Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation

An asymptotic solution is formulated for non-linear buckling of elastically restrained imperfect shallow spherical shells continuously supported on a non-linear elastic foundation. The asymptotic iteration method is introduced to result in a cubic non-linear analytical relation between the external load and central transverse displacement (deflection) of the structures incorporating the effects of geometrical imperfection, edge-restraint coefficients, moduli of foundation and characteristic geometrical parameter. The resulting expression can be used easily to evaluate the effects of these factors on buckling behaviors. Numerical examples are given, and comparisons of the available results show validity of the method suggested in the present work.     

Dynamics of shallow shells taking into account physical non-linearities

In this paper the author, has presented a solution to the problem of dynamics of shallow shell taking into account physical non-linearities. The shell is made of non-linear material obeying a cubic stress–strain law, and energy dissipation has been included in the formulation of the problem. Solutions for cylindrical and spherical shells and numerical results for these cases are based on approximate shape functions consisting of a single term in each. Some curves of amplitude–frequency relationships are given for cylindrical and spherical shells in the case of soft-type physical non-linearity.     

Buckling analysis of discretely stringer-stiffened cylindrical shells

Engineering approach for computation of stringer stiffened cylindrical shells is realized mainly using the structurally orthotropic theory with momentless pre-buckling state. On the other hand, experimental results suggest that in many cases the mentioned theory provides excessive values of buckling load. The influence of imperfections for stringer stiffened shells seems to be less important than in an isotropic case. Considering axially symmetric momentous components of pre-buckling state cannot essentially improve theoretical results. Specific experiments showed a significant influence of stringer discreteness on the buckling loads of reinforced shells. The mentioned influence can be divided into two parts: excitation of essentially non-axially symmetric pre-buckling and buckling states. Usually, only the latter phenomenon is taken into account. In this paper we show that the first factor dominates. We propose simple analytical expressions governing non-axially symmetric pre-buckling state components. We also propose an asymptotic simplification of the buckling boundary value problem. Results obtained are compared numerically with the known theoretical and experimental data.     

Lateral-torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects

In this paper, lateral-torsional buckling behavior of open-section thin-walled beams is investigated based on a geometrically nonlinear formulation, which considers the effects of shear deformations. A finite element numerical solution along with an incremental-iterative solution procedure is adopted to trace the pre-buckling as well as the post-buckling equilibrium paths. Formulation is applicable to a general type of open-section and load position effects are also included. Numerical results are validated through comparisons with experimental results and those based on other formulations presented in the literature. Comparisons have also been made between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Examples illustrate the influence of beam slenderness and moment gradient on the effects of pre-buckling deformations in predicting bucking loads.     

Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading

This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to establish nonlinear equilibrium equations and buckling equilibrium equations, and analytical solutions for the limit instability and bifurcation buckling loads are obtained. It is found that the temperature influences the limit instability, bifurcation buckling and postbuckling behaviour of shallow arches significantly. The limit instability and bifurcation buckling loads increase with an increase of the temperature. A maximum temperature is shown to exist for the occurrence of bifurcation buckling of shallow arches, and when the temperature is higher than this value, bifurcation buckling of an arch is not possible.An arch geometric parameter is introduced to define switches between the limit instability and bifurcation buckling modes, and between buckling and no buckling. Formulae and methods for the calculation of the limiting values of the arch geometric parameter are developed. It is also found that the limiting values of the arch geometric parameter decrease with an increase of the temperature.     

Nonlinear stability analysis of infinitely long laminated cylindrical shallow shells including shear deformation under lateral pressure

This paper presents a theoretical analysis for the various kinds of buckling behaviour of infinitely long laminated cylindrical shallow shells subjected to lateral uniform pressure. The exact solutions of the nonlinear equilibrium equations, in which first-order shear deformation is included, are obtained and the buckling criteria corresponding to different kinds of buckling are constructed taking into account the effects of the transverse shear deformation.     

