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Effect of shear deformation on the elastica with axial strain
Author(s) -
Huddleston John V.
Publication year - 1972
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620040311
Subject(s) - compressibility , boundary value problem , deflection (physics) , eigenvalues and eigenvectors , mathematics , digital computer , shooting method , mathematical analysis , geometry , shear (geology) , structural engineering , mechanics , materials science , physics , classical mechanics , engineering , computer engineering , quantum mechanics , composite material
The problem of the elastica is generalized to include the effect if shear as well as axial strain. This leads to a non‐linear two‐point boundary‐value problem composed of five first‐order differential equations. At first the problem is linearized to study the way in which the bucking loads are modified by the combination of effects. For a simple column, the eigenvalues are found to be zeros of a third‐order polynomial, and these are evaluated by a straightforward Newton–Raphson technique using a digital computer. The postbucking behaviour is then studied by using the computer and a ‘shooting’ method to solve the non‐linear problem. For the special case of the prismatic column, graphs plotted by the computer are displayed to show the variation of load with both lateral and axial deflection for various combinations of axial compressibility and shear deformability. For one particular case, the deflected center line at various load levels is shown.