Motion equation of a finite dynamic elastic plane lineal element plane lineal element

A linear finite element with constant cross section can take any orientation in the plane and its ends or nodes bind it to the rest of the elements. The kinetic (T) and potential (V) energy of a dynamic elastic element are the basis for the implementation of the Hamilton principle for the definition of a finite element. The definition of kinetic and potential energy is the first step for the preliminary variational formulation to the finite element enunciation that is used to solve, say, the problems of mechanisms that move in the plane using the Hamilton Equation. The general objective was to define the equation of motion of a dynamic elastic flat linear finite element using the Hamilton equation, from the Lagrangian (T –V) obtained with the use of a fifth and first degree polynomial, with eight degrees of freedom, four in each node, which represented the deformations: axial (u (x)), transverse (w (x)), slope ((dw (x) / dx)) and curvature ((d ^ 2w ( x) / dx ^ 2)). The deformation due to the transverse, insignificant shear compared to the flexional and axial deformation, the rotational inertia and the frictional forces in the joints, were rejected in order to produce a friendly element. The specific objectives were to produce: (a) the translation mass matrix [MD], (b) the gyroscopic translation matrix [AD], (c) the total translation rigidity matrix [KD], and (d) the deformation vector (S). As a result, the equation of motion of a dynamic elastic flat linear finite element was forged

• Autores: G Hossne, Américo
• Fecha de publicación: 2010
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: spa
• OAI Identifier: oai:repository.eafit.edu.co:10784/14482
• Acceso en línea: http://hdl.handle.net/10784/14482
• Palabra clave: Hamilton Principle; Dynamic Elastic Flat Linear Finite Element; Four-Bar Elastic Mechanisms; Lagrangian; Mass Matrix; Rigidity Matrix And Gyroscopic Matrix; Principio De Hamilton; Elemento Finito Lineal Plano Elástico Dinámico; Mecanismos Elásticos De Cuatro Barras; Lagrangiana; Matriz De Masas; Matriz De Rigideces Y Matriz Giroscópica
• License: Copyright (c) 2010 Américo G Hossne