混凝土简支梁在均布荷载作用下的断裂过程区及自振特性

Fracture Process Zone and Natural Vibration Characteristics of Concrete Beam Under Uniform Distributed Forces

以"段-中川模型"为基础,叠加几种无限大体和半无限大体的弹性力学问题解答,用选点法近似满足边界条件,推导出了均布荷载作用下含断裂过程区混凝土简支梁的应力函数全场解析解;由能量法得到了梁的自振频率,分析了裂缝长度和断裂过程区长度对自振频率的影响;将断裂过程区的长度用节点非线性弹簧表示,采用Ansys软件数值模型模拟了带断裂过程区的混凝土简支梁,得到混凝土简支梁典型截面的应力分布、竖向位移、裂缝张开位移和自振频率。理论计算结果和仿真分析结果吻合较好。

The analytical solution of a simply supported beam under uniform distributed force with a fracture process zone is deduced based on the ＂Duan-Nakagawa＇s model＂ by superposition of several so- lutions of elastic mechanics problems, and its natural vibration frequency is calculated based on the ener- gy method. The influence of crack length and fracture process zone length on the natural frequency is analyzed. The FEA software ANSYS is used to simulate the fracture process for a simply supported concrete beam, in which, the cohesive forces in the fracture process zone are represented by the nonlin- ear springs. The stress distribution, the vertical displacement, the crack opening displacement, and the natural vibration frequency of the beam are demonstrated, which are in good agreement with the theo- retical calculation.