Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

Abstract

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill's theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed Keywords: laminated shell of revolution, thermoelastoplastic stress-strain state, Hill's theory of plasticity with isotropic hardeningIntroduction. Methods of numerical stress-strain analysis of inelastic anisotropic laminated shells are described in [3, 4, 6, 7, 9, 10, 12, 13, etc.]. The methods from [3,4,6,7,12,13] allow analyzing the stress-strain state (SSS) of shells under nonisothermal loading, but the numerical results presented in these publications are restricted to mechanical loading. In support of [3], we will detail the method developed therein with reference to the thermoplasticity of isotropic and transversely isotropic shells and will assess the effect of temperature on the SSS of a specific shell. Problem Formulation and Governing Equations.Consider a laminated shell of revolution with layers made of isotropic and transversely isotropic materials that have temperature-dependent properties and are in perfect mechanical and thermal contact. The shell, which is in stress/strain-free state at temperature T = Ò 0 , is subjected to axisymmetric nonuniform heating and arbitrary loads, except for twisting. The shell is described in a curvilinear orthogonal frame of coordinates (s, θ, ς), where s is the meridional coordinate of the continuous reference surface, s s s

Elastoplastic deformation of elements of an isotropic solid along paths of small curvature: Constitutive equations incorporating the stress mode

“…The system of governing equations (3.9) is solved by a numerical time-stepping method and by the method of successive approximations at each step, satisfying prescribed boundary conditions [5][6][7][8]. An algorithm to solve this system of equations may be the following.…”

Axisymmetric thermoelastoplastic stress-strain state of flexible laminated transversely isotropic shells

“…However, no numerical data are available on the stress-strain state (SSS) of such shells subject to nonuniform heating. The paper [1] reports on the results from an axisymmetric thermoelastoplastic stress-strain analysis of laminated isotropic and transversely isotropic shells subject to nonuniform heating. These results were obtained using a technique [8] based on the Kirchhoff-Love hypotheses and a geometrically linear formulation, and the effect of temperature on stresses and strains in these shells was evaluated.…”

“…Expanding upon the studies [1,8], the present paper generalizes the technique outlined therein to axisymmetric geometrically nonlinear problems of thermoplasticity for transversely isotropic shells and discusses numerical results.…”

Elastoplastic Axisymmetric Stress-Strain State of Laminated Shells Made of Isotropic and Transversely Isotropic Materials with Different Moduli

“…] and beyond [5,6,[12][13][14] the elasticity limits. The tensile and compressive moduli of these materials were assumed to be equal.…”

“…Methods for analysis of the axisymmetric thermoelastoplastic stress-strain state (SSS) of laminated shells of revolution have been developed for isotropic and anisotropic inelastic materials deforming within [3, 4, 11, 16, etc.] and beyond [5,6,[12][13][14] the elasticity limits. The tensile and compressive moduli of these materials were assumed to be equal.…”