Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation

The stress-strain state of a shallow shell with rectangular planform and varying thickness is analyzed in a refined formulation for different boundary conditions. A numerical-and-analytic method is developed based on the spline-approximation and discrete-orthogonalization methods. The stress-strain state of shallow shells with thickness varied without change in weight is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 80–91, October 2007.     

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed. Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells with variable thickness is studied     

Stress-strain analysis of a composite truncated conical shell

The stress-strain state of a nonshallow truncated conical shell made of a composite material and subjected to axial forces at the ends is studied. A variational difference method is used. Calculations are carried out for an orthotropic shell with low shear stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 66–72, July 2007.     

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.     

Determining the stress state of flexible orthotropic shells of revolution in magnetic field

A two-dimensional nonlinear magnetoelastic model of a current-carrying orthotropic shell of revolution is constructed taking into account finite orthotropic conductivity, permeability, and permittivity. It is assumed that the principal axes of orthotropy are aligned with the coordinate axes and that the orthotropic body is magnetically and electrically linear. The coupled nonlinear differential equations derived describe the stress-strain state of flexible current-carrying orthotropic shells of revolution that have an arbitrarily shaped meridian and orthotropic conductivity and are in nonstationary mechanical and electromagnetic fields. A method to solve this class of problems is proposed Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 64–76, August 2008.     

Thermoelastic bending of locally heated orthotropic shells

The thermoelastic bending of locally heated orthotropic shells is studied using the classical theory of thermoelasticity of thin shallow orthotropic shells and the method of fundamental solutions. Linear distribution of temperature over thickness and the Newton’s law of cooling are assumed. Numerical analysis is carried out for orthotropic shells of arbitrary Gaussian curvature made of a strongly anisotropic material. The behavior of thermal forces and moments near the zone of local heating is studied for two areas of thermal effect: along a coordinate axis and along a circle of unit radius. Generalized conclusions are drawn __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 80–85, March 2007.     

Free vibrations of shallow nonthin shells with variable thickness and rectangular planform

The free vibrations of shallow orthotropic shells with variable thickness and rectangular planform are studied. The shear strains are taken into account. The spline approximation of unknown functions is used. The natural frequencies are calculated for different boundary conditions. The dependence of the natural frequencies on the curvature of the midsurface is examined. The natural frequencies of shells with constant and variable thickness are compared     

The Thermoelastic State of Orthotropic Shells Heated by Concentrated Heat Sources

A problem on thin-walled orthotropic shells of arbitrary Gaussian curvature acted upon by concentrated heat sources is solved by means of the two-dimensional Fourier transformation. The temperature is assumed to distribute linearly throughout the shell thickness. Convective heat exchange with the environment under Newton's law is taken into account. Calculated results are presented. The influence of the curvature on the thermoelastic state of various orthotropic shells is studied     

Stress state of a cylindrical composite panel weakened by a circular hole

The paper studies the stress-strain state of a deep cylindrical panel weakened by a hole and subjected to a tensile load at the outer boundary. A variational difference method is used. A numerical analysis is carried out for an orthotropic panel with low shear stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 73–78, May 2006.     

Free vibrations of shallow orthotropic shells with variable thickness and rectangular planform

The free vibrations of shallow doubly curved orthotropic shells with rectangular planform and varying thickness is solved using a refined formulation and the spline-approximation method. Various boundary conditions are considered. The effect of the curvature of the mid-surface on the spectrum of natural frequencies is examined. The natural frequencies and modes of orthotropic shells of constant and varying thickness are compared and analyzed     

Spline-approximation solution of two-dimensional problems of statics for orthotropic conical shells in a refined formulation

An approach to solving two-dimensional stress-strain problems for orthotropic conical shells of variable thickness in a refined formulation is developed. The approach is based on the spline-approximation and the stable discrete-orthogonalization method, which is used to solve the one-dimensional problem. The dependence of the deflection and stresses on the thickness and apex angle of a shell of constant volume is given as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 43–54, November 2007.     

Free vibrations of rectangular orthotropic shallow shells with varying thickness

The paper proposes a numerical-analytic approach to studying the free vibrations of orthotropic shallow shells with double curvature and rectangular planform. The approach is based on the spline-approximation of unknown functions. Calculations are carried out for different types of boundary conditions. The influence of the mid-surface curvature and variable thickness on the behavior of dynamic characteristics is studied __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 102–115, June 2007.     

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.     

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.     

Nonlinear Axisymmetric Static and Transient Response of Orthotropic Annular Shallow Spherical Caps

ABSTRACT

This investigation deals with the nonlinear axisymmetric static and transient response of orthotropic annular shallow spherical caps with a free edge hole and with a rigid central mass, subjected to uniformly distributed load and a central load. The dynamic analogue of Marguerre equations, in terms of normal displacement w and stress function Ψ, are employed. An orthogonal point collocation method is used for spatial discretization and a Newmark-β scheme is used for time integration. Static load, step function load, and sinusoidal pulse load are considered. The influence of annular ratio on the response is studied for isotropic (β = 1) and orthotropic (β = 3) clamped caps, with a rise to thickness ratio of 1.5.     

Effect of transverse shear and material orthotropy in a cracked spherical cap

The elastostatic problem for a relatively thin-walled spherical cap containing a through crack is considered. The problem is formulated for a specially orthotropic material within the confines of a linearized, shallow shell theory. The theory used is equivalent to Reissner's theory of flat plates and hence permits the consideration of all five physical conditions on the shell boundaries separately. The solution of the problem is reduced to that of a pair of singular integral equations and the asymptotic stress state around the crack tips is investigated. The numerical solution of the problem is given for an isotropic shell and for two specially orthotropic shells. The results indicate that the material orthotropy as well as the shell curvature and thickness may have a considerable effect on the stress intensity factors at the crack tips.     

Effect of local loads on the stress-strain state of nonthin orthotropic conical shells

The paper analyzes the stress-strain state of nonthin orthotropic conical shells under local loads. The distribution of deflections and stresses in conical shells under local loads of some types is given as an example Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 103–113, August 2008.     

Stress-Strain Analysis of Orthotropic Closed and Open Noncircular Cylindrical Shells

The paper proposes an approach to the stress-strain analysis of orthotropic open and closed cylindrical shells of variable thickness and noncircular cross section under various loading and boundary conditions. As an example, the circumferential distribution of deflection and tangential force in shells with elliptic cross section is analyzed for some cases of orthotropy __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 83–92, July 2005.     

倾斜正交异性矩形板热振动分岔

研究了倾斜正交异性矩形板在热状态下的振动分岔,讨论分析了温度、长宽比、板厚、倾斜角对正交异性矩形板发生混沌运动区域的影响。     

Refined analysis of the stress state of orthotropic elliptic cylindrical shells with variable geometrical parameters

An approach developed earlier to solve boundary-value problems is used to analyze the behavior of the stress-strain state of orthotropic elliptic cylindrical shells with variation in the geometric parameters of their cross section at constant volume (weight) Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 53–62, September 2008.