断裂过程区内聚力分布对简支梁刚度和自振特性的影响研究

Study on Influence of the Cohesion in Fracture Process Zone Cohesion Distribution on the Stiffness and Natural Vibration Frequency of Simply Supported Beam

对于含切口和断裂过程区简支梁受均布荷载作用的问题,选择弯矩作用下对称边裂纹的无限大板、均布荷载作用下的简支梁、切应力作用下的半无限大板、拉应力作用下的无限大板4种基本问题的应力函数叠加求解。基于"Duan and Nakagawa's Model",通过数学解析法和选点法得到了含断裂过程区简支梁的全场解析解。分析对比了无裂缝简支梁和断裂过程区内聚力呈水压力型、恒定型分布或权函数为一次型时简支梁的拉应变软化曲线和自振特性,发现内聚力呈水压力型分布与一次权函数下拉应变软化曲线有相似的变化趋势;无裂缝简支梁自振频率最高,内聚力恒定型次之,水压力型和一次权函数型时最低。

To solve the uniformly distributed load problem of simply supported beam with anedge-crack and the fracture process zone,the stress functions of four kinds of basic problems are chosen,including the infinite plate with symmetrical edge cracks under bending moment and tensile stresses,the simply supported beam under the uniform load,the semi-infinite plate under distributed shear stresses,and the infinite plate under distributed shear stresses tensile stress.Based on the Duan and Nakagawa＇s model,agroup of analytic solutions of a simply supported beam with the fracture process zone is yielded through mathematical analysis and point selection method.The obtained tensile strain softening curves and natural vibration frequencies of the simply supported beam are compared with the different cohesive distribution with water pressure type,constant type,and the assumed weight function being linear in fracture process zone.The tensile strain softening curve of the water pressure distribution is similar to the one under the linear weight function.The frequency of non-cracked simply supported beam is the biggest;the cohesion constant type is the second;and the water pressure type of cohesive and the one under the linear weight function are the lowest.