钢筋混凝土三点弯曲梁裂缝扩展过程模拟

An extended finite element method for modeling crack propagation of reinforced concrete three-point bending beams

改进后的扩展有限元法位移函数能够更好地反映真实的裂缝尖端渐近位移场,而且无需后处理便可求得应力强度因子,从而为分析裂缝扩展过程提供了便利。为研究钢筋混凝土三点弯曲梁裂缝扩展过程的规律,采用改进后的扩展有限元方法模拟了不同配筋率和不同钢筋位置的三点弯曲梁。文中阐述了改进后扩展有限元法的基本原理,利用虚功原理推导了其支配方程,并介绍了钢筋混凝土三点弯曲梁的应力强度因子计算方法。研究表明:对于超筋结构,起裂断裂韧度与试件配筋率无关;钢筋处于临界位置时起裂韧度与失稳韧度均达到最小值0.567和1.666 9 MPa·m0.5,且钢筋贯穿裂缝时的断裂韧度小于钢筋未贯穿裂缝时的值,对含有宏观裂缝的结构进行锚杆加固时应将锚杆置于裂缝前端。

The displacement mode of the improved extended finite element method can reflect the true crack tip displacement and the stress intensity factor can be obtained without post-processing, so it is convenient to analyse the crack propagation process. In order to study the laws of crack propagation process, the reinforced concrete three-point bending beams having different steel reinforcement ratios and different positions are simulated by using the improved extended finite element method. The basic theory of the improved extended finite element method is studied, the governing equation is derived by using the virtual work principle, and then the stress intensity factor calculation method is described. The crack propagation process of the reinforced concrete three-point bending beams with different parameters is simulated by using the improved extended finite element method. The research results show that the initial fracture toughness is independent of reinforced ratio for surplus reinforcement beam. The fracture toughness reaches the minimum values when the bars are in the critical positions, which are larger when the bars don＇t run throughout the cracks than the bars running throughout the cracks. The bolt should be placed in the front of crack tip when the structure containing macroscopic crack is reinforced.