Thermoelastoplastic Stress–Strain State of Laminated Shells under Axisymmetric Loading Along Arbitrary Plane Paths

The paper sets forth a method of successive approximations along loading paths. The method is used to determine the thermoelastoplastic stress–strain state of laminated shells under axisymmetric complex loading. Deformation-type constitutive equations describing loading along arbitrary plane paths are employed. A numerical example is presented     

Thermoelastoplastic State of Flexible Laminated Shells under Axisymmetric Loading Along Various Plane Paths

The paper presents a technique for thermoelastoplastic stress–strain analysis of flexible laminated shells of revolution under complex axisymmetric loading. The constitutive deformation equations are used to describe loading along arbitrary plane paths. The problem is solved by the method of successive approximations. A numerical example is given     

Nonaxisymmetric Thermoviscoelastoplastic Deformation of Shells of Revolution

An analysis is made of the basic results obtained at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in developing a theory and methods for thermoviscoelastic stress—strain analysis of flexible laminated shells of revolution with a thickness variable in two directions under nonaxisymmetric nonisothermal deformation along rectilinear and slightly curved paths, with the loading history taken into account     

Thermoelastoplastic Stress—Strain State of Laminated Transversely Isotropic Shells under Axisymmetric Loading

A method is proposed for determining the thermoelastoplastic stress–strain state of laminated shells of revolution, made of isotropic and transversely isotropic materials, under axisymmetric loading. The method is based on the Kirchhoff–Love hypotheses for a layer stack, the theory of deformation along paths of small curvature for isotropic materials, and Hill's flow theory with isotropic hardening for transversely isotropic materials. The loading history is accounted for. The problem is solved by the method of successive approximations. Numerical examples are given     

Determining the Axisymmetric Geometrically Nonlinear Thermoviscoelastoplastic State of Laminated Shells by the Theory of Deformation Along Paths of Small Curvature

A technique is developed for determining the thermoviscoelastoplastic geometrically nonlinear axisymmetric stress–strain state of laminar shells of revolution under loads that induce meridional stress and torsion. The technique is based on the hypotheses of rectilinear element for the whole stack of layers. The relations of the theory of deformations along paths of small curvature are used as equations of state. The solution is reduced to the numerical integration of a system of ordinary differential equations. The technique is tried out by a test example and illustrated by determining the geometrically nonlinear thermoviscoelastoplastic state of a corrugated shell     

Contemporary perspectives in finite strain plasticity

From an internally consistent theory of finite strain plasticity in which are introduced a new stress tensor that includes rigid body rotation and a compatible finite strain tensor amenable to simple geometrical interpretation, a close correlation with experiment is obtained for stress paths of arbitrary composition and direction. Measured material constants are proportional to the elastic shear modulus, as indicated for dislocation theory. At large strain there exists a quantum mechanical structure for the continuum, in which are defined a series of relative reference configurations and second order transitions.     

Minimum Energy Characterizations for the Solution of Saint-Venant's Problem in the Theory of Shells

The linear theory of Cosserat surfaces is employed to study Saint-Venant's problem for cylindrical shells of arbitrary cross-section. We prove minimum energy characterizations for the solution of the relaxed Saint-Venant's problem previously obtained. Then, we determine the global measures of strain appropriate to extension, bending, torsion and flexure for certain classes of solutions to the relaxed problem. Mathematics Subject Classifications (2000) 74K25, 74G05.     

安全壳中钢衬壳热屈曲问题理论与实验研究(I)———理论分析部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题把铆固之间的钢衬壳视为钢衬板的特殊缺陷形式，利用Ｋｏｉｔｅｒ初始后屈曲理论分析了完善和具有初始缺陷钢衬壳的弹性热后屈曲性态给出了用挠度－温度载荷表示的钢衬壳的后屈曲平衡路径表达式和屈曲临界载荷表达式具体分析了三种钢衬壳模型：四点铆固钢衬壳、四边固支钢衬壳和五点铆固钢衬壳给出了钢衬的初始缺陷、锚钉间距、钢衬厚度等参数对钢衬热屈曲载荷的影响结果对安全壳中钢衬壳的设计有很好的参考价值     

A theory of shells with small strain accompanied by moderate rotation

This paper is concerned with a constrained theory of shells in the presence of small strain accompanied by moderate rotation. The constrained theory accounts for the effect of transverse normal strain and includes, of course, the special case (corresponding to the Kirchhoff-Love theory of shells) in which the effect of transverse normal strain is absent. After precise estimates for (local) moderate rotation and relative displacement gradients in terms of infinitesimal strain have been effected, a complete theory is formulated with the use of linear constitutive equations. The nature of the complete theory is further examined when initially the shell-like body is a plate; and it is shown that our kinematical formulae (strain-displacement relations), as well as the relevant differential equations of the theory in the absence of the effect of transverse normal strain, systematically reduce to those used in the von Kármán plate equations. Also, in the light of the present results, an assessment of kinematical aspects of previously developed theories of shells undergoing small strain and moderate rotation is indicated.     

