Exact solutions of toroidal shells in pressure vessels and piping

In this paper, according to the theory of thin shells, the inhomogeneous Heun equations in complex form are derived for toroidal thin shells with constant thickness under symmetric load, and exact solutions are given.     

Mathematical Model of Micropolar Thermo-Elasticity of Thin Shells

With the account of qualitative results of the asymptotic method of integration of the boundary-value problem of micropolar thermo-elasticity in three-dimensional thin domain of shell, adequate hypotheses are formulated. On the basis of these hypotheses, general mathematical models of micropolar thermo-elasticity of thin shells are constructed. Based on the constructed theories of thermo-elasticity of micropolar thin shells, main statements on the thermo-elasticity of microplar circular cylindrical shells are made. With the consideration of the irregular heating of axisymmetric thermo-elasticity, for the case of hinged supported edges, numerical results are obtained. Based on the analysis of numerical results, effects of micropolarity of the material are shown.     

THERMOELASTIC BUCKLING OF THIN CYLINDRICAL SHELLS BASED ON IMPROVED STABILITY EQUATIONS

The nonlinear strain-displacement relations in general cylindrical coordinates are simplified by Sander's assumptions for the cylindrical shells and substituted into the total potential energy function for thermoelastic loading. The Euler equations are then applied to the functional of energy, and the general thermoelastic equations of nonlinear shell theory are obtained and compared with the Donnel equations. An improvement is observed in the resulting equations as no length limitations are imposed on a thin cylindrical shell. The stability equations are then derived through the second variation of potential energy, and the same improvements are extended to the resulting thermoelastic stability equations. Based on the improved equilibrium and stability equations, the magnitude of thennoelastic buckling of thin cylindrical shells under different thermal loadings is obtained. The results are extended to short and long thin cylindrical shells.     

A theoretical elastic analysis of a transition cone region in pressure vessels

In this paper, according to the theory of thin shells, a basic equation in complex form is derived for a transition cone region that consists of a conical thin shell with linearly varying wall thickness under symmetrical load. Exact solutions are given.     

A simplified bending analysis of imperfect spherical pressure vessels

An analytical solution is presented for spherical shells with imperfections in the geometry. The model is based on bending equations of the shell, and the imperfection is considered by an equivalent load approach. Particular expressions for cosine shape imperfections are developed, leading to explicit forms of the equations for displacements and stress resultants. Convergence studies for typical axisymmetric and local imperfections in thin spherical shells are presented, and the limitations of the solution regarding the amplitude of the imperfection are discussed.     

Thermal Stress Analysis by Refined Multilayered Composite Shell Theories

This paper considers the thermal stress uncoupled problem of multilayered composite shells. An assumed linear distribution of temperature through the thickness is considered for thick/thin cylindrical and spherical shells including carbon fiber reinforced layers and/or a central soft core. The Carrera's Unified Formulation (CUF) and the Principle of Virtual Displacements (PVD) are extended to derive differential governing equations for the thermal analysis of shells with constant radii of curvature. Classical and refined two-dimensional models are treated in a unified form. Both Equivalent Single Layer (ESL) and Layer-Wise (LW) approaches are considered along with variable order of expansion in the thickness direction, from linear to fourth order. In the case of ESL, the typical zig-zag form of the displacement is accounted for via the Murakami's function. Classical models have also been considered for comparison purposes. The obtained results demonstrate the effectiveness of refined models for a correct evaluation of displacements and stress field in laminated shells.     

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.     

Stress concentration in cone–cylinder intersection

The finite element method and shell theory were employed to investigate cone–cylinder shell intersections. The developed special-purpose computer program Sais (stress analysis in intersecting shells) was used for elastic stress analysis of branch connections. A comparison of calculated results with experimental data is presented. A parametric study of non-radial models of the cone–cylinder shell intersection subjected to internal pressure loading was performed. The intersections of thin and middle thickness shells were analysed. The results are presented in graphical form. Non-dimensional geometric and angular parameters are considered to analyse the effects of changing these parameters on stress ratios in the shell intersection.     

内燃机油底壳加强板声学优化

对内燃机油底壳的加强板安装位置和长度进行了声学优化。优化目标函数取辐射声功率级和增加的质量两者的加权值。采用有限元方法和边界元方法建立了复杂结构辐射噪声预测模型，用于计算辐射声功率级。结果表明，对内燃机薄壳结构进行声学优化，可以大大减小噪声辐射。     

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.     

Axisymmetric elastic postbuckling of circular plates

This paper deals with the elastic postbuckling behaviour of axisymmetric thin plates. The analysis is based on an alternative boundary integral equation formulation which has been applied successfully in connection with the large deflection analysis of plates and shells. Numerical results are obtained and compared with corresponding ones available in the literature. Further applications of the proposed formulation to more advanced problems are also discussed.     

A theoretical elastic analysis of spherical thin shell segments in pressure vessels with a circular hole under transverse load P0 and Moment M0

In this paper, according to the theory of thin shells, the uniformly valid asymptotic homogeneous solution and the exact particular solution are derived for spherical thin shell segments with a circular hole under transverse load $\text{P}{}_0$ and moment $\text{M}{}_0$.     

On a Thermodynamic Theory of Porous Cosserat Elastic Shells

This paper presents a theory for porous thermoelastic shells using the model of Cosserat surfaces and the Nunziato–Cowin theory for materials with voids. To describe the porosity of the thin body, we introduce two scalar fields: one field accounts for the changes in volume fraction along the middle surface of the shell, and the other field characterizes the porosity variations along the shell's thickness. First, we postulate the principles of thermodynamics for these two-dimensional continua and we obtain the equations of the nonlinear theory. Then, we consider the linearized theory and prove the uniqueness of solution to the boundary initial value problem with no definiteness assumption on the constitutive coefficients. Finally, we consider the deformation of isotropic and homogeneous shells and determine the constitutive coefficients for Cosserat surfaces, by comparison with the results obtained from the three-dimensional approach to shell theory.     

