Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias / High order mass matrix, velocity dispersion and spurious wave reflection

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

The main subject of this work is to qualify, quantify and implement the numerical behavior of discrete structures through the finite element method. It will be investigated only the dynamic onedimensional linear elements, but the applicability of the proposed formulation can be extended to the bi and tri-dimensional cases. It begins with an introduction to the theme. With some mathematical development, the related numerical error can be isolated analytically. Once the truncation error is isolate, a high precision numerical response is obtained. Inspired in the Newmark time integrator, unconditionally stable elements for spurious effects are idealized. The evanescent effect is a spurious phenomenon where the wave propagates along the structure subjected to a numerical damping in the spatial domain. Another effect analyzed here is the spurious wave reflection. When two adjacent elements have different lengths, a reflected wave exists (two waves for the beam element) at their interface. This wave, which meaning is purely mathematical, exists due to the difference of their absolute mass and stiffness between the finite elements involved, even when both elements have the same physical properties. The rate between the time increment and the period of oscillation is conveniently employed as the main parameter to quantify the time discretization. In the spatial domain, the used parameter is the relation between the element and the wave length.

ASSUNTO(S)

structural dynamics timoshenko elementos finitos ondas espúrias dinâmica estrutural finite element timoshenko evanescent waves precisão numérica numerical precision ondas evanescentes spurious wave reflections

ACESSO AO ARTIGO

Documentos Relacionados