Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

The elastoplastic state of thin cylindrical shells with two circular holes under axial tension is analyzed considering finite deflections. The distributions of stresses along the contours of the holes and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for either physical nonlinearity (plastic deformations) and geometrical nonlinearity (finite deflections) alone and with a numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between the holes and the nonlinear factors accounted for__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 52–57, May 2005.     

Inelastic Deformation of Flexible Spherical Shells with Two Circular Openings

Elastoplastic analysis of thin-walled spherical shells with two identical circular openings is carried out with allowance for finite deflections. The shells are made of an isotropic homogeneous material and subjected to internal pressure of known intensity. The distributions of stresses (strains or displacements) along the contours of the openings and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for only physical nonlinearity (plastic deformations) and only geometrical nonlinearity (finite deflections) and with a numerical solution of the linearly elastic problem. The stress–strain state near the two openings is analyzed depending on the distance between the openings and the nonlinear factors accounted for     

Physically and Geometrically Nonlinear Deformation of Spherical Shells with an Elliptic Hole

The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed. The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations) or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic problem. The stress—strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 95–104, June 2005.     

Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account) and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities accounted for __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 88–95, November 2005.     

Inelastic deformation of flexible cylindrical shells with an elliptic hole

The elastoplastic state of isotropic homogeneous cylindrical shells with elliptic holes and finite deflections under internal pressure is studied. Problems are formulated and numerically solved taking into account physical and geometrical nonlinearities. The distribution of stresses (displacements, strains) along the boundary of the hole and in the zone of their concentration is analyzed. The data obtained are compared with the numerical solutions of the physically nonlinear, geometrically nonlinear, and linear problems. The stress-strain state of cylindrical shells in the neighborhood of the elliptic hole is analyzed with allowance for nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 46–54, May 2007.     

Inelastic deformation of flexible cylindrical shells with a curvilinear hole

The elastoplastic state of thin cylindrical shells weakened by a curvilinear (circular) hole is analyzed considering finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distributions of stresses (strains, displacements) along the hole boundary and in the zone of their concentration are studied. The results obtained are compared with solutions that account for physical (plastic strains) or geometrical (finite deflections) nonlinearity alone and with a numerical linear elastic solution. The stress-strain state around a circular hole is analyzed for different geometries in the case where both nonlinearities are taken into account __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 115–123, December, 2006.     

Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes

Results on stress concentration in thin shells with curvilinear holes subject to plastic deformation and finite deflections are reviewed. The holes (circular, elliptical) are reinforced with thin-walled elements (rings, rods) of different stiffness. A numerical method of solving doubly nonlinear problems of statics for shells of complex geometry is outlined. The stress distribution near curvilinear holes in spherical, cylindrical, and conical shells under statical loading is studied. The numerical results are analyzed     

Physically and Geometrically Nonlinear Static Problems for Thin-Walled Multiply Connected Shells

Physically and geometrically nonlinear two-dimensional problems are formulated for multiply connected thin shells (weakened by several curvilinear holes). A technique and algorithm are proposed for their solution with allowance for elastoplastic strains and finite deflections of shells under static loading. Numerical results for a shell with two circular holes are presented and the stress concentration is analyzed     

Elastoplastic state of flexible conical shells with a circular hole under axial tension

The elastoplastic state of thin conical shells with a circular hole is analyzed assuming finite deflections. The distributions of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress–strain state of shells around the hole under axial tension is analyzed taking into account two nonlinear factors. The numerical results are presented as plots and tables     

Physically and geometrically nonlinear deformation of thin-walled conical shells with a curvilinear hole

The elastoplastic state of thin conical shells with a curvilinear (circular) hole is analyzed assuming finite deflections. The distribution of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress-strain state around a circular hole in shells subject to internal pressure of prescribed intensity is analyzed taking into account two nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 73–79, April 2007.     

Stability of Cylindrical Shells with Local Imperfections

We propose a nonlinear approach to the stability analysis of imperfect cylindrical shells under axial compression. The approach takes into account the initial deflections (imperfections) of the shell shape from cylindrical. A series of typical initial deflections is analyzed: local and longitudinal bulges (dents) and unilateral annular corrugations. A nonlinear stability problem is solved. The results are represented as plots of the nondimensional stress versus the nondimensional amplitude of initial deflections. It is shown that the capabilities of the nonlinear theory for estimating the critical stresses for thin shells have not been exhausted yet and that it could be used in future to explain some phenomena experimentally observed in shells     

Effect of localized imperfections on the critical loads of ribbed shells

A numerical approach to the assessment of the critical stresses for imperfect ribbed shells is developed. Initial deflections occupying a part of the shell surface (they are circumferentially bounded) are considered. The couple stresses and nonlinearity of the precritical state are taken into account. Numerical examples are given     

Elastoplastic state of flexible cylindrical shells with a circular hole under axial tension

The elastoplastic state of cylindrical shells with a circular hole is studied considering finite deflections. The material of the shells is isotropic and homogeneous; the load is axial tension. The distribution of stresses, strains, and displacements along the hole boundary and in the zone of their concentration is studied by solving a doubly nonlinear problem. The data obtained are compared with the solutions of the physically and geometrically nonlinear problems and a numerical solution of the linear elastic problem __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 101–109, July 2008.     