On the nonlinear vibration of heated bimetallic shallow shells of revolution

The axisymmetrically nonlinear free vibration of a bimetallic shallow shell of revolution under uniformly distributed static temperature changes is investigated. Based on the nonlinear bending theory of thin shallow shells, the governing equations are established in forms similar to those of classical single-layered shells theory by redetermination of reference surface of coordinate. These partial differential equations are reduced to corresponding ordinary ones by elimination of the time variable with Kantorovich averaging method following an assumed harmonic time mode. The resulting equations, which form a nonlinear two-point boundary value problem, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude are obtained successfully. A detailed parametric study is conducted involving shell geometry and temperature parameters. The effects of these variables on the frequency-amplitude characteristics are plotted and discussed.     

Frequency correspondence between membranes and functionally graded spherical shallow shells of polygonal planform

The present work presents further development of the linking relationships between vibration frequencies predicted by different theories, and they are extended from a flat plate to a spherical shallow shell. In analogy with the membrane vibration problem, exact correspondences are found for vibration frequencies of a functionally graded spherical shallow shell using the classical theory and the first-order and third-order shear deformation theories. Only the predominantly stretching and thickness-shear vibration of dilatational type and predominantly flexural vibration are considered in this work. They are decoupled from the predominantly stretching and thickness-shear vibration of rotational type. These results apply to a simply supported functionally graded spherical shallow shell of polygonal planform with arbitrarily varying material properties in the thickness direction. A Winkler–Pasternak elastic foundation and rotary inertias are incorporated. It is proved that the mathematical analogy warrants positive free vibration frequencies for the shallow shell. Mori–Tanaka's scheme is used to estimate the material properties in the numerical results.     

Free vibration of multi-layered circular cylindrical shell with cross-ply walls,including shear deformation by using spline function method

The spline function technique is used to analyze the vibration of multi-layered circular cylindrical shells with cross-ply walls including first-order shear deformation theory. Both antisymmetric and symmetric cross-ply laminations are considered in this analysis. The governing equilibrium equations are obtained in terms of displacement and rotational functions. A system of coupled ordinary differential equations in terms of displacement and rotational functions are obtained by assuming the solution in a separable form. These functions are approximated by using Bickley-type splines of suitable order to obtain the generalized eigenvalue problem by applying point collocation techniques with appropriate boundary conditions. Parametric studies are performed to analyze the frequency response of the shell with reference to the material properties, number of layers, fiber orientation, thickness to radius ratio, length to radius ratio and circumferential node number. Reasonable agreement is found with existing results obtained by FEM and other methods. Valuable results are presented as graphs and discussed. This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho Dr. K. K. Viswanathan was born in 1962 in Vellore District, India. He received his B.Sc. in Mathematics from University of Madras and M.Sc. in 1992 and Ph.D. in 1999 from Anna University, India. Later he was a Project Associate in Indian Institute of Science, Bangalore. He served as lecturer in Crescent Engg. College and as Asst. Professor in SRM University, India. He did his post doctoral research in Korea for three years. At present he serves as Professor in the Dept. of Naval Architecture, Inha University, Incheon, Korea. His research areas of interest includes vibration of plates, shells and the application of numerical techniques in Engineering problems. Dr. Kyung Su Kim was born in Korea in 1954. He is a professor in Naval Architecture and Ocean Engineering at Inha University, Korea. He obtained his B.Sc. degree in Naval Architecture and Ocean Engineering from Seoul National University, Korea, in 1981. He worked for KR (Korean Register of Shipping) from 1981 to 1983. He obtained M.Sc. degree in Naval Architecture and Ocean Engineering in 1986, and Ph.D. degree in Structural Mechanics in 1991 from Rheinisch — Westfaelische Technische Hoch-schule Aachen, Germany. From 1986 to 1992, he was a Post Doctoral Research Engineer of Engineering Research Institute at Rheinisch — Westfaelische Technische Hochschule Aachen. He was appointed as a professor of Inha University, Korea, in 1994. His major area of study is Impact and Fatigue Fracture. Dr. Jang Hyun Lee was born in Korea in 1969. Currently, he is an Assistant professor of the Department of Naval Architecture and Ocean Engineering at Inha University, Korea. He obtained his B.Sc., M.Sc. and Ph.D. degrees in Naval Architecture and Ocean Engineering from Seoul National University, Korea, in 1993, 1995 and 1999 respectively. From 1999 to 2002, he was a Post Doctoral Research Engineer of Engineering Research Institute at Seoul National University. He joined the Inha University in 2005 after holding the Chief Technology Officer at Xinnos for four years. His research interests include press forming of thick plates and shells, computational welding mechanics and Product Lifecycle Management.     

