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     

Analysis of the thermoelastoplastic nonaxisymmetric stress-strain state of laminated circular cylindrical shells

A technique for analysis of the nonaxisymmetric thermoelastoplastic stress-strain state of laminated circular cylindrical shells is developed. It is assumed that the layers in a laminated package do not slip and separate relative to each other. The problem is solved using the geometrically linear theory of shells that is based on the Kirchhoff-Love hypotheses. The equations of thermoplasticity are written in the form of the method of additional strains. The order of the obtained system of partial differential equations is reduced with the help of trigonometric series in the cyclic coordinate. The systems of ordinary differential equations thus obtained are solved by Godunov's method of discrete orthogonalization. As an example, the nonaxisymmetric thermoelastoplastic stress-strain state of a two-layer cylindrical shell is considered. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 105–110, February, 2000.     

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     

Numerical Nonaxisymmetric Thermostress Analysis of Compound Solids of Revolution with Damage

A technique is proposed to allow for deformation damage of cylindrically orthotropic elastic materials in a thermoelastoplastic stress–strain analysis of composite bodies of revolution under nonaxisymmetric loading and heating     

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     

The Elastoplastic Axisymmetric Stress–Strain State of Flexible Laminated Shells Exposed to Radiation

A procedure is proposed to numerically study the thermoelastoplastic axisymmetric stress–strain state of laminated flexible shells exposed to radiation. The equations of thermoradiation plasticity describing simple processes are used. Results of an analysis of the elastoplastic state of a three-layer shell with regard for radiation effects are presented     

The Stress State of Stiffened Shallow Orthotropic Shells

An approach is proposed for stress analysis of elastic systems consisting of shallow shells having a rectangular planform and stiffened with rods in one direction. The shell curvature varying in the direction perpendicular to the ribs and piecewise-constant in another direction is taken into account. A system of ordinary differential equations and shell–rib conjugation conditions are derived after separation of variables for two simply supported opposite contours. A one-dimensional boundary-value problem is solved by a stable numerical method. The results of a stress–strain analysis of shipbuilding structural elements are presented as an example     

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     

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     

Stress–Strain Analysis of Smooth and Ribbed Shells under Local Loads

Static problems for smooth and discretely reinforced cylindrical shells under local loads and complex boundary conditions are solved. The stress–strain states of the casing and ribs are determined by the technical theory of shells and the Kirchhoff–Clebsch theory of rods, respectively. The reinforcing elements are arranged eccentrically. They are of equal or different stiffness, which is also variable along the length. The problems are solved using the finite-difference method. Theoretical results obtained from a refined mesh are compared with experimental data     

Solution of Dynamic Problems for Thin-Walled Structural Elements with Nonuniform Dynamic Boundary Conditions

The characteristics of the stress–strain state of thin-walled structural elements are determined in the case where dynamic boundary loads or displacements described by pulse functions are specified. A general scheme for realization of the method of natural-mode expansion is stated as applied to differential equations with unknown functions of one spatial coordinate and time. Theoretical relations for rods, plates, and shells are given. The potential of the approach developed is illustrated by solving specific problems     

Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 60–67, February 2005.     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Determining the Axisymmetric, Geometrically Nonlinear, Thermoelastoplastic State of Laminated Orthotropic Shells

A technique is developed to determine the axisymmetric, geometrically nonlinear, thermoplastic stress–strain state of laminated ortotropic shells of revolution under loads that cause a meridian stress state and torsion. The technique is based on the rectilinear-element hypotheses for the whole stack of layers. The active elastoplastic deformation of an ortotropic material is described by deformation-type equations that have been derived without resort to the existence conditions for the plastic potential. The scalar functions in the constitutive equations depend on the intensity of shear strains and temperature. The problem is solved through the numerical integration of a system of differential equations. The technique is tried out in designing tubular specimens subjected to axial force and torque. As an example, the elastoplastic state of a corrugated shell is analyzed     

Determination of the Axisymmetric Geometrically Nonlinear Thermoviscoelastoplastic State of Laminated Medium-Thickness Shells

A method is developed to determine the axisymmetric geometrically nonlinear thermoelastoviscoplastic stress–strain state of branched laminated medium-thickness shells of revolution. The method is based on the hypotheses of a rectilinear element for the whole set of layers. The shells are subject to loads that cause a meridional stress state and torsion. They can consist of isotropic layers, which deform beyond the elastic limit, and elastic orthotropic layers. The relations of thermoviscoplastic theory, which describe simple processes of loading, are employed as the equations of state for the isotropic layers. The solution of the problem is reduced to numerical integration of systems of differential equations. The geometrically nonlinear elastoplastic state of a two-layer corrugated shell of medium thickness is calculated as an example     

Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

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     

Nontraditional Substructuring Procedure for Analysis of Free-Form Shells

An efficient nontraditional scheme of the substructuring method is expounded. It is based on the curvilinear mesh method (CMM) used for analysis of complex shell structures. In forming the stiffness matrix, this approach excludes fully the shell displacement approximation errors. A numerical algorithm that preserves the efficiency of the CMM for shells of arbitrary form is developed. The stress–strain problem for a boxed beam with diaphragms and a cylindrical roof shell is solved numerically. The results are compared with those obtained by other numerical methods     

Thermoelastoplastic deformation of noncircular cylindrical shells

A method to determine the nonstationary temperature fields and the thermoelastoplastic stress-strain state of noncircular cylindrical shells is developed. It is assumed that the physical and mechanical properties are dependent on temperature. The heat-conduction problem is solved using an explicit difference scheme. The temperature variation throughout the thickness is described by a power polynomial. For the other two coordinates, finite differences are used. The thermoplastic problem is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. The theory of simple processes with deformation history taken into account is used. Its equations are linearized by a modified method of elastic solutions. The governing system of partial differential equations is derived. Variables are separated in the case where the curvilinear edges are hinged. The partial case where the stress-strain state does not change along the generatrix is examined. The systems of ordinary differential equations obtained in all these cases are solved using Godunov's discrete orthogonalization. The temperature field in a shell with elliptical cross-section is studied. The stress-strain state found by numerical integration along the generatrix is compared with that obtained using trigonometric Fourier series. The effect of a Winkler foundation on the stress-strain state is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 79–90, August 2008.     

The Thermoviscoelastoplastic State of Shells of Revolution Under Axisymmetric Deformation Along Various Flat Paths

The basic results obtained at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in developing a thermoviscoelastoplastic theory of thin-walled shells of revolution subject to arbitrary axisymmetric loading are analyzed. The theory includes the constitutive thermoviscoplastic equations describing the deformation of an isotropic body along arbitrary flat paths with functionals made specific in base experiments and the solutions of boundary-value problems, which indicate the influence of the geometry of strain paths on the stress–strain state of shells