On 3D and 1D mathematical modeling of physically nonlinear beams

In this work, mathematical models of physically nonlinear beams (and plates) are constructed in a three-dimensional and one-dimensional formulation based on the kinematic models of Euler–Bernoulli and Timoshenko. The modeling includes achievements of the deformation theory of plasticity, the von Mis...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2021-09, Vol.134, p.103734, Article 103734
Main Authors: Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Bodyagina, K.S., Krysko, V.A.
Format: Article
Language:English
Subjects:
3D (1D) theory
Boundary conditions
Elasticity
Euler–Bernoulli model
Finite element method
Mathematical models
Method of variable elasticity parameters
Nonhomogeneous plates
Parameters
Physical nonlinearity
Plastic properties
Stress-strain curves
Stress-strain relationships
Timoshenko model
Transverse loads
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Summary:In this work, mathematical models of physically nonlinear beams (and plates) are constructed in a three-dimensional and one-dimensional formulation based on the kinematic models of Euler–Bernoulli and Timoshenko. The modeling includes achievements of the deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the Birger theory of elasticity. The theory is built for arbitrary boundary conditions, transverse loads, and stress-strain diagrams. The issue of solving perforated structures is also addressed. The numerical investigations are based on the finite element method and the method of variable elasticity parameters. Convergence of the method is also investigated. •3D and 1D beam models are derived and compared.•Stress–strain states of beams in 3D/ 1D formulation are analyzed.•Reliability and validity of the obtained numerical results are provided.•Zones of elastic–plastic deformations using von Mises criterion are estimated.•Any boundary conditions, transverse loads, and stress–strains can be considered.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2021.103734