No abstract

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 Introduction. Stress analysis of simply connected and doubly connected thin and nonthin elastic shells made of metallic and composite materials was performed in [7, 8, 10, 11, 15, 16, 20, etc.]. The basic results have been obtained using analytical, variational, and numerical methods for various shells (plates) with curvilinear holes (notches).The nonaxisymmetric deformation of and stress distribution in isotropic spherical shells with an elliptic hole are studied with allowance for physical or geometrical nonlinearity in [6,7,9,12]. The stress concentration near a circular hole in both spherical and ellipsoidal shells was analyzed in [2, 7, 13] with allowance for physical nonlinearity, in [3,4,7] with allowance for geometrical nonlinearity, and in [1,6,7,14] with allowance for both nonlinear factors (plasticity and large deflections).It is of interest to solve two-dimensional nonlinear static problems for thin shells with curvilinear (noncircular) holes under high surface and contour loads.Using the method developed in [17] and tested against some linear and nonlinear elastic problems, we will numerically analyze the elastoplastic stress-strain state near an elliptic hole in flexible spherical shells. We will also analyze the influence of nonlinear factors on the stress distribution in the stress concentration zones in a shell under surface pressure of given intensity.

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 Stress distribution in multiply connected elastic isotropic shells (plates) was studied in [3, 4, 9, 11, etc.]. The basic theoretical and experimental results have been obtained by solving linearly elastic problems for shallow and deep thin-walled shells with two and more curvilinear or rectangular holes.Physically and geometrically nonlinear problems of stress (strain or displacement) distribution in various multiply connected thin shells under static loads (surface pressure, boundary forces, or bending moments) of high intensity were addressed in [1, 3-10, 12, etc.]. A numerical method for solving nonlinear static problems for arbitrary thin shells of complex geometry with regard for geometrical (finite or large deflections) or/and physical (plastic strains) nonlinearity is outlined in [12]. This paper also proposes an algorithm for approximate solution of doubly nonlinear two-dimensional boundary-value problems of stress concentration in multiply connected shells.Specific numerical results have been obtained in [13,14] in studying the elastoplastic stress-strain state near two circular holes in spherical and cylindrical flexible shells under uniform surface load (internal pressure) of given intensity. These results were used to study the influence of physical and geometrical nonlinearities on the stress (strain) concentration in shells, depending on the distance between the holes.Expanding upon the earlier studies [12,14], we will present numerical solutions of nonlinear problems for cylindrical shells subjected to boundary forces (axial tension) and weakened by two curvilinear (circular) holes.1. We will analyze the elastoplastic state of thin-walled flexible cylindrical shell having two circular holes with centers on a common generatrix. The shell is subject to axial tensile forces of given intensity P P = ⋅ 0 3 10 N/m (Fig. 1). These forces are assumed to induce plastic strains in the stress-concentration regions of the shell, which is made of an isotropic homogeneous material. The normal displacements become comparable to or exceed the thickness of the shell [3,12], yet remain small compared with the other linear dimensions. Considering certain boundary conditions at the contours of the holes, we will analyze the stress-strain state of a complex flexible shell with certain geometrical and physicomechanical parameters, taking plastic s...

No abstract

The elastoplastic state of thin cylindrical shells with two equal circular holes is analyzed with allowance made for finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distribution of stresses along the hole boundary and in the stress concentration zone (when holes are closely spaced) is analyzed by solving doubly nonlinear boundary-value problems. The results obtained are compared with the solutions that allow either for physical nonlinearity (plastic strains) or geometrical nonlinearity (finite deflections) and with the numerical solution of the linearly elastic problem. The stresses near the holes are analyzed for different distances between the holes and nonlinear factors.Theoretical and experimental data on stress concentration in isotropic and anisotropic structural elements (plates and shells) with two or more curvilinear (circular, elliptic, or rectangular) holes have been obtained mainly based on the linear elastic theory of thin shells [1, 4, 6-9, 11, 12, 15, etc.].The distribution of stresses (strains or displacements) in multiply connected thin-walled shells of various shapes with physical (plastic strain or creep) or geometrical (finite or large deflections) nonlinearities was addressed in a few studies [1-3, 5-10, etc.]. Note that the unsteady creep of multiply connected shallow shells was studied in the publications [2,5], which analyzed the stress state of internally loaded spherical shells with two equal circular holes and with cyclically symmetrically located holes centered on a circle of given radius. Experimental data for a cylindrical shell with two longitudinally arranged nonreinforced circular holes are presented in the papers [3, 10], which analyzed the elastoplastic stability of shells and determined the critical axial compressive forces.An important task is to solve static and dynamic problems for cylindrical shells taking physical and geometrical nonlinearities into account. The paper [13] includes a generalized formulation of nonlinear stress-concentration problems for arbitrary thin shells with several holes, the governing equations, and a solution technique. Numerical data for spherical shells with two circular holes under a surface load are presented in the paper [14], which studies the influence of one and two nonlinearities on the stress distribution in shells for different distances between the holes.

