Stress-Based Finite Element Methods for Dynamics Analysis of Euler-Bernoulli Beams with Various Boundary Conditions

Abstract

In this research, two stress-based finite element methods including the curvature-based finite element method (CFE) and the curvature-derivative-based finite element method (CDFE) are developed for dynamics analysis of Euler-Bernoulli beams with different boundary conditions. In CFE, the curvature distribution of the Euler-Bernoulli beams is approximated by its nodal curvatures then the displacement distribution is obtained by its integration. In CDFE, the displacement distribution is approximated in terms of nodal curvature derivatives by integration of the curvature derivative distribution. In the introduced methods, compared with displacement-based finite element method (DFE), not only the required number of degrees of freedom is reduced, but also the continuity of stress at nodal points is satisfied. In this paper, the natural frequencies of beams with different type of boundary conditions are obtained using both CFE and CDFE methods. Furthermore, some numerical examples for the static and dynamic response of some beams are solved and compared with those obtained by DFE method.

Modeling Dynamic Frequency Response on Slab Track of Shinkansen Railway Based on Finite Element Method

“…Since the rail is modeled by the Euler-Bernoulli beam elements, there is a (nonphysical) discontinuity in slope over the element boundaries due to the applied interpolation polynomials. us, insignificant disturbances in the wheel-rail contact force are observed when an element boundary is passed using Euler-Bernoulli beam elements [43,53,54].…”

Análise Dinâmica Do Modelo De Viga De Euler-Bernoulli via Método Das Diferenças Finitas

“…Em adição, é importante ressaltar que são latentes as pesquisas acerca do tema proposto que utilizam outros métodos numéricos que não o apresentado, tal como pode ser ilustrado pelas pesquisas de Scuciato, Carrer e Mansur (2016) e Heyliger e Reddy (1988). Gholampour et al (2017) avaliam a utilização de uma formulação de elementos finitos baseada em tensão e executam a análise estática e dinâmica de vigas com diversas condições de contorno comparando-a com a formulação de elementos finitos apoiada em deslocamentos. A configuração testada traz como grande vantagem a continuidade das tensões ao longo da malha nodal, além da continuidade dos deslocamentos.…”