Geodesic
Postbuckling analysis of flexible elastic frame
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 105-117

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A completely geometrically nonlinear beam model based on the hypothesis of plane sections and expressed in terms of engineering strains and apparent stresses is applied to the structural analysis of frames. The numerical results are obtained by the Raley–Ritz method with a representation of solutions as a sum of analytical basis functions which were previously proposed by the authors. The convergence of approximate solutions is investigated. High degree of accuracy is demonstrated for both determination of the solution components and the fulfillment of equilibrium equations. It is shown that the limit values of external loads can substantially differ from those predicted by the Euler buckling analysis, which may lead to catastrophic consequences in designing thin-walled structures.
Keywords: geometrically nonlinear deformation, postbuckling, flexible frame, the analytical basis. 
@article{SJIM_2018_21_1_a9,
     author = {S. A. Khalilov and V. B. Mintiuk},
     title = {Postbuckling analysis of flexible elastic frame},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {105--117},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a9/}
}
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S. A. Khalilov; V. B. Mintiuk. Postbuckling analysis of flexible elastic frame. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 105-117. http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a9/