Stress-strain State Of Shells Research Articles

Impact of engineering/technology factors and transient loads on the stress - strain state of a three-layer cylindrical shell

An issue of a stress-strain state of a three-layer cylindrical shell under variable loads has been considered. Assessment results of a three-layer cylindrical shell stress-strain state with regard to the physical and mechanical characteristics of an aggregate polymer filler and its reinforcement intensity by means of the stiffening rings rigidly connected to the shell coating are presented in the article. Calculations have been performed using the software Nastran. Values of displacements and stresses have been calculated by applying the direct transient dynamic process algorithm. The time interval was 0.0000025 sec, and the total number of steps was 200. Choice of the three-dimensional finite element type was conditioned by the need of acquiring more detailed and accurate calculation results. The finite element model included 8000 three-dimensional solid finite elements and 9360 nodes. Impact of the physical and mechanical characteristics’ parameters of integral polymeric filler through the stiffening rings on the shell’s stress-strain state under the axisymmetric inner impulse load has been investigated. Numerous results concerning dynamics of the three-layer structure, which have been obtained by the finite elements method, allow distinguishing the stress-strain state of a three-layered cylinder-type elastic structure at any moment within an analyzed time interval. Optimization of the shell design is recommended. Intensity of the polymeric filler reinforcement impacts considerably the stress-strain state of the shell, as well as its performance characteristics. Increasing the intensity of the shell’s polymeric layer reinforcement decreases considerably the deformation of the shell’s bearing layers. Comparison of the obtained results to the impact of other factors indicates the credibility of the approach used and that the unbiased information was received.

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

Thin-walled toroidal shells are widely used in the construction During operation, various defects appear on the surface of the shells, in particular, local depressions on the outer and inner surfaces, causing stress concentration in the structure. A three-dimensional spline option of the finite element method was developed to determine the stress-strain state of a toroidal shell with a local deepening on the outer and inner surface. The numerical experiments were carried out. The regularities of the changes in a stress-strain state of the shell with the change in the geometric parameters of the deepening were noted.

Stress-strain state of shell of revolution analysis by using various formulations of three-dimensional finite elements

The aim of the work is to perform a comparative analysis of the results of analyzing arbitrarily loaded shells of revolution using finite element method in various formulations, namely, in the formulation of the displacement method and in the mixed formulation. Methods. To obtain the stiffness matrix of a finite element a functional based on the equality of the actual work of external and internal forces was applied. To obtain the deformation matrix in the mixed formulation the functional obtained from the previous one by replacing the actual work of internal forces in it with the difference of the total and additional work was used. Results. In the formulation of the displacement method for an eight-node hexahedral solid finite element, displacements and their first derivatives are taken as the nodal unknowns. Approximation of the displacements of the inner point of the finite element was carried out through the nodal unknowns on the basis of the Hermite polynomials of the third degree. For a finite element in the mixed formulation, displacements and stresses were taken as nodal unknowns. Approximation of the target finite element values through their nodal values in the mixed formulation was carried out on the basis of trilinear functions. It is shown on a test example that a finite element in the mixed formulation improves the accuracy of the strength parameters of the shell of revolution stress-strain state.

Stress-strain state of a three-layer cylindrical shell under internal axisymmetric pulse load

The problem of dynamic deformation of a three-layer cylindrical shell under non-stationary loads in the case of rigid clamping of the shell ends is considered. The article presents the results of assessing the stress-strain state of a three-layer cylindrical shell, taking into account its structural feature, the ratio of the sheathing thickness and the physical and mechanical characteristics of a one-piece polymer filler. Calculations were performed by software complex Nastran. The values of displacements and stresses were calculated by the algorithm of direct transient dynamic process. The step duration of the time interval was 0.0000025 s, and the total number of steps was 200. The choice of the type of three-dimensional finite element was due to obtaining more detailed and accurate calculation results. The finite element model included 19000 three-dimensional finite elements and numbered 20800 nodes.
 The influence of geometrical parameters of shell layers with different physical and mechanical properties of one-piece filler on the stress-strain state under axisymmetric internal impulse load is investigated. Numerical results on the dynamics of the three-layer structure, obtained by the finite element method, allow to characterize the stress-strain state of the three-layer elastic structure of the cylindrical type at any time in the studied time interval. Optimization of the shell design is recommended. Changing the ratio of the thickness of the internal and external shells of the shell significantly affects the stress-strain state of the shell and its performance. Increasing the thickness of the internal layer of the shell significantly contributes to the increase of the latter. Comparison of the given results with materials of other similar researches and positions, testify to objectivity of the made approach.

