GEOMETRIC NONLINEAR ANALYSIS FOR 3-D BEAM WITH HINGE BASED ON FIELD CONSISTENCY

In the previous study for the geometric nonlinear analysis of a 3-D beam element, the element tangential stiffness matrix is generally acquired by the geometric consistency rather than by field consistency. In this paper, a differentiation method is directly employed to derive the relationship of the incremental displacements between the structural deformation in a local coordinate system and the total displacement in an integral coordinate system. The field consistency is then used to achieve the element tangential stiffness matrix of the 3-D beam element under the conditions of large rotation and small strain. Moreover, according to the mechanical characteristics of a hinged beam, an explicit expression of the non-linear tangent stiffness matrix is derived to consider the effect of the hinged beam. A computer program is developed to analyze the geometrical nonlinear behavior of several classic examples with and without hinges. The results demonstrate the accuracy of the proposed innovative element, and illustrate promising practical value.