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Buckling and post‐buckling of a nonlinearly elastic column
Author(s) -
Brojan M.,
Puksic A.,
Kosel F.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200710333
Subject(s) - buckling , column (typography) , bifurcation , nonlinear system , structural engineering , action (physics) , mathematics , constitutive equation , stress (linguistics) , materials science , mathematical analysis , mechanics , geometry , physics , finite element method , engineering , linguistics , philosophy , connection (principal bundle) , quantum mechanics
Abstract The classical problem of buckling of an inextensible elastic column, under the action of a compressive force is examined. The column is made of nonlinearly elastic material for which the stress‐strain relation is represented by the Ludwick constitutive law. An approximative formula for determination of the force at immediate post‐buckling is given. Further post‐buckling solutions are obtained for different values of the nonlinearity parameter by numerical integration using the Runge‐Kutta‐Fehlberg algorithm, and are presented in non‐dimensional diagrams. It is shown that no bifurcation point is found in the case of nonlinearly elastic column.