Stress State Of Shell Research Articles

Simplification of the calculation scheme for determining the stress state of non-thin cylindrical shells with a complex cross-sectional shape ellipticity

An alternative to full-scale experiments is computer simulation, which allows studying a variety of states, phenomena, processes, etc. occurring in the environment.
 Conducting a computational experiment is an integral part of the design phase of new structures and their elements. One of the important issues is the choice of research model, feasible calculation scheme and possibility of its simplification.
 This research investigates orthotropic non-thin cylindrical shells with corrugated ellipses as cross sections, which has the two-parameter deviation of the cross-section shape from a circular one. Considered are shells, for which the cross-section curvature radius of the reference surface has the positive sign. The shells are subjected to internal pressure under conditions of simple support on the ends.The subject of the study is the stress state of shells and, as a consequence, the establishment of the relationship between the geometric parameters of the reference surface of the cross sections and the possibility of simplifying the calculation scheme (excluding from consideration the parameter characterizing ellipticity).The problem is solved using the spatial model of linear elasticity theory based on the method of approximation of functions by discrete Fourier series.For the class of considered shells, we find the limits of possible simplification of the calculation scheme during calculations on durability with use of the fourth theory of durability (the theory of the greatest specific potential energy), due to exclusion from consideration of the parameter, which characterizes ellipticity of corrugated cylindrical shells.The cross-sectional radius of curvature of the reference surface in the zone of greatest rigidity was chosen as a criterion for the possibility of using a simplified scheme. It is found that a simplified scheme can be used when the cross-section curvature radius of the reference surface of elliptical corrugated cylindrical shells in this section differs from that for circular corrugated shells by no more than 17%.

НАПРЯЖЕННО-ДЕФОРМИРОВАННОЕ СОСТОЯНИЕ СФЕРИЧЕСКОЙ ОБОЛОЧКИ ПОД ДЕЙСТВИЕМ ПРОИЗВОЛЬНОЙ НАГРУЗКИ НА ОСНОВЕ НЕКЛАССИЧЕСКОЙ ТЕОРИИ

Considered is the stress state of an isotropic spherical shell exposed to an arbitrary load based on a non-classical theory. When building a mathematical model of the shell, three-dimensional equations of the theory of elasticity are applied. Displacements are represented in the form of polynomials along the coordinate normal to the middle surface two degrees higher relative to the classical theory of the Kirchhoff-Love type. As a result of minimization of the refined value of the Lagrange energy functional, a system of differential equilibrium equations in displacements and natural boundary conditions are obtained. The task of reducing two-dimensional equations to ordinary differential equations is carried out by decomposing the components of displacements and external loads into trigonometric series in the circumferential coordinate. Displacements are represented in form of polynomials along the coordinate normal to the middle surface by two degrees higher relative to the classical theory of the Kirchhoff-Love type. Resulting from minimization of the refined value of the Lagrange energy functional, a system of differential equilibrium equations in displacements and natural boundary conditions are received. The task of reducing two-dimensional equations to ordinary differential equations is carried out by decomposing the components of the displacements and the external loads into trigonometric series as per the circumferential coordinate. The formulated boundary problem is solved by the methods of finite differences and matrix sweep. As a result, displacements are obtained in the grid nodes, for approximation of which splines are used. The shell deformations are found using geometric relationship; tangential stresses are received from the correlations of Hooke's law. One of the features of this paper lies in the fact that the transverse stresses are determined by the direct integration of the equilibrium equations of the three-dimensional theory of elasticity. An example of the calculation of a hemispherical shell rigidly restrained along the lower base contour is brought. The shell is exposed to the wind load. Comparison of the results received by the refined theory with the data of the classical theory has shown that in the zone of distortion of the stressed state, the normal tangential stresses are substantially revised and the transverse normal stresses, which are neglected in the classical theory, are of the same magnitude with the maximum values of the main bending stress. Considered is the influence of the relative thickness on the stress state of the shell. It was discovered that the shell thickness significantly increases the error of the classical theory, while determining the stresses and assessing the strength of the elements of the aircraft structures.

Stress State of Branched Shells of Revolution Subject to Transverse Shear and Reduction

Anonclassical shell model that allows for transverse shears and reduction is used to develop a method for analyzing the stress state of shells of revolution with a branched meridian. The associated two-dimensional problems in multiply connected domains are solved by reducing them to one-dimensional problems that are solved by the orthogonal-sweep method, with the interface conditions satisfied automatically. The reduction effect in and the stress analysis of the shell structure are illustrated by designing a real branched structure with different parameters

Ultimate strength of large scale reinforced concrete thin shell structures

This paper presents ultimate behavior of large scale reinforced concrete shell structures: hyperbolic cooling tower shell and hyperbolic paraboloid (HP) saddle shell. Both geometrical and material nonlinearities were considered in the analysis. To investigate the influence of concrete tension cracks on the structural behavior, the smeared crack model having the capability of representing double crack and crack rotation was used in the analysis. The biaxial stress state in shells is represented by the improved work-hardening plasticity concrete model, where the ductility increase phenomenon can be depicted. The load-displacement relationship, stress fields, occurrence and propagation of cracks in concrete and steel yield patterns are presented. Due to the factors such as modification in plasticity model, stiffness contribution in the doubly cracked elements, the model predicts a more ductile behavior than the results reported in the current literature. The failure of cooling tower shell seems to occur due to local yielding of meridional reinforcement in the windward meridian. In the case of HP saddle shell, structural instability occurs due to severe tension cracks in the shell part before yielding of reinforcement could occur.

