Formulation of cracked beam element for analysis of fractured skeletal structures

Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks

“…Christides and Barr [3] modified the Euler-Bernoulli beam theory to include the e↵ect of one or more pairs of symmetric open cracks in a structural member of simple geometric form. In Bouboulas et al [4], a cracked beam finite element for the modeling of fractured skeletal structures is introduced. The sti↵ness matrix of the cracked beam element is derived by using the direct sti↵ness method, which is a function of the crack depth and position.…”

Finite element modeling of a vibrating beam with a breathing crack: observations on crack detection

“…Yuen 4 considered that a crack in a finite element causes a reduction in its Young's modulus, while Bachschmid et al 5 represented the crack by reducing the cross-sectional area of the finite element at the crack position. Recently, Bouboulas and Anifantis 6 constructed a cracked finite element to approximate a conventional finite element with a crack. These so-called open crack models are based on the assumption that the crack always remains open during vibration.…”

Vibration Analysis of Cracked Beams Using the Finite Element Method

“…The majority of published studies assume that the crack in a structural member always remains open during vibration [3][4][5][6][7]. However, this assumption may not be valid when dynamic loadings are dominant.…”