基于共旋法与稳定函数的几何非线性平面梁单元

A GEOMETRIC NONLINEAR PLANE BEAM ELEMENT BASED ON COROTATIONAL FORMULATION AND ON STABILITY FUNCTIONS

建立一个准确、高效的几何非线性梁单元对于描述杆系结构的非线性行为至关重要。该文基于共旋坐标法和稳定函数提出了一种几何非线性平面梁单元。该单元在形成中把变形和刚体位移分开,局部坐标系内采用稳定函数以考虑单元P-δ效应的影响,从局部坐标系到结构坐标系的转换则采用共旋坐标法以及微分以考虑几何非线性,给出了几何非线性平面梁单元在结构坐标系下的全量平衡方程和切线刚度矩阵;在此基础上根据带铰梁端弯矩为零的受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式。通过多个典型算例验证了算法与程序的正确性、计算精度和效率。

The establishment of an accurate and efficient geometric nonlinear beam element is significantly important for describing the nonlinear behavior of frame structures.This paper presents a geometric nonlinear plane beam element based on a co-rotational procedure and a stability function.The deformation is separated from the rigid body displacement during the formation of the element,and the stability function is used in the local coordinate system to consider the influence of the element P-δeffect.The co-rotational procedure method and the differential method are used to consider the geometric nonlinearity of the displacement transformation from the local coordinate system to the global one.The total equilibrium equation and tangent stiffness matrix of geometric nonlinear plane beam elements are developed in a global coordinate system.The expression of the element tangent stiffness matrix considering beam ends with hinges is derived according to the characteristics of zero bending moment at the end of the hinged beam.The accuracy and efficiency of the analytical method are verified by several typical examples.