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

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-δ effect. 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.