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Nonlinear stability analysis of functionally graded shells using the invariant‐based triangular finite element
Author(s) -
Levyakov S.V.,
Kuznetsov V.V.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200188
Subject(s) - finite element method , nonlinear system , invariant (physics) , mixed finite element method , strain energy , buckling , infinitesimal strain theory , extended finite element method , materials science , structural engineering , mathematical analysis , mathematics , geometry , physics , engineering , composite material , quantum mechanics , mathematical physics
Abstract The paper discusses a finite‐element approach for nonlinear analysis of thermal buckling and postbuckling behaviors of plates and shells fabricated of functionally graded materials. The triangular finite‐element is formulated using representation of the strain energy as a function of invariants of the membrane, bending, and transverse shear strains. The invariants are expressed in terms of the strain tensor components determined in the direction of the element edges, which provides some computational benefits. Numerical examples are given to demonstrate the application of the finite element in the investigation of nonlinear deformation and stability of functionally graded plates and shells with temperature dependent properties.