Fabrication and photoelectrochemical study of Ag@TiO2 nanoparticle thin film electrode

Ag@TiO₂ nanoparticle thin film was fabricated for photoelectrochemical water splitting in the visible light region. Under the irradiation of UV light, positive photocurrent was enhanced in both electrolytes of 0.1 M HNO₃ and 0.1 M NaOH owing to the excitation of photoelectrons within the TiO₂ shells. However, under the irradiation of visible light, the enhancement of positive photocurrent was observed only in 0.1 M HNO₃ because of the formation of a Schottky barrier band bending at the Ag-TiO₂ core-shell interface and the generation of photoelectrons resulted from the surface plasmon resonance of Ag cores. In 0.1 M NaOH, significant negative photocurrent was enhanced due to the influences of higher pH on the surface state and energy level of TiO₂ shells. Such a visible light-induced photoresponse enhancement and photocurrent direction switching made the Ag@TiO₂ nanoparticle thin film useful not only as a photoelectrode for water splitting but also as a photo-switch in a basic electrolyte.     

DYNAMIC STABILITY OF ROTATING COMPOSITE SHELLS WITH THERMOACTTVE SHAPE MEMORY ALLOY FIBERS

In this article the technique of the dynamic stability analysis proposed for the conventional laminated shells is extended to the activated shape memory alloy hybrid cylindrical shells. The thin symmetrically balanced laminated shell contains both the conventional (e.g., graphite or glass) fibers oriented at +? and ? ? to the shell axis and the activated shape memory alloy fibers axially oriented. Rotary and coupling inertias are neglected. The rotating with a constant angular velocity shell is simply supported at the edge hoops. The effect of returning to the original geometry after a large inelastic deformation is called the shape memory effect. Changing the temperature of the layer we modify the basic mechanical properties such as Young's modulus and the damping coefficient. The purpose of this article is to solve the dynamic stability problem and to answer the question, how does the temperature activation change dynamic stability domains of the shell. Using the standard stability technique leads to the effective sufficient criterion of the dynamic stability. The stability regions as Junctions of angular velocity, the damping coefficient, and properties of shell material are given. The results indicate that the global activation increases the admissible angular velocity both for the glass-epoxy /NiTi-epoxy and graphite-epoxy /NiTi-epoxy hybrid shells     

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.     

THERMOELASTICITY OF A REGULARLY NONHOMOGENEOUS THIN CURVED LAYER WITH RAPIDLY VARYING THICKNESS

A regularly nonhomogeneous (composite), anisotropic, thin curved layer with rapidly oscillating material parameters and thickness is considered for the case when mean thickness and period scale have small magnitudes of the same order. A three-dimensional thermoelasticity problem for this layer is reduced to a homogenized shell model by means of an asymptotic homogenization method for periodic structures. The effective thermoelastic and thermal material parameters of this shell are expressed in terms of solutions for auxiliary local problems in the cell of periodicity. Using the solution of the boundary-value problem for the homogenized shell and the solutions of the local problems, one can obtain a three-dimensional microstructure of the stresses, displacements and temperature with a high accuracy

This general model is applied to the derivation of thermoelastic and thermal constitutive equations for network periodic shells. The relations obtained lay the foundation for a new continuous model of thermoelasticity and heat conductivity for network periodic shells and plates.     

The design of thickness transition regions for GRP pressure vessels

A computer program (BOSOR4), which allows stress analysis of thin shells of linear elastic material, was used to investigate the design of thickness transitions between the end closure and cylindrical body of GRP pressure vessels. Attention is focussed on the junction of a hemispherical dome and cylinder. A simple geometry and tapered transition is proposed together with a simple but safe design procedure which gives a possible material saving of 16% for hemispherical domes compared with the recommendations of the GRP pressure vessel design code BS4994, 1973.     

FREE VIBRATIONS OF A CONICAL SHELL WITH TEMPERATURE-DEPENDENT MATERIAL PROPERTIES

This article presents an analysis of the free vibrations of a truncated conical thin shell subjected to thermal gradients. The governing equations of the shell are based on the Donnell-Mushtari theory of thin shells. Simply supported and clamped boundary conditions are considered at both ends of truncated conical shell. Temperature loading due to supersonic flow is assumed to vary along the meridian and across the thickness of the shell Hamilton's principle is used to derive the appropriate governing equations of a conical shell with temperature-dependent material properties. The shell material has a kind of inhomogeneity due to the varying temperature load and temperature dependency of material properties. The resulting differential equations are solved numerically using the collocation method. The results are compared with certain earlier results. The influence of temperature load on the vibration characteristics is examined for the conical shells with various geometrical properties.     

A comparative study of the stress field around a reinforced and an unreinforced normal intersection of two cylindrical shells

The results of a comparative study of the effects of reinforcement on the stress fields in the critical intersection region of two normally intersecting cylindrical shells are presented. The results for in-plane and out-of-plane moments have been obtained experimentally by the use of electrical resistance foil gages, and numerically by the use of a three-dimensional finite element program. The finite element analysis also includes internal pressure loading. A comparison of results obtained by using a thin shell element with six degrees of freedom at each of the four nodes (three displacements and three rotations) and a three-dimensional element with three displacement degrees of freedom at each of the eight nodes, is also given.