The purpose of this study is to present a solution scheme for the problem of out-of-plane instability of thin-walled members. Based on the second order kinematic field, the stiffness equation of linearized finite displacements is formulated for thin-walled members, and given in a concise and explicit form. As a particular case, an important and practical application is made for the lateral-torsional buckling of in-plane beams and frames. Numerical examples are given for straight and curved members, and are compared with existing results. The analysis scheme presented is proved accurate, efficient and versatile.
The purpose of this study is to establish a non-iterative efficient computational scheme to trace the nonlinear finite displacement behaviour of space frames, using the tangent stiffness equation of linearized fininte displacement of a thin-walled elastic straight beam element. Direct solution of the tangent stiffness equation is used, imposing adequately small increments. Local coordinates are updated at each incremental step, utilizing a vector multiplication scheme. Numerical results for a wide variety of spatial structures are given, demonstrating the versatility of the present scheme.
The explicit stiffness equations and the corresponding differential equations are formulated for a truss and a non-warping beam in the framework of the linearized finite displacement theory. The derivation is consistent with the theory of thin-walled members. One main objective is to show the exact correspondence between the stiffness equations and the differential equations with their boundary conditions. An alternative scheme of deriving the stiffness matrices is given as the direct modification of the already obtained matrix of thin-walled members.
The stiffness equation of linearized finite displacements for straight thin-walled members with inelastic material is derived. An arbitrary orthogonal coordinate system with a single reference point across the section need be introduced in the formulation, which is a clear distinction from the elasticity problem. Also distinct from the elastic analysis is a need to evaluate the magnitude of strains from time to time because of the dependence of the tangent modulus on strain levels. Illustrative examples are given to demonstrate the proposed method for the inelastic finite displacement analysis of spatial thin-walled members, with a simplified consideration on the effect of shear stresses.
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