Premium
Nonlinear analysis and elastic–plastic load‐carrying behaviour of thin‐walled spatial beam structures with warping constraints
Author(s) -
Wunderlich W.,
Obrecht H.,
Schrödter V.
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.1620220311
Subject(s) - image warping , virtual work , beam (structure) , finite element method , nonlinear system , stiffness , structural engineering , mathematics , timoshenko beam theory , bifurcation , displacement (psychology) , mathematical analysis , engineering , physics , computer science , psychology , quantum mechanics , artificial intelligence , psychotherapist
An analysis of the elastic–plastic load‐carrying behaviour of thin‐walled spatial beam structures is presented. It is based on a beam theory valid for large displacements and rotations, which admits arbitrary cross‐sections, curved axes, initial imperfections, a general material description, and which fully accounts for the influence of warping constraints as well as the stress‐history dependence of the elastic–plastic shear moduli. An incremental updated Lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle, and in the numerical solution procedure the displacement–finite element approach is followed. The associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle. Applications of the theory are given in which the influence of the loading configuration, material parameters, geometric nonlinearities and warping constraints on the load‐carrying behaviour and on the bifurcation and ultimate loads of thin‐walled beam structures is explored.