Reinforcing Inclusion Effect on the Stress Concentration within the Spherical Shell Having an Elliptical Opening Under Uniform Internal Pressure

The authors present the results of computer simulation of the stress-strain state of a thin-walled spherical shell with an elliptical opening and the surrounding reinforcing inclusion of another material. The effect of geometric and mechanical parameters of inclusions on the stress distribution around the opening and deformation of the shell under uniform internal pressure are investigated. The issue of stress concentration in modern leading fields of technology and industry, namely, in mechanical engineering, rocket, and space, is quite topical since it is associated with the reliability and durability of the designed structures or their elements. Stress concentrators can occur due to imperfections in the materials’ structure (cavities, cracks, foreign inclusions, etc.) or technological and structural necessity (openings, cutouts, leaks). Shell structures are used as load-carrying structures in many fields of engineering. They combine high strength with low weight, which contributes to their reliability and safety during operation. In most cases, shells in real structures have simple geometric surfaces (shells of rotation). Complex structures are usually a combination of such shells. It is important to investigate the effect of local stress concentrators as openings (considering inclusions) on the stress-strain state of shells. The methods of stress concentration reduction should be outlined. The authors performed a finite element analysis of the effect of reinforcements modeled by inclusions made of the different materials as compared with the shell material having an opening on the parameters of its stress-strain state. Such investigations are crucial for the design and optimization of the structures in many engineering fields.

Research of the influence of rectangular cutout dimensions on the stress-strain state of shells using an effective finite element model

The effect of the dimensions of a rectangular cut on the stress-strain state of a cylindrical shell using an effective finite element model is investigated. A cylindrical finite element rectangular in the plan is used for thin moment shells built on the Kirchhoff – Love hypotheses. The considered finite element is based on functions of the form received at approximation of the generalized deformations with the subsequent satisfaction to the equations of compatibility of deformations. The functions of the form accurately consider displacements as rigid bodies. A comparison of convergence of results obtained with the help of the considered finite element and other known finite elements of foreign authors is given. The example of a cylindrical shell with notches shows a good correspondence of the solution radiated by the considered finite element with the method of grids, as well as the efficiency of the applied finite element having 20 degrees of freedom as compared to the common finite element having 24 degrees of freedom. The influence of the cutout dimensions on the maximum values of deflections and longitudinal forces for a cylindrical shell is shown.

Optimal design of geometrically nonlinear shells of revolution with using the mixed finite element method

The article is concerned with a methodology of optimal design of geometrically nonlinear (flexible) shells of revolution of minimum weight with strength, stability and strain constraints. The problem of optimal design with constraints is reduced to the problem of unconstrained minimization using the penalty functions method. Stress-strain state of shell is determined within the geometrically nonlinear deformation theory. A special feature of the methodology is the use of a mixed finite-element formulation based on the Galerkin method. Test problems for determining the optimal form and thickness distribution of a shell of minimum weight are considered. The validity of the results obtained using the developed methodology is analyzed, and the efficiency of various optimization algorithms is compared to solve the set problem. The developed methodology has demonstrated the possibility and accuracy of finding the optimal solution.

Stress-strain state investigation of the “YASUNI” shell by bionic architecture methods based on numerical modeling

It is hard to imagine architecture and construction without large-span shells of various applications and taking into consideration the requests of architects, the new achievements in numeral modeling of the surfaces and introduction of new groups of tailored surfaces, the appearance of new forms and types of thin-walled shell structures of this kind is inevitable. The bionic method of solving these tasks pushes the boundaries of these opportunities. The subject being studied is the stress strain state of new uncanonical shell “YASUNI”, designed of monolithic reinforced concrete with the use of modern finite element analysis settlement system. The form of the shell is built on the basis of images of the Ecuadorian flora. The form of the shell imitates a leaf of a flower laying on the lay of the land. The triangle finite-element mesh is created with a harmonic fusion of lily and daisy in a single structure. The shell is designed as a solid-cast one, made of different classes of reinforced concrete (В25, В30, В35) with thickness from δ = 5 cm to δ = 10 cm with a step 1 cm without contouring beams. The structure is subjected to self-weight. The article introduces the first results of the research of stress strain state of the shell “YASUNI”. The authors continue the research of the work this shell with different geometrical parameters, the boundary conditions with the addition of contour elements. Due to the computing complex SCAD OFFICE, precision of which is enough to perform calculations it is possible to reach the most advantageous technical-and-economic indexes of the researched uncanonical shell.