An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression

In this research, mechanical buckling of circular plates composed of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM circular plate under uniform radial compression are derived, based on the higher order shear deformation plate theory (HSDT). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations are established. A buckling analysis of a functionally graded circular plate (FGCP) under uniform radial compression is carried out and the results are given in closed-form solutions. The results are compared with the buckling loads of plates obtained for FGCP based on the first order shear deformation plate theory (FSDT) and classical plate theory (CPT) given in the literature. The study concludes that HSDT accurately predicts the behavior of FGCP, whereas the FSDT and CPT overestimates buckling loads.     

Free vibration of laminated cross-ply plates including shear deformation by spline method

Spline function approximation technique is used to analyze the free vibration of symmetric and anti-symmetric cross-ply plates under shear deformation theory. The equations of motion of the plate are derived using YNS theory. A system of coupled differential equations in terms of displacement and rotational functions are obtained by assuming the solution in a separable form. These functions are approximated using Bickley-type splines of suitable orders. A generalized eigenvalue problem is obtained on applying the process of point collocation with suitable boundary conditions. Parametric studies have been made to investigate the frequency response of the plates with reference to the material properties, number of layers, fiber orientation, side-to-thickness ratio, aspect ratio and relative layer thickness. Some results are compared with existing solution obtained by FEM.     

Optimal design of stepped circular plates with allowance for the effect of transverse shear deformation

Presented herein is a canonical exact deflection expression for stepped (or piecewise-constant thickness) circular plates under rotationally symmetric transverse loads. The circular plates may be either simply supported or clamped at the edges. As the plates may be very thick or certain portions of the optimal design may become rather thick, the significant effect of transverse shear deformation on the deflections cannot be ignored. This effect was taken into consideration in accordance to the Mindlin plate theory. Based on the analytical deflection expression, necessary conditions are derived for the optimal values of segmental lengths and thicknesses that minimize the maximum deflection of stepped circular plates of a given volume. These optimality conditions are solved using the Newton method for the optimal segmental lengths and thicknesses. Local minima are observed for this nonlinear problem at hand and they may pose some difficulties in getting the solutions. The shear deformation effect increases the plate deflections, but interestingly it affects the thickness variation marginally.     

Large scale PIV-measurements at the surface of shallow water flows

To measure the flow dynamics at the surface of shallow water flows over a large measuring field, a simple and reliable method has been developed using the advantages of Particle Image Velocimetry (PIV). Besides the determination of mean flow conditions and turbulent flow characteristics, this method makes it possible to track two-dimensional large coherent structures, which are the dominating flow phenomena in many shallow flow applications. As basic equipment, a commercial PIV software system has been used. The measurements are carried out at the water surface, which means that no laser light sheet is needed. Depending on the time scales of the flow and camera characteristics, it is even possible to work with a constant light source. A particle dispenser to provide a homogeneous distribution of particles on the water surface is also presented. Because floating particles have a strong tendency of sticking together, different types of particles and special coatings have been tested to reduce this problem. A laboratory application of this method is presented to analyze the effects of shallow dead-water zones on exchange processes in rivers where large coherent two-dimensional flow structures in the mixing layer dominate the flow characteristics.     

Vibration of functionally graded cylindrical shells based on different shear deformation shell theories with ring support under various boundary conditions

In the present work, study of the vibration of thin cylindrical shells with ring supports made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. Effects of boundary conditions and ring support on the natural frequencies of the FGM cylindrical shell are studied. The cylindrical shells have ring supports which are arbitrarily placed along the shell and which imposed a zero lateral deflection. The study is carried out using different shear deformation shell theories. The analysis is carried out using Hamilton’s principle. The governing equations of motion of a FGM cylindrical shells are derived based on various shear deformation theories. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin M. M. Najafizadeh received his BS degree in 1995 from Azad University (Arak) and the Ms Degree in 1997 from Azad University (Arak), and his Ph.D. degree in 2003 from Science and Research Branch Islamic Azad University (Tehran, Iran), all in mechanical Engineering. He is member of faculty in Islamic Azad University (Arak) since 1998. He teaches courses in the areas of dynamics, theory of plates and shells and finite element method. He has published more than 20 articles in journals and conference proceeding. Mohammad Reza Isvandzibaei received his Ms Degree from Azad University (Arak), and now he is the student of Ph.D. in university of Pune, (India) all in mechanical Engineering. He is member of faculty in Islamic Azad University (Andimeshk).     

