Macro-Element With Generalized Degrees Of Freedom For Beam Fracture Analysis

Beams are the framework part of engineering structures, they often worked with crack defects in their service time. Under long-term load effect, crack will grow and may cause structure break down, so beam fracture behavior analysis is necessary. Stress intensity factor is the main parameter in fracture analysis, focused on traditional discrete models’deficiencies:1D beam(link) element discretization model cannot simulate singular field,2D (3D) entity element discretization model have large discrete degrees of freedom, and it’s hard to be applied in large-scale construction projects. Given this, Macro-element with generalized degrees of freedom are proposed for cracked beam fracture analysis, it realized the united of beam element and plane element. In fracture analysis, only crack area is meshed by2D element, main body still used ID beam element with low degree of freedoms, so it can reduce discrete degree of freedoms while simulating singular region in crack tip precisely. Main works in paper are as follows:(1) Responses of ID beam model and2D plane model are discussed, Transformation stiffness equation from plane element to Euler beam element is established, and so conversion between beam model and plane model in finite element method is proved to be practicable. (2) Based on Euler beam theory, involved Williams element, Macro-element with generalized degrees of freedom are proposed for cracked beam fracture analysis. The united of beam element and plane element are realized in it. Through FORTRAN95program, SIFs of I-II mixed mode crack in beam are determined.(3) Variation of neutral axis and applicability of Euler beam assumption in cracked beam is analyzed, theoretical Macro-element length is determined, at the same time, size effect function of SIF is established to improve the calculation accuracy and enhance applicability of this Macro-element.