A novel finite element model for large deformation analysis of cracked beams using classical and continuum-based approaches

A new one-dimensional finite element model is developed to investigate the nonlinear elastic response of cracked beams. Classical and continuum-based approaches are adopted into four different nonlinear theories to derive relationships which characterize the influence of initial cracks on the bending behavior of beams subjected to quasi-static loading. A linear rotational spring is used to simulate the crack whose stiffness factor is considered in terms of the geometric parameters of the crack. A cracked element is subdivided into two sub-elements, and the conditions of continuity are maintained in the crack position. By implementing a novel technique in this element, the tangent and secant stiffness matrices and the internal force vector are originally enriched due to the crack properties. Some case studies are performed to compare the rate of convergence, the accuracy of the theories, the difference in results obtained from linear and nonlinear analyses and the effects of the depth and the position of single and double cracks on the deflection pattern.