Thin Shells Of Revolution Research Articles

Effects of Internal Boundary Layers and Sensitivity on Frequency Response of Shells of Revolution

New applications introduced capsule designs with features that have not been fully analysed in the literature. In this study, thin shells of revolution are used to model drug delivery capsules both with closed and open designs including perforations. The effects of internal boundary layers and sensitivity on frequency response are discussed in the special case with symmetric concentrated load. The simulations are carried out using high-order finite element method and the frequency response is computed with a very accurate low-rank approximation. Due to the propagation of the singularities induced by the concentrated loads, the most energetic responses do not necessarily include a pinch-through at the point of action. In sensitive configurations, the presence of regions with elliptic curvature leads to strong oscillations at lower frequencies. The amplitudes of these oscillations decay as the frequencies increase. For efficient and reliable analysis of such structures, it is necessary to understand the intricate interplay of loading types and geometry, including the effects of the chosen shell models.

Forced Geometrically Nonlinear Vibrations of Thin Shells of Revolution with Piezoelectric Layers*

Forced Geometrically Nonlinear Vibrations of Thin Shells of Revolution with Piezoelectric Layers*

Funicularity in elastic domes: Coupled effects of shape and thickness

Abstract An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without ‚exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one.

Explicit Parameterizations of Non-Bending Torus-Like Surfaces

We explore an interesting three parametric family of essentially non-circular torus-like thin shells of revolution deforming under symmetrical loading without bending. It was found that these non-bending torus-like shells split naturally into two classes of shells lying either outside or inside of a given right circular cylinder. For each of these classes we obtain uniform parameterizations in terms of elliptic integrals. Explicit formulas for the aspect ratio of the non-bending toroids measuring their non-circularity are presented as well.

Use of the Riesz method to calculate axisymmetric vibrations of composite shells of revolution supported by rings and filled with a liquid

We consider the axisymmetric vibrations of a composite structure shaped as a system of thin shells of revolution connected by rings and filled with an ideal incompressible liquid. The structure is divided into independent shell blocks and frame rings. According to the Riesz method, the displacements of each free block treated as a momentless shell are represented as a series in prescribed functions supplemented with local functions of the shell boundary bending.

Influence of the Stress Mode on the Strength of High-Pressure Vessels

A numerical method for the analysis of the stress–strain state and strength of a thin-walled structural member subject to increasing internal pressure is proposed. It is based on the constitutive equations describing the elastoplastic deformation of isotropic materials along small-curvature paths and taking into account the stress mode, the theory of thin shells of revolution, failure criterion, and a method to solve a boundary-value problem of plasticity. Numerical values of the critical load are found

Hamiltonian approach to studying thin shells of revolution made of composite materials

A method for constructing defining relations of the linear theory of shells of revolution in complex Hamiltonian form has been proposed. Based on the Lagrange variational principle, we have constructed a mathematical model of a multilayer orthotropic shell of revolution. We have obtained explicit expressions for the coefficients and right-hand sides of the Hamiltonian complex system of equations describing the statics of shells of revolution in terms of their rigid characteristics and acting loads. The Hamiltonian resolving system of linear differential equations, formulated in the axially symmetric case, has some specific properties facilitating both analytical studies and numerical procedures of their solution.

An improved adaptive formulation for the computation of limit analysis problems of thin axisymmetrical shells

An improved adaptive technique for the finite element formulation of limit analysis problems of symmetrically loaded thin shells of revolution is presented. Bending, membrane behavior and changes of curvature are simulated by using an axisymmetrical thin shell element of three nodes associated with a new piecewise linear (PWL) yield surface. The results obtained show better upper bounds when compared to other numerical and analytical solutions reported in the literature. Finally, an a posteriori error measure is re-written to include the new displacement rate and PWL strain rate fields, resulting in an adaptive scheme for refining the finite element mesh.

