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Application of the J 2 Plastic Flow Theory in Stability Analysis of an Elastic‐Plastic Open Sandwich Cylindrical Shell under Shear Forces and External Pressure
Author(s) -
Jerzy Zielnica
Publication year - 2000
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.20000801438
Subject(s) - nonlinear system , isotropy , galerkin method , mechanics , compressibility , constitutive equation , mathematics , plasticity , mathematical analysis , linear elasticity , deflection (physics) , materials science , classical mechanics , physics , finite element method , thermodynamics , composite material , quantum mechanics
The paper deals with linear and nonlinear stability analysis of a free‐supported sandwich cylindrical panel loaded by shear forces and external pressure. The faces of the shell are assumed to be made of an isotropic, compressible material with stress hardening and these are of the same thickness. The core, of the lightweight type, resists transversal forces only. The constitutive relations of the J 2 plastic flow theory are assumed in the analysis. Stability equations are derived on the basis of strain energy approach. With the use of Shanley concept the problem is reduced to a set of partial differential equations with the following unknown functions: stress function F, displacement function Ψ and deflection function w. In nonlinear approach the two parametrical deflection function is accepted in the solution and the equilibrium equation is solved by Galerkin method. Finally, a nonlinear stability equation is obtained which makes possible to determine the equilibrium paths and critical loads for the considered shell. Numerical calculations are performed by a special iterative procedure.