A Study of the Effect of Friction Between Delaminated Layers on the Stress-Strain State of Thick Laminated Anisotropic Cylindrical Shells by the Semianalytical Finite Element Method

An approach to studying the stress-strain state of axisymmetrical cylindrical shells with allowance for the delamination of layers by friction between them has been constructed within the framework of the three-dimensional theory of elasticity. The approach is based on the separation of shell across its thickness into a number of constituent shells with fixed curvature of each layer at the level of its median surface. To approximate the unknown functions in plan, linear polynomials are used, and their distribution over the thickness is found on the basis of the analytical solution of the corresponding system of differential equations. The proposed approach may be classified as a semianalytical finite element method. The effect of friction in the delamination zone on the stress-strain state of the shell has been analyzed.

Математическая модель напряженно деформированного состояния оболочек при осесимметричном нагружении с учетом пористых свойств материала и сложной реологии сжатого скелета

Математическая модель напряженно деформированного состояния оболочек при осесимметричном нагружении с учетом пористых свойств материала и сложной реологии сжатого скелета

The Stress–Strain State of a Ribbed Cylindrical Shell Interacting with an Elastic Foundation Under Short-Term Loads

A method for analyzing the stress-strain state of a ribbed cylindrical shell that interacts with an elastic foundation under dynamic axisymmetric loading is presented. The effect of the duration of loading and the parameters of the foundation on the deflection and bending moments of the shell is analyzed Introduction. The effect of the ambient medium on the vibrations, stability, and stress-strain state of shells under dynamic loading was addressed in many studies (5-17, 19, etc.). A literature review indicates that the dynamics of ribbed shells interacting with the ambient medium is of interest. In the present paper, we will use the Pasternak model (4) and the Winkler model to describe the ambient medium as an elastic foundation. 1. Problem Formulation. Basic Equations. Below, we will analyze the stress-strain state (SSS) of a ribbed closed cylindrical shell under short-term loads distributed over its surface. The shell interacts with an elastic foundation that prevents the normal displacements of the shell and the rotations of its mid-surface about a circumferential coordinate line. Let the longitudinal stiffening ribs (stringers) be arranged regularly and the shell be hinged at the ends. To solve the problem, we will use the classical theory of shells and rods (1) and the energy method. The total potential energy of the disturbed elastic system and the kinetic energy are given by

Подкрепления в вариационно-разностном методе расчета оболочек сложной формы

We have already considered an introduction of reinforcements in the variational-difference method (VDM) of shells analysis with complex shape. At the moment only ribbed shells of revolution and shallow shells can be calculated with the help of developed analytical and finite-difference methods. Ribbed shells of arbitrary shape can be calculated only using the finite element method (FEM). However there are problems, when using FEM, which are absent in finiteand variational-difference methods: rigid body motion; conforming trial functions; parameterization of a surface; independent stress strain state. In this regard stiffeners are entered in VDM. VDM is based on the Lagrange principle — the principle of minimum total potential energy. Stress-strain state of ribs is described by the Kirchhoff-Clebsch theory of curvilinear bars: tension, bending and torsion of ribs are taken into account. Stressstrain state of shells is described by the Kirchhoff-Love theory of thin elastic shells. A position of points of the middle surface is defined by curvilinear orthogonal coordinates α, β. Curved ribs are situated along coordinate lines. Strain energy of ribs is added into the strain energy to account for ribs. A matrix form of strain energy of ribs is formed similar to a matrix form of the strain energy of the shell. A matrix of geometrical characteristics of a rib is formed from components of matrices of geometric characteristics of a shell. A matrix of mechanical characteristics of a rib contains rib’s eccentricity and geometrical characteristics of a rib’s section. Derivatives of displacements in the strain vector are replaced with finite-difference relations after the middle surface of a shell gets covered with a grid (grid lines coincide with the coordinate lines of principal curvatures). By this case the total potential energy functional becomes a function of strain nodal displacements. Partial derivatives of unknown nodal displacements are equated to zero in order to minimize the total potential energy. As an example a parabolic-sinusoidal shell with a stiffened hole is analyzed. It is shown that ribs have generally beneficial effect to the zone of the opening: cause a reduction in a modulus of a stress, but an eccentricity affects differently, so material properties and design solutions should be taken into account in an analysis.

