Thermoelastoplastic axisymmetric stress-strain state of laminated orthotropic shells

A method is developed for analysis of the elastoplastic stress-strain state of laminated shells of revolution under axisymmetric loading. The shells are made of isotropic and transversally isotropic materials with different moduli. The method is based on the Kirchhoff-Love hypotheses for the whole laminate, the theory of deformation along paths of small curvature (for isotropic materials), and the theory of elasticity with different tensile and compressive moduli (transversely isotropic materials). The problem is solved by the method of successive approximations. Numerical examples are given Keywords: laminated shells of revolution, elastoplastic stress-strain state, theory of elasticity with different tensile and compressive moduli Introduction. 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. It is a well known fact [2, 8, 15, etc.] that modern composite materials used in thin-walled structures often have not only anisotropy but also different tensile and compressive moduli. Therefore, to analyze the SSS of thin-walled structural members made of such materials, we need methods that would take these properties into account. There are publications, such as [1, 8, etc.], that describe methods of successive approximations and solutions to nonlinear problems for single-layer shells made of elastic heteromodulus materials. Methods for laminated shells combining isotropic and anisotropic heteromodulus materials are yet unavailable in the literature. In this connection and in support of the studies [3-6, 11-14, 16], here we set forth an approach to the elastoplastic stress-strain analysis of laminated transversely isotropic shells with different tensile and compressive moduli.1. Problem Formulation. Consider a shell of revolution with layers made of isotropic and transversely isotropic materials. The shell, which is initially unstrained and at temperature Ò = Ò 0 , is subjected to axisymmetric nonuniform heating and arbitrary loads, except for twisting. The layers are assumed to be in perfect mechanical and thermal contact. Let the shell be referred to a curvilinear orthogonal coordinate system s, , θ ς, where s is the meridional coordinate of the continuous reference surface, s s s

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

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confidence: 99%

“…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.…”

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confidence: 99%

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

Babeshko

Shevchenko

2005

Int Appl Mech

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“…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.…”

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Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

Babeshko

Shevchenko

2006

Int Appl Mech

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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

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“…These data were partially used in [7][8][9]13] to solve boundary-value problems of the theory of shells. We will also calculate the coefficients of transverse plastic strain, since many authors (such as those of [11,18,20,25,30]) use them to determine anisotropic yield criteria.…”

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Plastic Incompressibility of Anisotropic Material

Babeshko

Shevchenko

2005

Int Appl Mech

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Some characteristics of an initially anisotropic aluminum alloy are investigated. The coefficients of transverse elastoplastic and plastic strain are calculated. It is established that the coefficients of transverse plastic strain are much different from 0.5 in directions that are not in the plane of isotropy. It is also shown that the material is plastically incompressible. The possibility of using Hill's theory of flow with isotropic hardening to describe the inelastic behavior of the material is examined Keywords: orthotropic solid, plastic incompressibility, isotropic hardening Introduction. The hypotheses that the yield point is independent of the mean normal stress and that the material is plastically incompressible are among the most important initial assumptions made in many theories of anisotropic plasticity. The former hypothesis underlies Hill's and Mises' theories of anisotropic plasticity [14,19]. Because of this assumption, the plastic strains following from the associate flow rule satisfy the plastic-incompressibility condition. The nonquadratic Hill criterion later formulated in [15] is also based on this assumption. Developing methods for description of anisotropic plasticity, many authors assumed that the yield point is independent of the mean normal stress, referring mainly to Bridgeman's experiments. The authors of [23] pointed to the importance of the assumptions that yield is independent of hydrostatic pressure and plastic incompressibility in the theory of plasticity. The relationship between the effect of hydrostatic pressure on the yield point and plastic compressibility was analyzed in [21,24], where it was revealed for various steels and polymers that the yield point strongly depends on pressure, without the corresponding plastic change in volume. Using experimental data for aluminum alloys and carbon steels, the authors of [16] confirmed the hypothesis that during inelastic deformation the volume of a material does not change while the strains are less than 4%. The authors of [12] experimentally detected the plastic compressibility of flat aluminum-alloy samples and attributed that to plastic anisotropy.Many publications describe anisotropic plasticity using various assumptions, including the hypothesis that the material is plastically compressible. A theory of anisotropic plasticity for plastically compressible materials was addressed in [10,[26][27][28][29]. The paper [10] proposed a generalized potential for anisotropic materials that accounts for the Bauschinger effect and plastic compressibility (a special case of this potential is the Hill potential) and showed, based on experimental data for a titanium alloy, that the behavior of yield locus is essentially dependent on the compressibility parameter introduced by the author.Deformation-type equations describing the inelastic behavior of an anisotropic material under proportional loading were derived in [22]. There are many publications that propose deformation-type equations to describe anisotropic plasticity (see, e.g., [1,3,5,6...

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Thermoelastoplastic axisymmetric stress-strain state of laminated orthotropic shells

Cited by 9 publications

References 11 publications

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

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

Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

Plastic Incompressibility of Anisotropic Material

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