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Buckling and Postbuckling of Conservative Systems
The static bifurcations of conservative systems are analyzed. With reference to discrete systems, the equilibrium points are classified. Then, a short review is given on the continuation numerical methods, which allow to construct the equilibrium paths as a function of the bifurcation parameter. By using analytical (perturbation) methods, the bifurcation from a trivial path is studied for general multi-degree of freedom systems. In particular, the bifurcation point is determined along the path, and the bifurcated branch is built in the neighborhood of the bifurcation point. The imperfections, both of geometric and load type, are successively included in the algorithm. Systems exhibiting precritical deformations are finally addressed, for which, first, the procedure for the asymptotic construction of the nontrivial path is illustrated and, then, a change of variable is introduced, able to transform the non-trivial into a trivial path. With reference to the latter form of the equations, the bifurcation point is determined.
Buckling and Postbuckling of Conservative Systems
The static bifurcations of conservative systems are analyzed. With reference to discrete systems, the equilibrium points are classified. Then, a short review is given on the continuation numerical methods, which allow to construct the equilibrium paths as a function of the bifurcation parameter. By using analytical (perturbation) methods, the bifurcation from a trivial path is studied for general multi-degree of freedom systems. In particular, the bifurcation point is determined along the path, and the bifurcated branch is built in the neighborhood of the bifurcation point. The imperfections, both of geometric and load type, are successively included in the algorithm. Systems exhibiting precritical deformations are finally addressed, for which, first, the procedure for the asymptotic construction of the nontrivial path is illustrated and, then, a change of variable is introduced, able to transform the non-trivial into a trivial path. With reference to the latter form of the equations, the bifurcation point is determined.
Buckling and Postbuckling of Conservative Systems
Luongo, Angelo (Autor:in) / Ferretti, Manuel (Autor:in) / Di Nino, Simona (Autor:in)
Stability and Bifurcation of Structures ; Kapitel: 4 ; 69-96
17.02.2023
28 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Static systems , Classification of the equilibrium points , Continuation numerical methods , Asymptotic construction of branched paths , Geometric and load imperfections , Limit load <italic>vs</italic> imperfection , Stability analysis via energy criterion , Precritical deformations , Asymptotic construction of non-trivial paths , Bifurcation from a nontrivial path Engineering , Mechanical Statics and Structures , Solid Mechanics , Mechanical Engineering , Structural Materials , Solid Construction , Building Construction and Design
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