Анализ напряженно-деформированного состояния нетонких конических оболочек переменной толщины

On the base of developed approach to solving the problems of statics of non-thin conical shells, the analysis of an influence of thickness parameters change on the stress-strain state of shells is carried out

Stress-strain analysis of closed nonthin orthotropic conical shells of varying thickness

The approach developed to solve two-dimensional static problems for nonthin conical shells of varying thickness is used to examine the effect of the geometrical parameters on the stress-strain state of shells. The approach is based on spline-approximation and a stable numerical method of solving one-dimensional problems

Stress-strain analysis of conical shells with different boundary conditions and thickness varying in two directions at constant mass

A method developed for solving two-dimensional problems in the theory of conical shells is used to analyze the stress-strain state of shells with different boundary conditions and thickness varying in two directions at constant mass. Numerical results are given in the form of plots and tables

Mixed functionals in the theory of nonlinearly elastic shells

Results obtained on the basis of linearized functionals in the theory of nonlinearly elastic composite shells are analyzed and generalized. The Kirchhoff-Love and Timoshenko hypotheses are used. Possible membrane or shear locking is taken into account. New approaches are proposed to improve the convergence of numerical solution for new classes of nonlinear problems for thin and nonthin shells with a curvilinear (circular, elliptical) hole. The stress-strain state of shells is analyzed using different versions of shell theory. The influence of the nonlinear properties and orthotropy of composite materials on the stress distribution in structural members is studied.

Problem-Oriented Functionals in the Theory of Nonlinearly Elastic Composite Shells

Based on the Kirchhoff-Love or Timoshenko hypotheses and with regard for a possible membrane or shear degeneration, mixed linearized functionals for four variants of shell theory are presented. The convergence of numerical methods is improved by choosing small strain components as additional variable functions. New classes of problems for thin and nonthin shells are solved. The stress-strain state of shells is studied using different variants of this theory.

Determination of the axisymmetric geometrically nonlinear thermoviscoelastoplastic stress-strain state of shells of revolution

A method is developed for determining the axisymmetric thermoviscoelastoplastic stress-strain state of shells subjected to bending and torsion. The problem is solved in a geometrically nonlinear formulation with allowance for transverse shear. The geometrically nonlinear deformation of an annular plate, the thermoviscoelastoplastic deformation of a cylindrical shell, and the limiting state of a corrugated shell are studied as examples.

Elastoplastic deformation of shells of revolution under nonaxisymmetric loading (review)

Problems of determination of the elastoplastic stress-strain state of shells of revolution under nonaxisymmetric force and heat loads are solved and the results are examined. The deformation characteristics of shells of revolution whose thickness varies in two directions are related using the theory of thin shells for plasticity problems. The mechanical effects are determined by the axial asymmetry of the loads, the thickness variability, and the functional dependence of stresses on deformation, temperature, and time.

Static Analysis of Shells With Developable Middle Surfaces

This review article is devoted to an analysis of the literature on the stress-strain state of shells with developable middle surfaces. Wide choices of design methods for the developable surfaces provide not only the necessary shapes and special properties; they also prove to be convenient to apply. Representative examples are given for the static analysis of thin elastic shells by both analytic and numerical methods. Generally, the curvilinear non-orthogonal conjugate coordinates of the developable middle surface are used. Lines of principal curvatures are used as coordinates only for the strength analysis of thin shells in the form of Monge’s ruled surfaces. It is shown that momentless and moment theories give similar results if certain conditions are met a priori. The parabolic (isometric) bending of thin developable shells is also analyzed. This review article contains 97 references.