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 Introduction. The stress-strain state of simply connected conical shells made of metals or composites and having curvilinear and rectangular holes was analyzed only for the elastic stage of their deformation [1, 2, 6-9, etc.].Some experimental data and a review on dynamic problems for thin-walled shells and plates with holes can be found in [4]. Experimental data for multiply connected conical shells are given in [6,16] with reference to static problems of elasticity. Theoretical results are also reported in the paper [3], which studies the frequencies and circular modes of conical shells with a circular hole that is not loaded and not reinforced.In [5], a perforated conical shell under axial compression was analyzed for stability. Axisymmetric buckling was studied by partitioning the shell into longitudinal strips regarded as compressed rods on an elastic foundation. The critical loads for a shell with (n) square holes in its middle part were determined. Numerical results were presented for a shell with four holes.Note that the elastoplastic state of conical shells with curvilinear holes was analyzed in just a few studies [6,7]. Therefore, it is of importance to solve static and dynamic problems for conical shells with both physical and geometrical nonlinearities. Note also that a generalized formulation of physically and geometrically nonlinear problems for arbitrary thin isotropic shells with one or several curvilinear holes was given in the paper [10], which also presents governing equations and a numerical method for solving static boundary-value problems for thin shells with allowance for several nonlinear factors (elastoplastic strains and finite deflections). Numerical results for spherical and cylindrical shells with a curvilinear hole under uniform pressure of prescribed intensity are used in [11][12][13] to analyze the distribution of stresses (strains, displacements) in shells and the effect of several nonlinearities on their stress-strain state.Expanding upon [10-15], we will discuss specific results on the elastoplastic stress-strain state of thin-walled flexible conical shells with a circular hole under distributed surface and edge loads.1. Let us analyze the elastoplastic state of a flexible conical shell with a curvilinear (circular, elliptic) hole in the side wall [6,10]. The shell is thin-walled, deep, made of an isotropic homogeneous material with known mechanical characteristics, and subjected to surface and edge static loads.We assume that large loads cause large deflections in the shell (along the normal to its surface) and elastoplastic deformation of its material [6].To derive...
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 Introduction. The stress-strain state of shell structures of different curvature weakened by curvilinear holes (cutouts) of different shapes is addressed in [1,4,5]. The basic results on the subject were obtained by solving linear elastic problems for thin and nonthin shells made of homogeneous (isotropic) metals and inhomogeneous (anisotropic) composites. Conical shells with stress concentrators of such types and forms were studied using analytic, variational, and numerical methods [1,4,7,9,14].Nonlinear problems of stress concentration around circular and rectangular holes in thin-walled shells of zero Gaussian curvature are addressed in a few studies [2,3,8,10]. In the case of elliptic (noncircular) holes, numerical results were obtained only for spherical [16] and cylindrical [11] elastoplastic shells under a surface load of set magnitude. It is of interest to solve nonlinear boundary-value problems for flexible conical shells with an elliptic hole on the lateral surface, taking into account physical (plastic deformation) and geometrical (finite deflections) nonlinearities. Note that the method developed in [12,15] can be used to analyze the stress distribution around curvilinear holes taking into account either one of the nonlinearities or both of them.Expending upon the studies [12-17], we will present numerical results on the elastoplastic stress-strain state around an elliptic hole in a flexible thin-walled conical shell subjected to surface pressure of high magnitude. We will analyze the effect of plastic strains, finite (large) deflections, and hole ellipticity on the distribution of stresses, strains, and displacements on the boundary of the hole and in zones of their concentration for certain geometrical and mechanical characteristics of the shell.1. Let us analyze the elastoplastic stress-strain state of thin circular conical shells made of an isotropic homogeneous material and weakened by an elliptic hole on the lateral surface ( Fig. 1; à and b are the ellipse semiaxes). The shells are subjected to uniformly distributed internal pressure q = const (q q = 0 ×10 5 Pa) that causes finite (large) deflections comparable with or
The elastoplastic state of thin conical shells with two circular holes is analyzed. The stress distribution in the stress-concentration zone is examined using a proposed technique. The stress-strain state around the two circular holes in shells under internal pressure is analyzed taking plastic strains into account. Numerical results are presented in a tableIntroduction. Study of the interaction between the boundaries of holes in thin-walled conical shells is an important task of solid mechanics. Most results on stress concentration around curvilinear and rectangular holes in conical shells made of metals and composites were obtained by solving linear elastic problems with analytic, variational, and numerical methods and are most fully reported in [2,3,9,13].Also of great interest are the solutions of two-dimensional problems for thin shells with holes of various shapes under high surface and boundary loads, which makes it necessary to take into account both the real properties of materials (plastic strains) and deformation behavior (finite deflections).Physically nonlinear cases of stress-concentration in conical shells with holes were examined in few publications. This is because the system of governing equations becomes very complicated when nonlinear factors are allowed for and there are holes in the lateral walls. Therefore, most studies of the nonlinear deformation of conical shells with holes use mesh-based methods [14]. Note that most results on the nonlinear deformation of conical shells were obtained for the case of one hole. For example, numerical results were obtained, using a variational difference method, for an elastoplastic isotropic conical shell with rectangular [4] and circular [15] holes and for a nonlinear elastic orthotropic shell with a circular hole [1]. The combined effect of plastic strains and finite deflections on the stress-strain state of a conical shell with an elliptic or circular hole was studied in [7,8]. Numerical finite-element analyses were conducted for shells subject to uniform internal pressure. Two-dimensional nonlinear problems for a shell with a circular hole under axial forces were solved numerically in [6].Most numerical results on the stress-strain state around two circular holes were obtained for spherical [11,12] and cylindrical [10] shells. The FEM was used to analyze the effect of nonlinear factors on stress concentration and the interaction of the edges of holes in shells under known uniform internal pressure. For a cylindrical shell, the case of axial tension was numerically analyzed as well. The influence of plastic strains on the stress concentration around two circular holes in the lateral wall of a conical shell under tensile forces was studied in [5].Here we formulate elastoplastic problems for isotropic conical shells with two curved holes and develop a numerical technique to solve them. We will present specific numerical results on the inelastic deformation of a conical shell with two circular holes under high uniform internal pressure.
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