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基于Euler-Bernoulli梁单元基本假定,通过静力凝聚获得截面特性沿单元轴向连续变化的变截面梁单元高精度刚度矩阵,并提出一种基于随动坐标法求解变截面梁杆结构大位移、大转动、小应变问题的新思路。首先依据插值理论和非线性有限元理论推导出三节点变截面梁单元的切线刚度矩阵,然后使用静力凝聚方法消除中间节点自由度,从而得到一种新型非线性两节点变截面梁单元。结合随动坐标法,在变形后位形上建立随动坐标系,得到变截面梁单元的大位移全量平衡方程。实例计算表明,该新型变截面梁单元具有较高的计算精度,可应用于变截面梁杆系统大位移几何非线性分析。
Based on the basic assumption of the Euler-Bernoulli beam element, the high-precision stiffness matrix of the variable-section beam element with continuous cross-section changes along the element axis is obtained by static coalescence. A new method based on the follow-up coordinate method is proposed to solve the large- Great Turn, a small strain of new ideas. Firstly, the tangent stiffness matrix of three-element beam with variable cross section is deduced based on interpolation theory and nonlinear finite element theory. Then, the static cohesion method is used to eliminate the degree of freedom of the intermediate node, so a new type of nonlinear two-node beam with variable section is obtained. In conjunction with the follow-up coordinate method, the follow-up coordinate system is established on the deformed shape, and the large-displacement total mass balance equation of the variable-section beam element is obtained. The case study shows that the new variable cross-section beam element has high calculation accuracy and can be applied to the geometric nonlinear analysis of large displacement beam-rod system.