Describing the thermoelastoplastic deformation of compound shells under axisymmetric loading with allowance for the third invariant of the stress deviator

The paper outlines a procedure for the numerical analysis of the thermoelastoplastic stress–strain state of thin compound shells of revolution under axisymmetric nonisothermal loading. The constitutive equations describing the thermoelastoplastic deformation of isotropic materials along paths of small curvature and incorporating the third invariant of the stress deviator are used. A numerical example is presented     

Elastoplastic stress-strain state of flexible layered shells made of isotropic and transversely isotropic materials with different moduli and subjected to axisymmetric loading

The paper proposes a numerical technique for analysis of the elastoplastic stress-strain state of flexible layered shells of revolution under axisymmetric loading. It is assumed that the shells are made of isotropic and transversely isotropic materials with different moduli in tension and compression. The technique is based on a geometrically nonlinear theory of shells that takes into account the squared angles of rotation and the Kirchhoff-Love hypotheses for a layer stack. The deformation of isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of transversely isotropic materials is described using the theory of elasticity with different moduli in tension and compression. The problem is solved by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 31–42, November 2007.     

Free-surface roughness of thin-walled tubes in reduction

The problem of the stress-strain state of thin-walled tubes in axisymmetric steady-state deformation is solved using the membrane theory of shells and the model of an ideal rigid-plastic material satisfying the Mises yield condition and the associated flow law. The obtained solution is used together with the empirical relation between the strain state at an arbitrary point of the free surface and the surface roughness parameters at the same point to determine the influence of some tube reduction parameters on the surface roughness parameters in the product. The employed empirical relation is derived assuming that the free surface roughness parameters depend on two independent kinematic variables.     

Analysis of Stresses and Displacements in Orthotropic Noncircular Cylindrical Shells Under Centrifugal Loads

This paper addresses the class of stress–strain problems for thin orthotropic cylindrical shells of arbitrary cross section under centrifugal loads. Separating out the variables for a simply supported shell yields a system of ordinary differential equations for which the boundary-value problem is solved by a stable numerical method. Study is made of the distribution of displacements in shells of elliptical cross section versus the ratio of ellipse exes and the eccentricity of the axis of revolution relative to the geometrical axis of symmetry     

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

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 __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 88–96, August 2005.     

High-frequency response of isotropic-laminated cylindrical shells modeled by a layer-wise theory

In this paper, the high-frequency response of isotropic-laminated cylindrical shells is investigated using a layer-wise theory. The cylindrical shell is discretized in an arbitrary number of layers in the radial direction, and a three-dimensional stress state is assumed in each layer. Approximate numerical results obtained by the layer-wise theory are compared with the exact wave-dispersion analytical results. The very good agreement between approximate and exact results indicates that the layer-wise theory can accurately describe of the dynamic response of cylindrical shells in the high-frequency (short-wavelength) range.     

A general nonlinear theory of elastic shells

This paper presents a general nonlinear theory of elastic shells for large deflections and finite strains in reference to a certain natural state. By expanding the displacement components into power series in the coordinate θ³ normal to the undeformed middle surface of shells, the expansions of the Cauchy-Green strain tensors are expressed in terms of these expanded displacement components. Through the modified Hellinger-Reissner variational principle for a three-dimensional elastic continuum, a set of the fundamental shell equations is derived in terms of the expanded Cauchy-Green strain tensors and Kirchhoff stress resultants. The Love-Kirchhoff hypothesis is not assumed and higher order stretching and bending are taken into consideration. For elastic shells of isotropic materials, assuming the strain-energy to be an analytic function of the strain measures, general nonlinear constitutive equations are then derived. Thus, a complete and consistent two-dimensional shell theory incorporating the geometrical and physical nonlinearities is established. The classical theories of shells are directly derivable from the present results by proper truncations of the series.     

任意形状薄壳统一的非线性稳定性方程

从文献（１）任意曲线坐标系中任意形状壳体非线性理论的普适平衡方程出发，导出了任意曲线坐标中任意形状壳体的非线性稳定笥方程手统一形式。     

A Donnell type theory for finite deflection of stiffened thin conical shells composed of composite materials

A Donnell type theory is developed for finite deflection of closely stiffened truncatedlaminated composite conical shells under arbitrary loads by using the variational calculusand smeared-stiffener theory.The most general bending-stretching coupling and the effectof eccentricity of stiffeners are considered.The equilibrium equations,boundary conditionsand the equation of compatibility are derived.The new equations.of the mixed-type ofstiffened laminated composite conical shells are obtained in terms of the transversedeflection and stress function.The simplified equations are also given for some commonlyencountered cases.     

Modeling complex plastic deformation and fracture of metals under disproportionate loading

A mathematical model is developed to describe fatigue-damage accumulation in structural materials (metals and their alloys) on multiaxial paths of disproportionate combined heat and power loading. The effect of the shape of the strain path on the fatigue life of metals was studied to obtain qualitative and quantitative estimates of the obtained constitutive relations. It is shown that the proposed constitutive relations adequately describe the main elastoplastic deformation effects and damage accumulation in structural materials for arbitrary strain paths.     

Modeling of processes of complex plastic deformation of materials along arbitrary temperature and force loading paths

We develop a mathematical model describing the processes of complex plastic deformation of structural materials (metals and their alloys) under multiaxial nonproportional paths of complex temperature and force loading. To obtain qualitative and quantitative assessment of the constitutive relations developed here, we study how the strain path shape affects the plastic behavior of metals. We show that the version of constitutive relations developed here correctly represents the main elastoplastic deformation effects in metals for arbitrary strain paths.