Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element

Abstract

When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of motion for a single finite element. The paper presents an alternative method of calculation theses using the Gibbs−Appell (GA) formulation, which requires a smaller number of calculations and, as a result, is easier to apply in practice. For this purpose, the energy of the accelerations for one single finite element is calculated, which will be used then in the GA equations. This method can have advantages in applying to the study of multi-body systems with elastic elements and in the case of robots and manipulators that have in their composition some elastic elements. The number of differentiation required when using the Gibbs−Appell method is smaller than if the Lagrange method is used which leads to a smaller number of operations to obtain the equations of motion.

Keywords

• gibbs–appell
• energy of accelerations
• finite element
• nonlinear system
• elastic elements
• analytical dynamics
• robotics