No abstract

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 Introduction. Thin shells and plates are used as structural members in various fields of modern engineering. In most cases, they have complex geometry (geometry variations, holes, notches, and inclusions of various shapes) for the purposes of design or technology. High loads on structural members made of homogeneous isotropic materials (metals, alloys) may cause structural changes (plastic or creep strains) near stress concentrators and microcracks, which may lead to failure of structural members and then the whole structure. There are also large or finite displacements or strains in the zone of high stresses. One of the basic and most important tasks in the mechanics of shell structures is to analyze the distribution of stresses and strains in structural members of complex form. Therefore, in designing and manufacturing load-bearing structures or their elements with high strength and minimum weight, the need arises to take into account the real operation conditions of structural members and the real properties of structural materials (plastic strains) and their deformation (large or finite displacements).Results of theoretical and experimental analysis of the stress distribution in shells (plates) obtained by solving linear elastic boundary-value problems (linear Hooke's law, small displacements, strains) are discussed in a great many publications most fully generalized in the monographs [2,21,22,25,26,58,65]. They mainly discuss solutions of linear (elastic) problems for thin (spherical, cylindrical, conical, etc.) shells weakened by curvilinear holes of various shapes and made of advances metallic materials.The available theoretical and applied results on the stress distribution in thin and nonthin anisotropic (composite) shells made of materials obtained by solving linear elastic problems (generalized Hooke's law; Kirchhoff-Love or Timoshenko hypotheses) are presented in [27,50].To solve this class of problems in linear elastic formulation, analytic, variational, and numerical methods are used. Methods and results of solving specific classes of physically and geometrically nonlinear problems for some metal shells are discussed in the monographs [20,32,38,42,67,70]. The issue of stress concentration in shells (plates) involving the development of methods of solving nonlinear problems is analyzed in the reviews [24,89,93,94].Note that most studies on nonlinear stress concentration in shells, including problem formulation, development of methods for solving certain classes of nonlinear problems, a...

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 Introduction. The distribution of stresses (strains, displacements) around curvilinear and rectangular holes in thin-walled (including cylindrical) shells made of metallic (isotropic) and composite (anisotropic) materials is studied in monographs and review papers [1, 2, 8, 9, etc.]. The major results in this area were obtained in solving one-and two-dimensional static problems of elasticity for thin shells with one, most often circular or rectangular hole.So far solutions have been found to individual classes of stress-concentration problems in a physically nonlinear formulation (nonlinear elastic, elastoplastic strains, creep) and in a geometrically nonlinear formulation (large or finite displacements, deflections), which are involved when surface and edge loads are of high intensity [6-13].Elastoplastic problems for cylindrical shells with curvilinear holes are addressed in just a few studies [3-5, 11, 12]. Of current importance is study into the stress concentration in shells of zero Gaussian curvature with curvilinear (circular, elliptic) holes in an inelastic formulation and with allowance for both physical and geometrical nonlinearities.Nonlinear problems for arbitrary thin isotropic shells occupying simply and multiply connected domains are given a generalized formulation in the publications [8,9], which outline a method for numerical solution of these problems in view of the shape of shells and holes and the nature and stage of loading. Some numerical solutions to nonaxisymmetric (two-dimensional) nonlinear problems for spherical and cylindrical thin shells with one or two curvilinear (circular) holes subjected to surface pressure of given intensity are presented in [9][10][11][12][13].In support of the studies [9, 13], we will discuss the results from an analysis of the elastoplastic stress-strain state around a curvilinear (circular) hole in a flexible cylindrical shell subjected to distributed internal pressure of high intensity. We will examine the influence of a combination of several nonlinear factors (plastic strains and finite deflections) on the distribution of displacements, strains, and stresses along the boundary of the hole and in zones of their concentration in shells with certain geometrical and mechanical parameters and boundary conditions.