惯性矩二次变化变截面梁柱几何非线性分析

为研究考虑剪切变形的变截面梁杆结构几何非线性问题,应用Timoshenko梁理论,采用位移、转角独立插值的方法,获取考虑剪切影响的惯性矩二次变化变截面梁单元的形函数;从严格的虚功增量方程出发,建立同时考虑轴力、剪切、弯曲效应及其耦合项的平面变截面梁柱单元几何非线性增量平衡方程,得到惯性矩二次变化变截面梁单元大位移切线刚度阵;与经典算例进行对比,验证了本文方法的精确性与有效性．

Geometric nonlinear analysis of tapered beam with inertia moment vary quadratic

To research the geometric nonlinear problem of tapered beam with shear deformation, based on Timoshenko theory, the displacement and rotation independent interpolation method was adopted to obtain the shape functions of tapered beam considering shear deformation, whose inertia moment varied quadratic. Then, started from the virtual work increment equation, the geometric nonlinear incremental equilibrium equation of the plane tapered beam element was established, including axial force, shear effect, bending effect and its coupling term, and the large displacement tangential stiffness matrix of the tapered beam was obtained. Finally, the classical examples are calculated, and the results show that the proposed method is accurate and effective.