Buckling of Functionally Graded Cylindrical Shells Under Combined Thermal and Compressive Loads

This article focuses on analytical solutions for bifurcation buckling of FGM cylindrical shells under thermal and compressive loads. A new solution methodology is established based on Hamilton's principle. The fundamental problem is subsequently transformed into the solutions of symplectic eigenvalues and eigenvectors, respectively. Then, by applying a unidirectional Galerkin method, imperfection sensitivity of an imperfect FGM cylindrical shell is discussed in detail. The solutions reveal that boundary conditions, volume fraction exponent, FGM properties, and temperature rise distribution significantly influence the buckling behavior. Critical stresses are reduced greatly due to the existence of initial geometric imperfections.     

THERMAL VIBRATIONS OF THIN CYLINDRICAL SHELLS

Abstract

Solutions are developed for dynamic elastic displacements and stresses in thin, circular, cylindrical shells subjected to general temperature distributions. These are specialized to axisymmetric problems with variations in the radial and longtiduinal directions. Specific loadings considered are sequential pulses and suddenly applied thermal distributions. Numerical results generally indicate that moderate variations in the temporal and spatial distribution of temperature strongly influence response amplitudes and the times at which maximum displacements and stresses occur.     

Local load stresses in cylindrical shells at plate clips

Site personnel have to ascend columns, tanks, etc., and to stand on platforms; insulation has to be kept in position to preserve energy; equipment has to be lifted on occasions. Quite a number of such loads are small and often simple plate clips are used to fasten ladders, platform and hoisting cables. But sometimes it is desirable to assess quickly the stresses at such clips. Here we provide some simple but accurate formulae for a wide range of clip/cylinder geometries. These non-dimensional parameter expressions were developed from a large number of linear elastic FEM analyses. In addition a generally applicable stress limit is proposed for the local stresses in cylindrical shells at clip points.     

Isoparametric finite-element thermoelasto-plastic creep analysis of shells of revolution

First the strain-displacement relations of a third order isoparametric shell element are derived. Using the variational approach the stiffness and force matrices of a shell under distributed and concentrated loads and temperature gradient on distributed or concentrated elastic foundations are presented. Considering the factors that influence the material properties and the yield function, the thermoelasto-plastic and thermoelasto-plastic creep constitutive equations are introduced. Finally, a solution algorthm is proposed and applied to investigate the nature and variations of stresses produced in cylindrical shells with spherical and torospherical heads.     

Corrosion-fatigue testing of Ni-based superalloy RR1000

Operation of gas turbines at high temperatures can lead to corrosion of turbine materials. A programme was designed to understand the corrosion-fatigue behaviour of two grain size variants of RR1000 under cyclic loading at elevated.

Tests were conducted on cylindrical specimens under a range of loading conditions. Results indicated that salted specimens tested in air-SO_x had shorter fatigue lives than unsalted specimens tested in air, and this deficit was dependent on stress and/or test duration. Examination of specimens showed that the extent of corrosion was dependent on exposure time and stress. Additional salt loading resulted in faster initial pit growth which led to lower fatigue lives at higher stresses.

This paper is part of a thematic issue on the 9th International Charles Parsons Turbine and Generator Conference. All papers have been revised and extended before publication in Materials Science and Technology.     

Design of steel storage tanks with spherical bottoms

A new approach to the design of a vertical cylindrical storage vessel with a spherical bottom, based on bending theory instead of membrane analysis of shells, is proposed. The design of cylindrical shells employs the analysis of a cylindrical shell subjected to a wind load. Axial membrane stresses along the height caused by wind loading are evaluated from the prepared charts for various R/h ratios. These stress values are multiplied by a multiplication factor to obtain the meaningful bending stresses. The design of the spherical bottom involves the analysis of a shallow spherical shell on a Pasternak foundation. The distribution of membrane and bending stresses in the spherical bottom is plotted against the radial distance. To facilitate the work of the designer charts have been provided for rapid determination of various terms involved in the calculation of net stresses in the bottom.     

Effects of Thermal Loading on the Buckling and Vibration of Ring-Stiffened Functionally Graded Shell

A theoretical method is developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory (FSDT) considering rotary inertia. Heat conduction equation across the shell thickness is used to determine the temperature distribution. Material properties are assumed to be graded across the shell wall thickness of according to a power-law, in terms of the volume fractions of the constituents. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The effects of stiffener's number and size on natural frequency of functionally graded cylindrical shells are investigated. Moreover, the influences of material composition, thermal loading and shell geometry parameters on buckling and vibration are studied. The obtained results have been compared with the analytical results of other researchers, which showed good agreement. The new features of thermal vibration and buckling of ring-stiffened functionally graded cylindrical shells and some meaningful and interesting results obtained in this article are helpful for the application and the design of functionally graded structures under thermal and mechanical loads.     