Stability of conical shells made of composites with one plane of elastic symmetry

The paper proposes a technique for stability analysis of anisotropic laminated thin shells of revolution made of a composite with one plane of symmetry. The technique is used for numerical analysis of truncated cones made of binder-impregnated filaments continuously wound along geodesic lines. It is shown that the effect of low symmetry on the critical loads depends not only on the number of laminas, but also on the cone angle

On the influence of the reinforcement structure of fibrous shells of revolution on the heat conduction in them

The initial boundary-value problem on the heat conduction in shells reinforced with fibers of constant cross section has been considered. It has been established that the specific, anisotropic, inhomogeneous properties of such a shell are determined by its heat conductivity dependent on the thermophysical properties of the phases of the composite material of the shell, the parameters of its reinforcement, and the geometry of this shell. The ways of reducing the three-dimensional problem on heat conduction to the two-dimensional one and the possibilities of reducing the dimension of this problem for thin shells of revolution reinforced symmetrically relative to their axis by two units have been determined. The stationary temperature fields of concrete thin shells of revolution with different Gaussian curvatures and different reinforcement structures have been compared. It is shown that the reinforcement structure and the geometry of a shell of revolution substantially influence the temperature distribution in this shell, which opens up a wide range of ways selecting designs of such shells with improved thermophysical parameters.

Postbuckling analysis of elastic shells of revolution considering mode switching and interaction

The postbuckling response of shells is known to exhibit complex phenomena including mode switching and interaction, particularly in the advanced postbuckling range. The existing literature contains many initial postbuckling analyses as well as advanced postbuckling analyses for a single buckling mode, but little work is available on the advanced postbuckling analysis of shells of revolution considering mode switching and interaction. In this paper, a numerical method for the advanced postbuckling analysis of thin shells of revolution subject to torsionless axisymmetric loads is presented, in which such mode switching and interaction are properly captured. Numerical results obtained using the present method for several typical problems not only demonstrate the capability of the method, but also lead to significant observations concerning the postbuckling behavior of thin shells of revolution. In particular, the results show that strong interaction between different harmonic modes may exist and the transition of deformation mode from one to another is gradual. Consequently, the conventional approach of finding the postbuckling path of a shell as the lower festoon curve of postbuckling paths of individual harmonic modes is not valid and is at best a convenient approximation.

Shell forms for egg-shaped concrete sludge digesters: A comparative study on structural efficiency

The structural feasibility of a variety of non-conventional sludge digesters, in the form of thin shells of revolution constructed in concrete, has formed the subject of investigation of a recent programme of research at the University of Cape Town. Such forms are usually known in the literature as "egg-shaped", and the advantages of these over conventional digesters of the wide-cylindrical type are now well-recognised: superior mixing efficiency, less accumulation of deposits at the bottom, easier removal of bottom deposits and surface crust, reduced heat losses, and so forth. With the aim of exploring the structural feasibility of various non-conventional forms for concrete sludge digesters, and making available usable analytical data and practical guidelines for the design of such thin shell structures, a number of theoretical studies have recently been undertaken, and these have covered conical assemblies, spherical assemblies and parabolic ogival configurations. The purpose of the present paper is to bring together the different analytical approaches employed in each of these studies, summarise the main findings in each case, draw comparisons among the various studied configurations with regard to structural efficiency and functional suitability, and make appropriate conclusions and recommendations.

Asymptotic investigation of vehicle shock absorber with reversing shell of revolution

An energy absorber, which contains an elastic thin shell of revolution, is considered. An asymptotic method is suggested for the investigation of non-linear behaviour of the structure. An analytical solution, which is valuable for sthe design of energy absorber, has been obtained. The influence of the geometrical and stiffness parameters of the structure on the force-displacement characteristics, stresses and absorption energy are studied.