Two-dimensional elastoplastic problems in the theory of flexible shells with curvilinear holes

Most theoretical investigations of the stress state of shells with stress concentrators of various types, taking account of both physical and geometric nonlinearity, have focused on axisymmetric problems [4], with the exception of [1,2], where some numerical results for two-dimensional problems were obtained on the basis of the theory of flexible shells and deformational plasticity theory.

Stress analysis near holes in shells of revolution: Geometrically nonlinear problem

An approach is proposed to numerical analysis of the stress state of shells of revolution in the geometrically nonlinear setting. It is based on a combination of linearization and discrete orthogonalization methods. Stress concentration is analyzed for a flexible spherical shell with a central hole, depending on load intensity, hole size, and the boundary conditions on the contours in the precritical strain region.

Thermoelastic-plastic stress state of shells of revolution reinforced by annular ribs

Thermoelastic-plastic stress state of shells of revolution reinforced by annular ribs

Influence of anisotropy of the elastic properties on the stress state of shells of revolution

(1960). 4. E. I. Grigolyuk and V. I. Tolkachev, Contact Problems of the Theory of Plates and Shells [in Russian], Mashinostroenie, Moscow (1980). 5. V.S. Gudramovich, "Allowance for plastic strains of reinforced shells, supported by a foundation, when subjected to a certain contact pressure," Sopr. Mater. Teor. Sooruzh., 16, 47-,48 (1972). 6. V.S. Gudramovich, Eo M. Makeev, V. I. Mossakovskii, and P. Io Nikitin, "Contact interaction of shell structures with elastic bases under complex service conditions," Probl. Prochn., No. 10, 108-114 (1985). 7. A.A. II'yushin, Plasticity [in Russian], Gostekhizdat, Moscow, Leningrad (1948). 8. V.I. Kuz'menko, "Contact problems for an elastoplastic strip subjected to complex loading," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 6, 128-135 (1985). 9. V. Io Mossakovskii, V. S. Gudramovich, and E. M. Makeev, Contact Problems of the Theory of Shells and Rods [in Russian], Mashinostroenie, Moscow (1978). I0. V. Orshak and A. Savchuk, Inelastic Behavior of Shells, [Russian translation], Mir, Moscow (1969). 11. I. V. Pasechnik, "Contact interaction of a shell and a circular foundation in accordance with the elastic base scheme of V. Z. Vlasov," in: Strength and Reliability of Structural Elements [in Russian], Naukova Dumka, Kiev (1982), pp. 104-109. 12. I. S. Tsurkov, "Design of beams, plates, and shells on the basis of the theory of plastic flow," Issled. Teor. Sooruzh., 22, 44-52 (1976).

Study of the stress state of shells of revolution loaded on areas of different forms

Study of the stress state of shells of revolution loaded on areas of different forms

Stress state of shell with unidirectionally contacting layers of different curvature

Stress state of shell with unidirectionally contacting layers of different curvature

Determining the stress state of shells of revolution with complex boundary conditions

Determining the stress state of shells of revolution with complex boundary conditions

Elastic-plastic stress state of shells of revolution, taking the deformational anisotropy of the material into account

Elastic-plastic stress state of shells of revolution, taking the deformational anisotropy of the material into account

Complementary methods in the problems of the state of stress in shells of revolution: PMM vol. 42, no. 4, 1978. pp. 724–730

Minimum energy and orthogonal projection methods are discussed for the problems of the state of stress in orthotropic shells of revolution, of variable thickness. The methods provide approximate solutions and make it possible to estimate their error in the energetic norm. The formulation of the orthogonal projections method which is the complementary of the minimum energy method, makes possible the estimation of the errors of the approximate solutions in the energetic norm. It was given in [1], where the above methods were also used in connection with the three-dimens-ional problems of the theory of elasticity, and for plates of constant thickness.

On a method of separating the state of stress in shells of negative curvature with asymptotic edges: PMM vol. 39, n≗2, 1975, pp. 333–341

The method of separating the state of stress is the following for shells with nonasymptotic edges: the total state of stress of the shell for which all the conditions of applicability of membrane theory are satisfied, is separated into the fundamental state of stress and simple edge effects. The boundary conditions are hence also separated: the tangential conditions are satisfied because of arbitrariness of the membrane theory, and the nontangential conditions because of the simple edge effects. The possibility is shown in this paper of using this method to analyze shells of negative curvature with four asymptotic edges. The theory of the generalized edge effect has been constructed in [I], Here. the formulas of the generalized edge effect are derived by another method for convenience in the subsequent exposition. Boundary conditions are formulated for membrane theory and the generalized edge effect for diverse edge fixings. All the terminology, notation, equations and relations of shell theory are borrowed from [1].

The axisymmetric elastoplastic stress state of shells of revolution

The axisymmetric elastoplastic stress state of shells of revolution