Elastic analysis of cylindrical pressure vessels with various end closures

The well-known problem of the elastic analysis of cylindrical pressure vessels with hemispherical, torispherical and ellipsoidal heads, involving the partial differential equations for the classical theory of thin shells of revolution axisymmetric in character, is attempted here using a step-by-step integration procedure and a segmentation technique. The numerical results are obtained with a generalised computer program for a number of cases and for a given set of values of elastic moduli, Poisson's ratio and $\text{thickness}\text{diameter}$ ratio. The results are compared with the known results available in literature and also with the stresses predicted by the ASME Code.     

Experimental and numerical investigations of aerodynamic loads and 3D flow over non‐rotating MEXICO blades

This paper presents the experimental and numerical study on MEXICO wind turbine blades. Previous work by other researchers shows that large deviations exist in the loads comparison between numerical predictions and experimental data for the rotating MEXICO wind turbine. To reduce complexities and uncertainties, a non‐rotating experimental campaign has been carried out on MEXICO blades Delft University of Technology. In this new measurement, quasi‐2D aerodynamic characteristics of MEXICO blades on three spanwise sections are measured at different inflow velocities and angles of attack. Additionally, RANS simulations are performed with OpenFOAM‐2.1.1 to compare numerical results against measured data. The comparison and analysis of aerodynamic loads on the blade, where three different airfoil families and geometrical transition regions are used, show that for attached flow condition, RANS computation predicts excellent pressure distribution on the NACA airfoil section (r/R = 0.92) and good agreement is observed on the DU (r/R = 0.35) and RISØ (r/R = 0.60) airfoil sections. Unexpected aerodynamic characteristics are observed at the intermediate transition regions connecting the RISØ and DU airfoils, where sudden lift force drop is found at the radial position r/R = 0.55. Through numerical flow visualization, large‐scale vortical structures are observed on the suction side of the blade near the mid‐span. Moreover, counter‐rotating vortices are generated behind the blade at locations where unexpected loads occurs. Consequently, the RISØ airfoil could not give expected 2D aerodynamic characteristics because of upwash/downwash effects induced by these counter‐rotating vortices, which make 3D effects play an important role in numerical modeling when calculating the aerodynamic loads for MEXICO rotor. ©2016 The Authors Wind Energy Published by John Wiley & Sons Ltd     

Method to derive thermoelastic Green’s functions for cylindrical domains

This article presents a new method to derive Green’s functions for boundary value problems (BVPs) of steady-state thermoelasticity for domains described in cylindrical system of coordinate. The proposed method is based on new integral representations for main thermoelastic Green’s functions (MTGFs) in terms of Green’s functions for incompressible Lamé equations written in a cylindrical system of coordinates. The method is demonstrated on a BVP for cylindrical half-wedge for which MTGFs and Green-type integral formula are derived. The obtained MTGFs for half-wedge are validated by MTGFs for respective BVP for thermoelastic wedge that are obtained earlier using ΘG convolution method (ΘGCM). New MTGFs for octant, quarter-space, and half-space as particular cases of the cylindrical half-wedge also can be easily written. The advantages of the proposed method, called method of incompressible cylindrical integral representations (MICIR), in comparison with ΘGCM, are: (a) it is not necessary to construct influence functions for elastic volume dilatation Θ^(q), caused by unit point body force; and (b) it is not necessary to compute complicated convolution (volume integral of product between Θ^(q) and Green’s function G_T) in heat conduction equation.     

BUCKLING OF COMPOSITE CYLINDRICAL SHELLS UNDER MECHANICAL AND THERMAL LOADS

In this article the buckling of specially orthotropic laminated composite cylindrical shells is investigated. The nonlinear equilibrium equations based on the Sander's assumption of simplified nonlinear strain-displacement relations and the linearized stability equations for a circular cylindrical thin shell are considered. The equations include the rotations and transverse shear force. The resulting equations are improved compared to the Donnell stability equations. The mechanical and thermal buckling loads of a thin composite circular cylindrical shell based on Donnell and improved stability equations are obtained.     

Stresses at the junctions of axisymmetric shells under axially varying load

This paper deals with the investigation of stresses and deformations in the neighborhood of junctions of axisymmetric shells, made of segments of different geometries and subjected to different edge restraints and axially varying internal pressure. The method of investigation involves solution of a set of six first order highly nonlinear differential equations seeking the state of deformation of the shell at which, for a given pressure, the potential energy in the deformed shell is a relative minimum. The basic concept of the multisegment integration, as developed by Kalnins and Lestingi (On nonlinear analysis of elastic shells of revolution, J. Appl Mech. 1967;34:59–64), has been utilized for obtaining the solutions of the governing equations. Solutions for various problems are obtained for increasing loading, starting from a low value. The soundness of the method and the correctness of the computer program used in the analysis are verified by comparing the results with that of the corresponding analytical results available in the literature. Results are presented in the form of curves for stresses and deformations for varying loads and varying shell parameters which can be used for locating the critical zones and determining suitable values of shell parameters. The results include both stresses and deformations in their nondimensional forms based on both the linear and nonlinear theories.     