Physically and geometrically nonlinear deformation of conical shells with an elliptic hole

The elastoplastic state of conical shells weakened by an elliptic hole and subjected to finite deflections is studied. The material of the shells is assumed to be isotropic and homogeneous; the load is constant internal pressure. The problem is formulated and a technique for numerical solution with allowance for physical and geometrical nonlinearities is proposed. The distribution of stresses, strains, and displacements along the hole boundary and in the zones of their concentration is studied. The solution obtained is compared with the solutions of the physically and geometrically nonlinear problems and a numerical solution of the linear elastic problem. The stress-strain state around an elliptic hole in a conical shell is analyzed considering both nonlinearities __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 69–77, February 2008.     

Large deflections of deep orthotropic spherical shells under radial concentrated load: asymptotic solution

Nonlinear behavior of deep orthotropic spherical shells under inward radial concentrated load is studied. The singular perturbation method is developed and applied to Reissner’s equations describing axially symmetric large deflections of thin shells of revolution. A small parameter proportional to the ratio of shell thickness to the sphere radius is used. The simple asymptotic formulas describing load–deflection diagrams, maximum bending and membrane stresses of the structure are derived. The influence of boundary conditions on the behavior of the shell by large deflections is considered. Obtained asymptotic solution is in close agreement with the experimental and numerical results and has the same accuracy (in the asymptotic meaning) as the given equations of nonlinear theory of thin shells.     

Stress-strain state of a flexible spherical shell with an eccentric circular hole

The stress-strain state of thin flexible spherical shells weakened by an eccentric circular hole is analyzed. The shells are made of an isotropic homogeneous material and subjected to internal pressure. A problem formulation is given, and a method of numerical solution with allowance for geometrical nonlinearity is outlined. The distribution of displacements, strains, and stresses along the hole boundary and in the region of their concentration is examined. The data obtained are compared with numerical solutions of the linear problem. The stress-strain state around the eccentric circular hole is analyzed with allowance for geometrical nonlinearity __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 92–98, October 2007.     

Stress Analysis of Biconvex Laminated Orthotropic Shells that are Shallow to a Variable Degree

The stress–strain state of biconvex laminated orthotropic shells is analyzed against the degree of shallowness and the parameters of orthotropy. Numerical values of deflections and stresses are obtained by solving two-dimensional boundary-value problems using spline-functions and the discrete-orthogonalization method. The effect of the rise of shells on the displacement and stress fields is analyzed for different parameters of orthotropy     

Nonlinear deformation and stability of oval cylindrical shells under combined loading

A study is made of the stability of cylindrical shells of oval cross section loaded by a shear force combined with torsional and bending moments. The variational method of finite elements in displacements is used. The subcritical stress-strain state of the shells is considered momental and nonlinear. The effects of the nonlinearity of shell deformation and shell ovalization on the critical load and buckling mode are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 134–138, January–February, 2008.     

Nonlinear behavior of composite sandwich beams in three-point bending

The load-deflection behavior of a composite sandwich beam in three-point bending was investigated. The beam was made of unidirectional carbon/epoxy facings and a polyvinyl chloride closed-cell foam core. The load-deflection curves were plotted up to the point of failure initiation. They consist of an initial linear part followed by a nonlinear portion. A nonlinear mechanics of materials analysis that accounts for the combined effect of the nonlinear behavior of the facings and core materials (material nonlinearity) and the large deflections of the beam (geometric nonlinearity) was developed. The theoretical predictions were in good agreement with the experimental results. It was found that the effect of material nonlinearity on the deflection of the beam is more pronounced for shear-dominated core failures in the case of short span lengths. It is due to the nonlinear shear stress-strain behavior of the core. For long span lengths, the observed nonlinearity is small and is attributed to the combined effect of the facings nonlinear stress-strain behavior and the large deflections of the beam.     

Fully-coupled nonlinear analysis of single lap adhesive joints

This paper presents novel closed-form and accurate solutions for the edge moment factor and adhesive stresses for single lap adhesive bonded joints. In the present analysis of single lap joints, both large deflections of adherends and adhesive shear and peel strains are taken into account in the formulation of two sets of nonlinear governing equations for both longitudinal and transverse deflections of adherends. Closed-form solutions for the edge moment factor and the adhesive stresses are obtained by solving the two sets of fully-coupled nonlinear governing equations. Simplified and accurate formula for the edge moment factor is also derived via an approximation process. A comprehensive numerical validation was conducted by comparing the present solutions and those developed by Goland and Reissner, Hart-Smith and Oplinger with the results of nonlinear finite element analyses. Numerical results demonstrate that the present solutions for the edge moment factor (including the simplified formula) and the adhesive stresses appear to be the best as they agree extremely well with the finite element analysis results for all ranges of material and geometrical parameters.