Stress–Strain State and Stability of a Flexible Circular Cylindrical Shell with Transverse Shear Strains*

International Applied Mechanics - A geometrically nonlinear problem for a long cylindrical shell compliant to transverse shear and subject to a local static load is formulated and exactly solved....     

Bending of a Cantilever Rectangular Plate Loaded Discontinuously

The cantilever rectangular plates discussed previously are all loadedcontinuously.For example,the load may be either a uniform or a concen-trated load at the free edge of the plate.Now we go a step further todeal with the case of a discontinuously loaded rectangular cantilever plate.The problem to be solved will involve a concentrated load at the centerof the plate,as shown in Fig.1.The method of solution used is the sameas before.     

Transverse Stiffness of a Sinusoidally Corrugated Plate∗

Abstract

An analytical model for the initial transverse stiffness of a sinusoidally corrugated plate is derived, incorporating deformations due to extension, shear, and bending. A nondimensional plot is developed for determining transverse stiffness based on thickness and corrugation for a range of plate geometries. This model shows that for most corrugated plates the transverse stiffness is dramatically decreased from that of an uncomigated plate of the same thickness. For thin plates, a simple approximate polynomial expression for initial transverse stiffness is obtained. For thick plates with a small degree of corrugation, transverse stiffness is not negligible relative to longitudinal stiffness. The exact model is verified using a linear-elastic two-dimensional finite element model.     

The Stress–Strain State of Geometrically and Physically Nonlinear Plates with One-Sided Corrosive Wear

A technique is proposed to investigate one-sided corrosive wear. The problem is solved with regard for geometric and physical nonlinearity. Two, Dolinskii's and Gutman's corrosion models are considered. The quasistatic problem is solved by the method of variational iterations, which reduce ordinary differential equations to a system of nonlinear equations with approximation o(h ²) to be solved by Newton's method. At each step, to allow for physical nonlinearity, the method of variable elastic parameters is used. Also a technique is developed to consider various boundary conditions and ⁱ(e ⁱ) diagrams. Specific numerical results are presented.     

Study of the Elastoplastic Axisymmetric Stress–Strain State of Irradiated Laminated Shells with a Loading History

A technique is proposed to determine the axisymmetric state of laminated shells under thermoradiation loading. The deformation is assumed simple. The axisymmetric elastoplastic stress–strain state of a two-layered continuous plate under a distributed load and a neutron flux incident on one of the plate surfaces is studied within the framework of the Kirchhoff–Love hypothesis for a layer stack. The results obtained with and without regard for the loading history are presented. An important role of the loading history in a stress analysis is confirmed     

The Thermoviscoelastoplastic Axisymmetric Stress–Strain State of Laminated Flexible Orthotropic Shells

A technique is proposed to determine the thermoviscoelastoplastic axisymmetric stress–strain state of laminated shells made of isotropic and orthotropic materials. The paper deals with processes of shell loading such that both instantaneous elastoplastic and creep strains occur in isotropic materials and elastic and creep strains in orthotropic materials. The technique is developed within the framework of the Kirchhoff–Love hypotheses for a stack of layers with the use of the equations of the geometrically nonlinear theory of shells in a quadratic approximation. The deformation of isotropic materials is described by the equations of the theory of deformation along slightly curved trajectories, while the deformation of orthotropic materials is described by Hooke's law with additional terms allowing for creep. A numerical example is given     

Stress State of an Elastic Space with a Toroidal‐Shaped Cavity

Solutions are obtained for the stress state problem for an elastic space with an internal toroidalshaped cavity that can be expanded in a trigonometric series in the angle in cylindrical coordinates. Displacements and stresses are specified on the boundary. An analytic solution of the problem is found using generalized analytic functions. Stresses and displacements of points in the elastic space are calculated.     

Stress State of a Threaded Joint in a Dental Implant–Bone System*

International Applied Mechanics - The load distribution over the turns of an implant–bone threaded joint is studied. Such a joint is modeled by a rod structure in which the functional axial...     

Determination of the Inhomogeneous Preliminary Stress–Strain State in a Piezoelectric Disk

The problem of steady radial vibrations of a thin electroelastic hollow disk in the presence of a preliminary inhomogeneous plane stress–strain state is solved. Vibrations are induced by applying a potential difference across the electrodes placed on the end surfaces of the disk. Equations of the vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lam´e problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining a pre-stress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial data specified with an error is analyzed.     

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