are beginning to use it with predilection in the analysis of modern mechanical systems [14]. The feedback linearization technique in the case of control systems with which robots and manipulators are equipped naturally leads to the application of these types of equations They are a simple way to obtain the equations of motion of the system in the case of non-holonomic liaisons. The Hamilton method could have the advantage of providing us with a system of first-order equations, a system that can be used directly for numerical solving, without the need for the prior processing of obtained systems [25]
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