Research Article
Jun 1971
Inelastic Finite Deformation of Planar Frames
Publication: Journal of the Engineering Mechanics Division
Volume 97, Issue 3
Abstract
A theoretical analysis and a numerical procedure are presented for the determination of the inealstic load-deformation relationship, as well as buckling or collapse load for a planar frame made of general work-hardening materials subjected to general in-plane loadings and loading histories. Lagrangian descriptions are used to describe the variables involved in the finite deformations. A variational principle involving Kirchhoff stress tensor, green strain tensor, and their rates is established and employed in a numerical procedure to determine, in a quasi-static sense, the velocities caused by given loadings and their rates. The derivatives in the functional are expressed in terms of finite differences of the velocities at chosen locations and the integration is replaced by a finite summation. The variation of the functional with resepct to each velocity leads to a set of linear algebraic equations for the solution of the discrete velocities and the subsequent displacements. The interactions between a number of members meeting at a joint are governed by a set of equations also obtained by the variational principle. The test results of two aluminum frames are presented.
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Published In
Journal of the Engineering Mechanics Division
Volume 97 • Issue 3 • June 1971
Pages: 773 - 789
Copyright
© 1971 American Society of Civil Engineers.
History
Published in print: Jun 1971
Published online: Feb 3, 2021
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Authors
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Raouf A. Ridha, AM.ASCE
Analytical Specialist, Analytical Mechanics Dept., Energy Controls Div., The Bendix Corp., South Bend, Ind.
Lawrence H.N. Lee, F.ASCE
Prof., Dept. of Aerospace and Mechanical Engrg., Univ. of Notre Dame, Notre Dame, Ind
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.