The existing finite element software mainly uses solid and shell elements of the preset crack to simulate the bending effect of the crack structure but not the beam element. This paper proposes a new element based on fiber beam element, which can be used to perform bending analysis of cracked structures.
In the simplified computational model based on the Euler-Bernoulli theory, the Dirac-delta function is introduced into the beam element’s curvature function to represent the crack. The shape function of the cracked beam element is obtained by combining the displacement field function obtained by the integral curvature function with the finite element theory. Then, using the principle of virtual displacement, the element stiffness matrix is obtained by the Strain matrix that differential shape function. The crack section’s deformation and resisting force is calculated utilizing the properties of the d function.
Two numerical examples of the element are presented in order to substantiate the proposed element. They cover both the numerical model of linear and nonlinear static bending analysis. The analysis result was compared with the corresponding analytical solution and numerical solution, thus proving the quality of the proposed cracked fiber beam element.
The cracked fiber beam element is proposed and implemented in the finite element program framework.