Wind Energy literature survey no.1

In order to help keep readers up‐to‐date in the field, Wind Energy contains a list of recently published articles drawn from issues of the following periodicals: IEEE Transactions on Energy Conversion, IEEE Transactions on Power Electronics, IEEE Transactions on Control Systems Technology, International Journal of Energy Research, Journal of Wind Engineering and Industrial Aerodynamics, American Institute of Aeronautics and Astronautics Journal and Transactions of the ASME: Journal of Dynamic Systems Measurement and Control. The list is arranged alphabetically by author. Compiled by Martin Hird, UMIST, PO Box 88, Manchester, M60 1QD, UK. Please e‐mail any suggestions to martin.hird@stud.umist.ac.uk martin.hird@stud.umist.ac.uk . Copyright © 2000 John Wiley & Sons, Ltd.     

Elasto/visco-plastic dynamic response of thin shells of revolution subjected to mechanical or thermal loads or both

An analytical method for the elasto/visco-plastic dynamic problems of axisymmetrical thin shells subjected to mechanical or thermal loads or both is developed. The equations of motion and the relations between the strains and displacements are derived by extending Sanders' elastic-shell theory. For the constitutive relations, Perzyna's elasto/visco-plastic equations, including the temperature effect, are employed. The derived fundamental equations are numerically solved by the finite-difference method. As numerical examples, simply supported cylindrical shells made of mild steel are treated, and the following two cases are analyzed: a non-uniformly heated cylindrical shell subjected to impulsive internal pressure, and an internally pressurized cylindrical shell subjected to impulsive thermal load. In both cases, the variations of displacements and internal forces with time are discussed.     

Organising a joint green European electricity market: the model ElGreen

In this paper, the features and the most important results of the computer model ElGreen will be presented. With the help of the computer model it is possible to simulate various promotion strategies for different technologies in all EU countries. Policies that can be selected are the most important price driven strategies (feed-in tariffs, investment subsidies, tax incentives), capacity driven instruments (tradable green certificates, national or international wide trading system) and a voluntary green pricing system.The following recommendations are derived:

(i)Regardless of which strategy is chosen credible sources must guarantee that the promotional strategy will survive a specified planning horizon;

(ii)The differences between either national trading, international trading or feed-in tariffs are very small if the design of the promotional system is optimised;

(iii)When introducing a TGC system it is of paramount importance that no mix up between existing and new capacities takes place.

     

Deformation and perforation of cylindrical shells struck normally by blunt projectiles

An approximate theory is proposed in this paper to predict the deformation and perforation of metallic cylindrical shells struck normally by blunt projectiles at velocities up to 229 m s⁻¹. On the basis of the experimental observations of quasi-static load–displacement characteristics, the problem of a cylindrical shell impacted normally by a blunt projectile can be tackled through the solution of an equivalent clamped circular plate struck transversely by the same projectile. It is shown that the approximate theoretical predictions are in good agreement with the experimental results for cylindrical shells in terms of the maximum permanent transverse displacements and the critical impact velocities (ballistic limits) when material strain rate sensitivity is taken into account.     

Estimation of global solar radiation in Benin

Following Frère and Rietveld's model, correlation constants a and b were determined for many stations in Benin using:

• - a graphical relationship between the average annual relative sunshine SS/SS′o and the constants (Frère's model).

• - a linear relationship between constant a and the appropriate value of sunshine duration and a hyperbolic relationship between constant b and the relative average annual sunshine (Rietveld's model).

Knowledge of constant for a location can be used to predict global solar radiation for other locations using the Angström-Page approach using a statistical relationship between global solar radiation and sunshine duration.The estimated values were compared with measured values.     

Mather Invariants and Smooth Conjugacy on \mathbb{S}^2

We construct a Mather invariant for certain classes of diffeomorphisms of the sphere. We show that two such maps f and g are smoothly conjugate if and only if the eigenvalues of Df and Dg at the fixed points agree and the Mather invariants are equivalent. We also show that the Mather invariant is onto as a functional and give conditions on the invariant under which a diffeomorphism is embeddable in a flow.     

Thermoelastic Deformations of Cylindrical Multi-Layered Shells Using a Direct Approach

In this article we study the deformation of thermo-elastic multi-layered shells, using a Cosserat model. By this direct approach, the shell-like bodies are modeled as deformable surfaces with a triad of rigidly rotating directors assigned to every point. The thermal effects are described with the help of two independent temperature fields. Concerning cylindrical orthotropic layered shells, we establish a general solution procedure for a class of thermal stresses problems. These analytical solutions are compared in some special cases with the corresponding three-dimensional solutions and thus, the thermo-elastic coupling coefficients for shells are identified in terms of the material/geometrical parameters of the layers. Finally, we present a comparison between our theoretical results and the numerical solutions obtained by a finite element analysis of a 3-layered cylindrical shell.     

Confluence of Several Regular Singular Points into an Irregular Singular One

Consider the systems and , where s and t are variables, is a parameter, and A and B = diag(₁,..., _n ) are n by n matrices. (1) has only regular singular points, and (2) has an irregular singular point at t = . Several kinds of special solutions having particular behavior near singular points were selected in previous papers. In the present paper, the author shows how (2) results from (1) in a process of confluence as . It is analyzed how the special solutions of (1) converge to those of (2) in that process. As a consequence new proofs of earlier results about connection problems are obtained.