Elastic Buckling of Multilayered Anisotropic Conical Shells

On the basis of 3D elasticity, asymptotic solutions for buckling analysis of multilayered anisotropic conical shells under axial compression are presented. By means of proper nondimensionalization, asymptotic expansion, and successive integration, the classical shell theory is derived as a first-order approximation to the 3D theory. Because the governing equations for various orders consist of partial differential equations with variable coefficients, the use of analytical techniques is restricted. The method of differential quadrature is adopted in the present study. The modifications of the buckling loads and associated buckling modes can be determined in a consistent and hierarchic manner by considering the solvability and normalization conditions for various orders. The critical loads of cross-ply conical shells with simply supported–simply supported boundary conditions are studied to demonstrate the performance of the present asymptotic theory.     

Thermal Stresses in Spherical Shells

This paper presents an iterative finite-difference technique for the analysis of axisymmetric spherical shells with variable wall thickness. The formulation is based on thin elastic shell theory. One-dimensional finite-difference points are used to discretize the shell into strips along the meridian, and an iterative technique is employed to determine the normal and meridional displacements. The stress resultants and bending stresses are then evaluated. Unlike existing analytical and finite-difference techniques, the proposed method is applicable with ease to any variation in rigidity along the meridian, to general loading conditions, and to steep and shallow shells. Results are presented and compared with those of the finite-element method.     

Buckling and Postbuckling of Antisymmetrically Laminated Cross-ply Shear-Deformable Cylindrical Shells under Axial Compression

The generalized Donnell-type equations governing large deflection of antisymmetrically laminated cross-ply cylindrical shells counting for transverse shear deformations are derived and presented. An asymptotic series solution is constructed by regular perturbation technique for postbuckling behaviors of the cylindrical shells with simply supported edges subjected to axial compression. Boundary layer influence at both ends of the shells on overall buckling and postbuckling are considered, and for consistency of the boundary valued problem, the boundary layer solutions are also designed to match the out-of-plane edge conditions by singular perturbation approach. Effects of transverse shear deformation, Batdorf’s parameter, elastic moduli ratio, and initial geometric imperfection on buckling and postbuckling performance of the shells are examined. Some numerical examples are taken for comparison of the present results of buckling loads and load–deflection curves of the shells with corresponding theoretical predictions to show effectiveness and accuracy of the present asymptotic perturbation solution.     

Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure

A mathematical approach based on the perturbation theory has been used for axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure. The equilibrium equations have been derived using the energy principle and considering the second-order shear deformation theory (SSDT), which includes shear deformation effects. This system of ordinary differential equations with variable coefficients has been solved analytically using the matched asymptotic expansion method of the perturbation theory. A comparison of the results with the finite-element method and the first-order shear deformation theory shows that the SSDT can predict the displacements and stresses of the shell for a wide range of thicknesses as well with less calculations than other analytical methods such as the Frobenius series method.     

Imperfection Sensitivity of Laminated Cylindrical Shells According to Different Shell Theories

The imperfection sensitivity of laminated cylindrical shells is considered—via the initial postbuckling analysis—on the basis of three different shell theories: Donnell in 1933; Sanders in 1963; and Timoshenko in 1961. The procedure involves nonlinear partial differential equations, which are converted into a sequence of three linear sets. The equations are solved with the variables expanded in Fourier series in the circumferential direction and in finite differences in the axial directions. A general code is developed and used in studying the effect of higher exactness of the shell theory on the sensitivity behavior, and in a parametric study of the sensitivity of anisotropic angle-ply cylindrical shells.     

Vibration of Axially Loaded Rotating Cross-Ply Laminated Cylindrical Shells via Ritz Method

This paper presents the free vibration analysis of axially loaded rotating cross-ply laminated cylindrical shells with the consideration of the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to the rotation. The Ritz method is employed for the solution of this problem. Adopting the trigonometric series as the admissible displacement functions, a set of frequency characteristics equations is derived. The frequency characteristic analysis for shells of simply supported boundary conditions is examined and the frequency characteristics of various lamination schemes are investigated. The results from the present analysis are compared with the available solutions to validate its accuracy.     

Natural Vibrations of Open-Variable Thickness Circular Cylindrical Shells in High Temperature Field

The feasibility of using the transfer matrix method (TMM) to analyze open-variable thickness circular cylindrical shells exposed to a high-temperature field is explored theoretically. In the approach to the problem, the thermal degradation (TG) of thermoelastic characteristics of the material is considered. Natural frequencies and mode shapes for the cylindrical shells are investigated in detail by combining the vibration theory with the TMM. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrices are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth-order Runge-Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix can compose the matrix of the entire structure. The frequency equations and mode shape are formulated in terms of the elements of the structural matrices. Finite-element numerical simulation has validated the present formulas of natural frequencies. Numerical illustrations, supplying pertinent information on the implications of the TG, are presented for various curvatures, aspect ratios, boundary conditions, and thickness ratios, and the pertinent conclusions are outlined.     

