Thermal stress state of laminated shells of revolution made of isotropic and linearly orthotropic materials

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 4, pp. 3–9, April, 1995.     

The nonaxisymmetric thermostressed state of laminated isotropic and rectilinearly orthotropic solids of revolution

A technique for determination of the nonaxisymmetric elastoplastic stress-strain state of laminated isotropic and rectilinearly orthotropic solids of revolution under nonisothermal loading is described. The semianalytic method of finite elements is used together with the method of successive approximations. The deformation of isotropic materials is described by the equations of the theory of deformation along trajectories of small curvature, and the deformation of orthotropic materials is described by the equations of the theory of elasticity. The thermostressed state of a three-layered solid of revolution of complex form made from isotropic and cylindrically and rectilinearly orthotropic materials subject to nonaxisymmetric heating is studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 88–95, April, 2000.     

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.     

On two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic bimodulus materials

The paper compares two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different elastic moduli in tension and compression. The approaches use different nonlinear constitutive equations describing the elastic deformation of the transversally isotropic bimodulus materials. Both approaches employ the theory of deformation along paths of small curvature and the Kirchhoff-Love hypothesis for the whole laminate to describe the deformation of the isotropic materials. The problem is solved by the method of successive approximations. The solutions of specific problems obtained by the two approaches are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 59–69, June 2008.     

Stress state of compound solids of revolution made of damaged orthotropic materials with different tensile and compressive moduli

A technique is proposed to allow for damages and different tensile and compressive moduli of orthotropic materials in stress-strain analysis of compound bodies of revolution under nonaxisymmetric loading and heating. The technique combines the semi-analytic finite-element method and the method of successive approximations __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 57–68, November 2006.     

The nonaxisymmetric elastoplastic state of isotropic and cylindrically orthotropic solids of revolution under nonisothermal loading

A technique for numerical analysis of the nonaxisymmetric elastoplastic stress-strain state of laminated isotropic and cylindrically orthotropic bodies of revolution under nonisothermal loading with allowance for its history is stated. The strain of isotropic materials is described by the equations of the theory of strain along small-curvature trajectories, while Hooke's law is used to describe the strain of orthotropic materials. The necessity of accounting for the loading history is shown by an example of a nonaxisymmetrically heated sandwich solid of revolution. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 83–90, February, 2000.     

Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear

The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied. Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method. The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.     

Nonaxisymmetric thermal and stressed state of layered bodies of revolution with rectilinearly orthotropic layers

A procedure is described for investigating the temperature fields and stressed states of multilayer bodies of revolution consisting of inelastically deformed, isotropic materials and rectilinearly orthotropic materials, in which one of the principal directions of anisotropy of the thermophysical and mechanical characteristics of the material coincides with the axis of revolution of the body. The procedure combines a semianalytical finite element technique with the method of successive approximations.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 9–15, September, 1994.     

Radiation and scattering from loaded bodies of revolution

The problem of electromagnetic radiation and scattering from loaded bodies of revolution of arbitrary shape is considered. The analysis assumes the existence of an impedance function relating the tangential electric field to the surface current on the body. A solution is obtained by the method of moments applied to the potential integral formulation of the problem. The results are expressed in terms of generalized network parameters, using formulas previously obtained for unloaded bodies. Representative computations are given for plane-wave scattering and radiation from apertures in loaded cylinders and hemispheres. A general computer program for arbitrary bodies of revolution is available.     

Calculation of nonaxisymmetric thermally stressed state of discrete homogeneous bodies of revolution with orthotropic layers

The nonaxisymmetric thermally stressed state of laminar bodies of revolution made of isotropic and orthotropic materials is considered. The procedure used is based on the semi-analytical finite-element method and the method of successive approximations. The results from calculations for the stressed state of a structural element are reported. The structure has layers of isotropic and orthotropic materials with principal axes of anisotropy that coincide with the directions of the axes of the cylindrical and Cartesian coordinate systems.Translated from Prikladnaya Mekhanika, Vol. 32, No. 2, pp. 53–58, February, 1996.     

Symmetry relations for orthotropic and transversely isotropic materials

Archive for Rational Mechanics and Analysis -     

On the existence of stress concentrations in loaded bodies made of polycrystalline materials

We study the character of stress distributions near the corner point of the interface between the two joined crystals. The interface forms a dihedral angle. The joined crystals have a cubic symmetry and consist of the same material. They have a single common principal direction of elasticity, which is parallel to the edge of the dihedral angle. The other principal directions do not coincide and are oriented arbitrarily.In the framework of elasticity, we consider problems of out-of-plane and plane strain of the twocrystal. We show that, in the case of longitudinal shear in the direction of the common principal axis of elasticity, there is no stress concentration near the corner point of the interface between the two joined crystals.For the case of plane strain in which all displacements and strains occur only in the planes perpendicular to the common principal direction, we use separation of variables to construct the characteristic equation that determines the stress concentration degree and find the roots of this equation, which determine the order of singularities of the stresses.     

Surface instability of orthotropic laminated materials under compression

The piecewise-homogeneous material model and the three-dimensional linearized theory of stability with the assumption of small subcritical strains are used to study the surface buckling of orthotropic and transtropic laminates. A plane problem is formulated, and characteristic equations are derived. A solution is found for a specific transtropic material with different orientations of the isotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 64–72, July 2006.     

Thermoelastoplastic axisymmetric stress-strain state of laminated orthotropic shells

A method is proposed for the numerical analysis of the thermoelastoplastic stress-strain state of laminated shells of revolution, made of isotropic and orthotropic 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 Hills theory of flow with isotropic hardening for orthotropic materials. The problem is solved by the method of successive approximations. A numerical example is given.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 84–91, December 2004.