球壳大开孔平齐接管补强设计方法评价

为了对球壳大开孔补强结构做出合理安全评价,利用我国现行标准中的补强方法,对D=500 mm,直径厚度比D/T=68、接管与壳体半径比r/R分别为0.5,0.6,0.7,0.8的球壳大开孔结构进行了补强计算,对补强后的球壳大开孔平齐接管结构,选择其高应力区的若干截面,按照"分析设计"方法进行了应力强度评定.结果表明,按极限分析法和压力面积法进行补强后的结构按分析设计可以通过;随着D/δ的增大,接管有效厚度与最小厚度之比g值随之增加;时多数大开孔情况,利用极限分析法补强后的结构更安全.     

Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells

Non-linear buckling analyses of imperfect functionally graded truncated conical shells with simply supported boundary conditions and subjected to an axial compressive load have been presented in this work. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The non-linear prebuckling deformations and initial geometric imperfections of an FGM truncated conical shell are both taken into account. The fundamental relations, modified Donnell type non-linear stability and compatibility equations of an imperfect FGM truncated conical shell are obtained and are solved by superposition and Galerkin methods, and the upper and lower critical axial loads has been found analytically. The numerical illustrations concern the non-linear buckling response of FGM truncated conical shells with different values of truncated conical shell parameters, initial imperfections and compositional profiles. Comparing the results of this study with those in the literature validates the present analysis.     

Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale

The torsional and axially compressed buckling of an individual embedded multi-walled carbon nanotube (MWNTs) subjected to an internal and/or external radial pressure was investigated in this study. The emphasis is placed on new physical phenomena which are due to both the small length scale and the surrounding elastic medium. Multiwall carbon nanotubes which are considered in this study are classified into three categories based on the radius to thickness ratio, namely, thin, thick, and almost solid. Explicit formulas are derived for the van der Waals (vdW) interaction between any two layers of an MWNT based on the continuum cylindrical shell model. In most of the previous studies, the vdW interaction between two adjacent layers was considered only and the vdW interaction among other layers was neglected. Moreover, in these works, the vdW interaction coefficient was treated as a constant that was independent of the radii of the tubes. However, in the present model the vdW interaction coefficients are considered to be dependent on the change of interlayer spacing and the radii of the tubes. The effect of the small length scale is also considered in the present formulation. The results show that there is a unique buckling mode (m,n) corresponding to the critical shear stress. This result is obviously different from what is expected for the pure axially compressed buckling of an individual multi-walled carbon nanotube.     

The influence of elastic shear deformation on the transverse shear failure of a fully clamped beam subjected to idealized blast loading

The influence of elastic shear deformation on the transverse shear response of a fully clamped beam is investigated in the present paper. The beam is made from a rigid, perfectly plastic material and subjected to a uniformly distributed pressure pulse loading. The elastic shear deformation is idealized by an elastic, perfectly plastic spring with a constant spring coefficient. Analytical solutions are obtained for the transverse shear response, which are then used to predict the occurrence of a transverse shear failure. The method presented in the paper may be extended to study the blast-induced shear failure of other structural elements when the elastic shear deformation needs to be considered.     

Hygrothermal effects on the postbuckling of shear deformable laminated plates

The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.     

重力影响下滚子链传动的横向振动分析

基于多自由度系统的振动理论,建立了竖直拉伸下滚子链传动系统横向振动动力学模型。考虑了链条重力及张力对链传动系统横向振动固有特性的影响,并利用M atlab软件对该系统横向振动固有频率进行了数值分析。在此基础上研究了不同边界激励条件对该链传动系统横向振动稳定性的影响。所得结论可为用于生产实践中的机械传动装置的动态分析与设计提供参考。