Three-Dimensional Vibration Analysis of Thick Shells of Revolution

A 3D method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight-line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components u;gf, uz, and u;gu in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ? and z directions. Potential (strain) and kinetic energies of the entire body are formulated, and upper-bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations and completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.     

Vibration of Open Cylindrical Shells with Stepped Thickness Variations

This paper presents the first-known exact solutions for vibration of open circular cylindrical shells with multiple stepwise thickness variations based on the Flügge thin shell theory. An open cylindrical shell is assumed to be simply supported along the two straight edges and the remaining two opposite curved edges may have any combination of edge support conditions. The shell is subdivided into segments at the locations of thickness variations. The state-space technique is adopted to derive the homogenous differential equations for a shell segment and the domain decomposition method is employed to impose the equilibrium and compatibility requirements along the interfaces of the shell segments. The correctness of the proposed method is checked against existing results in the open literature and results generated from finite element package ANSYS and excellent agreement is achieved. Several open shells with various combinations of end boundary conditions are studied by the proposed method.     

Postbuckling Analysis of Geometrically Imperfect Conical Shells

A suitable postbuckling analysis, based on geometrically nonlinear behavior, is developed for arbitrary imperfect conical shells. The conical shell was chosen as a representative case exhibiting the entire range of sensitivity to imperfection. A general symbolic code (using the MAPLE compiler) was programmed to create the differential operators of the nonlinear partial differential equations, based on Donnell’s type shell theory. The code then uses the Galerkin procedure, the Newton-Raphson and arc-length procedures, and a finite-differences scheme for automatic development of an efficient FORTRAN code. The code is used for parametric study of the nonlinear behavior and yields the sensitivity characteristic for a wide range of cone semivertex angles. A typical nonlinear behavior of a conical shell is investigated. Comparison with a simpler procedure, based on the initial postbuckling analysis (Koiter’s theory), confirms the need for the present more accurate one, especially for shells with prebuckling nonlinear behavior. The present investigation summarizes the sensitivity behavior with respect to imperfection shapes and amplitudes for the entire range of cone semivertex angles.     

Nonlinear Transient Response of Laminated Composite Shells

This paper first compares the writers’ results of static and dynamic analyses of plates, cylindrical and spherical shells employing four-, eight-, and nine-noded elements with different integration rules with those of earlier investigators and including some of the recent composite theories. Thereafter, the nonlinear transient responses of laminated composite cylindrical and spherical shell panels with cutouts are investigated taking up additional examples that are yet to appear in the published literature. For these, the finite-element model is employed using eight-noded C0 continuity, an isoparametric quadrilateral element considering von Karman large deflection assumptions. In the time integration, the Newmark average acceleration method is used in conjunction with a modified Newton–Raphson iteration scheme. Important conclusions with respect to nonlinear transient responses are summarized for cylindrical and spherical shells with and without cutouts.     

Asymptotic Approach for Thermoelastic Analysis of Laminated Composite Plates

A thermoelastic model for analyzing laminated composite plates under both mechanical and thermal loadings is constructed by the variational asymptotic method. The original three-dimensional nonlinear thermoelasticity problem is formulated based on a set of intrinsic variables defined on the reference plane and for arbitrary deformation of the normal line. Then the variational asymptotic method is used to rigorously split the three-dimensional problem into two problems: A nonlinear, two-dimensional, plate analysis over the reference plane to obtain the global deformation and a linear analysis through the thickness to provide the two-dimensional generalized constitutive law and the recovering relations to approximate the original three-dimensional results. The nonuniqueness of asymptotic theory correct up to a certain order is used to cast the obtained asymptotically correct second-order free energy into a Reissner–Mindlin type model to account for transverse shear deformation. The present theory is implemented into the computer program, variational asymptotic plate and shell analysis (VAPAS). Results from VAPAS for several cases have been compared with the exact thermoelasticity solutions, classical lamination theory, and first-order shear-deformation theory to demonstrate the accuracy and power of the proposed theory.     

Vibration of Annular Mindlin Plates with Small Cores

In most publications on vibration of annular plates, the natural frequencies are only presented for inner radius as small as one-tenth of its outer radius, but there are hardly any results presented for cores smaller than this inner radius value. This is attributed to severe scaling problems upon using numerical techniques to obtain the fundamental frequency of plates when the inner radius becomes very small. This study aims to solve this class of plate vibration problem where the annular plates are thick and their core radii are much less than one-tenth of the outer radius. The analysis involved using the Mindlin plate theory so as to allow for the effects of transverse shear deformation and rotary inertia and the truncation of the terms in the Bessel functions defining the characteristic equations in order to overcome the scaling problem. Eventually, the fundamental frequency of a thick annular plate could be deduced as finite or zero when the inner radius approaches zero.     

Postbuckling of Shear Deformable Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear deformable laminated cylindrical shell of finite length subjected to compressive axial loads. The governing equations are based on Reddy’s higher-order shear deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, cross-ply laminated cylindrical shells. The effects of transverse shear deformation, shell geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

Axisymmetric Pressures and Thermal Gradients in Conical Missile Tips

An iterative finite difference technique is presented for the analysis of axisymmetric conical shells with variable thickness. Temperature, surface pressure, and friction loadings due to supersonic flow are considered. The temperature loading is assumed to vary along the meridian and across the thickness of the shell. The variation of the material properties with temperature is taken into account. The applicability of classical thin shell theory is assumed in the analysis. The governing partial differential equation is presented in terms of the meridional and normal displacements. The proposed method of solution is applicable to short and long conical shells. Complete and truncated conical shells are treated, and results are presented and compared with those of existing solutions.     

Buckling of Circular Mindlin Plates with an Internal Ring Support and Elastically Restrained Edge

This paper is concerned with the elastic buckling problem of circular Mindlin plates with a concentric internal ring support and elastically restrained edge. In solving this problem analytically, the circular plate is first divided into an annular segment and a core circular segment at the location of the internal ring support. Based on the Mindlin plate theory, the governing differential equations for the annular and circular segments are then solved exactly and the solutions brought together by using the interfacial conditions. New exact critical buckling loads of circular Mindlin plate with an internal ring support and elastically restrained edge are presented for the first time. The optimal radius of the internal ring support for maximum buckling load is also found. An approximate relationship between the buckling loads of such circular plates based on the classical thin plate theory and the Mindlin plate theory is also explored.     

Closed-Form Solution of Axisymmetric Slender Elastic Toroidal Shells

Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper.     

口环密封对多级离心泵湿转子横--轴双向耦合动特性的影响

为探究口环密封对多级离心泵转子横-轴双向耦合振动的影响,基于空间欧拉角变换及有限元法,建立了多级离心泵转子系统叶轮和轴系的微分运动方程,在此基础上,充分考虑口环流体激振力和多种轴向力的耦合作用,利用矩阵运算方法建立了多级离心泵湿转子的横-轴双向耦合振动模型,并采用Newmark法对双向耦合系统的瞬态动力学特性进行求解,重点研究了口环密封长度、压差和间隙对系统耦合振动特性的变化规律,计算了不同密封参数下的流体激振力.计算结果表明,口环密封对转子系统横向振动的洛马金效应随着密封长度和压差的增大以及间隙的减小愈发明显,转子系统的横向稳态振动收敛速度快于轴向稳态振动的收敛速度,两向瞬态振动的振动频率呈现出完全不同的特性.此外,密封的流体激振力与密封长度呈现非线性变化关系,而与密封压差和间隙呈现线性变化关系.      

Structural changes in the endoplasmic reticulum of starfish oocytes during meiotic maturation and fertilization

The endoplasmic reticulum (ER) of live starfish oocytes was observed during meiotic maturation and fertilization. The ER was visualized by injection into the cytoplasm of an oil drop saturated with the fluorescent lipophilic dye DiI; DiI spread throughout the oocyte endoplasmic reticulum and the pattern was imaged by confocal microscopy. The ER in the immature (germinal vesicle stage) oocyte was composed of interconnected membrane sheets. In response to 1-methyladenine, the sheets of ER appeared to become associated with the yolk platelets, forming spherical shells. A few of these spherical shells could sometimes be seen in immature oocytes, but their number was much greater in the egg at the first meiotic spindle stage. At about the time that the first polar body formed, the spherical shells disappeared, and the ER returned to a form like that of the immature oocyte. The spherical shells did not reappear during the second meiotic cycle. During maturation, the ER also began to move; the movement was apparent by the time of germinal vesicle breakdown and continued throughout both meiotic cycles and in eggs with second polar bodies. When eggs at the first meiotic spindle stage were fertilized, the form of the ER changed. Within 1 min after sperm addition to the observation chamber, the circular cross sections of the spherical shells of the unfertilized egg ER were no longer distinct. At this point, the form of the ER could not be discerned with the resolution of the light microscope; however, the rate of spreading of DiI from an injected oil drop decreased, providing strong evidence that the ER had become fragmented. The ER remained in this form for several minutes and then gradually, the appearance of the ER and the rate of DiI spreading returned to be like those of the unfertilized egg. Injection of inositol trisphosphate caused a similar change in the ER structure. These results indicate that the ER is a dynamic structure, the form of which changes during oocyte maturation and fertilization.     

喷雾造粒中钼粉颗粒形貌分析

喷雾造粒是将溶液或悬浊液等原料喷雾固化后制成一定形状和强度的颗粒的一种重要的造粒方法。喷雾造粒通常会产生实心球状颗粒,还会产生环形、蜂窝状、纤维状等颗粒。另外,空心球、破损的球壳和碎片也会出现。本文对其形成的机理进行了阐述。