Exact statement of the instability problem for frames and its direct numerical solution
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A general approach for the systematic evaluation of the critical buckling load and the determination of the buckling mode is presented. The Navier-Bernoulli beam model is considered, having the possibility of variable cross-section under any type of load (including pressures and thermal loading). With this purpose, the equilibrium equations of each beam element in its deformed configuration under the hypothesis of infinitesimal strains and displacements is considered, resulting in a system of differential equations with variable coefficients for each element. To obtain the nonlinear response of the frame, one should impose the compatibility of displacements and the equilibrium of forces and moments in each beam-end, also in the deformed configuration. The solution is obtained by requiring that the total variation of potential energy is zero at the instant of buckling. The objective of this work is to develop a systematic method to determine the critical buckling load and the bucklingmode of any frame without using the common simplifications usually assumed in matrix analysis or finite element approaches. This way, precise results can be obtained regardless of the discretization done.
Keywordscritical buckling load buckling mode variable inertia thermal loading
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- 1.A. Chajes, Principles of Structural Stability Theory ((Prentice Hall, New Jersey, 1974).Google Scholar
- 2.S. Timoshenko, Theory of Elastic Stability (McGraw-Hill, New York, 1963).Google Scholar
- 3.M. Crisfield, Non-linear Finite Element Analysis of Solids and Structures. Vol.1: Essentials (JohnWiley & Sons, New York, 2000).Google Scholar
- 7.J. Marsden and T. Hughes, Mathematical Foundations of Elasticity (Dover Publications, New York, 1994).Google Scholar
- 8.R. Burden and J. Faires, Numerical Analysis (Thomson, Mexico, 1998).Google Scholar
- 10.D. A. Gulyaev, A. A. Zagordan, and V. I. Shalashilin, “Some Nonconventional Buckling Problems for a Beam under Transverse Loads,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 111–117 (2006) [Mech. Solids (Engl. Transl.) 41 (2), 87–92 (2006)].Google Scholar
- 11.COSMOS/M, v.2.95 (Structural Research and Analysis Corp., Los Angeles, 2006).Google Scholar
- 12.V. A. Postnov and G. A. Tumashik, “Stability Optimization of a Cantilever Beam Subjected to a Non-Conservative Compressive Force,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 93–103 (2006) [Mech. Solids (Engl. Transl.) 41 (2), 72–80 (2006)].Google Scholar