Elastoplastic nonlinear analysis of functionally graded beams utilizing the symplectic method

Elastoplastic nonlinear bending behaviors of ceramic–metal composite functionally graded material (FGM) beams are investigated using the symplectic method in Hamilton system with the classical beam theory. The mechanical properties of two-phase materials are assumed to be power function of the thick...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) 2021-12, Vol.91 (12), p.4735-4750
Main Authors: Peng, Wei, He, Tianhu
Format: Article
Language:English
Subjects:
Beams (structural)
Classical Mechanics
Constitutive equations
Constitutive relationships
Eigenvalues
Elastic bending
Elastoplasticity
Engineering
Exact solutions
Functionally gradient materials
Material properties
Mechanical properties
Nonlinear analysis
Original
Plastic deformation
Slenderness ratio
Theoretical and Applied Mechanics
Two phase materials
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Summary:Elastoplastic nonlinear bending behaviors of ceramic–metal composite functionally graded material (FGM) beams are investigated using the symplectic method in Hamilton system with the classical beam theory. The mechanical properties of two-phase materials are assumed to be power function of the thickness, and the elastoplastic material properties of the FGM beams are given by the linear rule of mixtures. The bilinear hardening elastoplastic constitutive equations are established based on the Tamura–Tomota–Ozawa hybrid reinforcement model. And the von-Mises yield condition is introduced to judge whether the beams have entered the plastic deformation. The canonical equations are solved by the symplectic method, and the loads and deflections are transformed into the symplectic eigenvalues and symplectic eigensolutions in symplectic space and obtained by analytical solutions. Examples of bending behaviors varying with load, deflection, slenderness ratio and power law index are presented. The obtained results reveal that the zones of the elastic bending and the elastoplastic bending as well as the peak values of the deflections vary with material and geometric properties.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-021-02030-z