An alternative formulation of geometrical stiffness matrix for thin-walled I-beam element

摘要

To simplify laborious procedure in formulating geometric stiffness matrix of thin-walled beam element, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. First the Yang et al.'s simplified geometric stiffness matrix [k_g]_(12×12) of a rigid beam element was applied to the basis of geometric stiffness of a narrow beam element. So we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [k_g]_(14×14) of an I-beam element. It is emphasized that the nodal warping deformations are included. From the derived [k_g]_(14×14) matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [k_g]_(14×14) matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures.