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Archive of Applied Mechanics

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01.09.2021 | Original

Elastoplastic nonlinear analysis of functionally graded beams utilizing the symplectic method

verfasst von: Wei Peng, Tianhu He

Erschienen in: Archive of Applied Mechanics | Ausgabe 12/2021

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Abstract

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.

Vorheriger Artikel Analysis of large deflection of nanobeams based on the modified couple stress theory by using finite element method

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Titel: Elastoplastic nonlinear analysis of functionally graded beams utilizing the symplectic method
verfasst von: Wei Peng
Tianhu He
Publikationsdatum: 01.09.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Archive of Applied Mechanics / Ausgabe 12/2021
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-021-02030-z

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