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A simplified finite element method for large deformation, post‐buckling analyses of large frame structures, using explicitly derived tangent stiffness matrices
Author(s) -
Kondoh K.,
Atluri S. N.
Publication year - 1986
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.1620230107
Subject(s) - tangent stiffness matrix , deformation (meteorology) , tangent , buckling , finite element method , structural engineering , stiffness , stiffness matrix , frame (networking) , nonlinear system , bending , point (geometry) , path (computing) , mathematical analysis , mathematics , geometry , computer science , materials science , engineering , physics , composite material , telecommunications , quantum mechanics , programming language
In this paper, a simplified, economical and highly accurate method for large deformation, post‐buckling, analyses of frame‐type structures is presented. Using the concepts of polar‐decomposition of deformation, an explicit expression for the tangent stiffness matrix of a member/element of the frame, that accounts for the nonlinear bending‐stretching coupling, is derived in closed form, at any point in the load‐deformation path. The ranges of validity of the present simplified approach are discussed. Several example problems to demonstrate the feasibility of the present approach, over ranges of deformation that are well beyond those likely to occur in practical large frame structures, are included.