Exact Dynamic Element Stiffness Matrix of Shear Deformable Nonsymmetric Thin-walled Beams Subjected to Initial Forces

초기하중을 받는 전단변형을 고려한 비대칭 박벽보의 엄밀한 동적 요소강도행렬

Derivation procedures of exact dynamic element stiffness matrix of shear deformable nonsymmetric thin-walled straight beams are rigorously presented for the spatial free vibration analysis. An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The natural frequencies are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.