Stress Analysis of Anisotropic Inhomogeneous Shells of Revolution Subjected to Centrifugal Forces

An approach is proposed to analyze the stress state of thin shells of revolution under centrifugal loads with regard for anisotropy, the meridional variability of geometrical and mechanical parameters, and the eccentricity of the axis of revolution relative to the axis of geometric symmetry. Allowance is also made for the change in the dimensions of the shell due to deformation, which results in a nonaxisymmetric distribution of stresses and strains and their nonlinear dependence on the squared frequency of rotation. By separating variables, the problem is made one-dimensional and then solved numerically. The stress state of an ellipsoidal filament-winded composite shell is analyzed

Parametric stress distribution in shell-of-revolution sludge digesters of parabolic ogival form

Egg-shaped sludge digesters have become popular in relatively recent times owing to their superior functional performance and lower maintenance costs in comparison with conventional cylindrical digesters. These innovative structures are usually constructed as thin shells of revolution in concrete, designed to withstand principally the hydrostatic pressure loading from the contained liquid. As regards the precise shape of the egg shell, a number of mathematical shell surfaces may be envisaged, and the stress distribution will very much depend on the chosen form. In this paper, it is desired to explore the possible adoption of the parabolic ogival shell as a sludge digester. The stress distribution in such a shell is expressed in terms of a single governing parameter ξ, greatly facilitating the investigation. For various values of ξ covering the most practical range for egg-shaped digester shells, recommendations are made regarding the positioning of supports. Taking into account maximisation of tank capacity, minimisation of peak stress resultants in the shell, and ease of prestressing, the best range of ξ for parabolic ogival digester shells is identified. The overall conclusion is that from a structural and functional point of view, the parabolic ogival profile is suitable for adoption in the design of egg-shaped concrete sludge-digester shells.

Effect of structural and mechanical characteristics of the composite material on the deformation of a reflector antenna

This is a study of the effect of structural and mechanical characteristics of a composite material on the stress–strain state of a reflector antenna shaped as a composite thin shell of revolution subjected to gravity, wind, and temperature loads. The boundary‐value problem for the system of partial differential equations governing the behavior of this structure is reduced to a sequence of boundary‐value problems for inhomogeneous systems of ordinary differential equations with variable coefficients. The resulting stiff systems of equations are solved by Godunov's method of discrete orthogonalization.

The effect of the reinforcement structure on the heat conductivity of shells of revolution with a system of tubes filled with a liquid heat-transfer agent

The initial boundary-value heat-conduction problem for shells reinforced by tubes filled with a flowing liquid heat-transfer agent is considered. The dependence of the coefficients in the heat-conduction equations on the thermophysical characteristics of the composition phases, reinforcement parameters, and shell geometry is studied. A comparative analysis of the stationary temperature fields in thin shells of revolution of different Gaussian curvature is performed for various reinforcement structures and heat-exchange regimes. It is shown that the temperature distribution in the shells depends strongly on the reinforcement structure and the shell geometry, which opens up new possibilities of designing optimal structures.

Membranes of revolution under partially vanishing normal load

This paper investigates the existence and uniqueness of solutions of some boundary value problems modeling the deformation of a membrane of revolution under a partially vanishing normal load. The frame of the membrane models we deal with is the Reissner theory of thin shells of revolution, in which strain-displacement relations are nonlinear, although it assumes a linear stress-strain relation.

Solving problems on the stress state of thin shells of revolution under local loads

An approach to the solution of problems on the deformation of locally loaded orthotropic shells of revolution is proposed. Some analytical transformations are carried out to reduce the initial resolving system of partial differential equations to the form where the constant terms representing the surface loads are continuous functions of the circumferential coordinate. This allows us to accelerate the convergence of the trigonometric series that represent the desired solution. One-dimensional boundary-value problems are solved by a stable numerical method. Examples of solving problems on the stress state of a cylindrical shell are presented.

Effect of Fibre Bundle Structure on Stretch Forming Properties of Plain Weft-Knitted Fabric Composites

Knitted fabrics are known for their excellent stretchability and their flat composites have recently been shown to be easily stretch-formed into thin shells of revolution. In this paper, the stretch-forming properties are being investigated with due attention given to the fibre bundle loop structure. The capability of a plain weft-knitted fabric composite sheet to be stretch-formed is elucidated with reference to the fibre bundle structure.