Buckling of laminated anisotropic shells including transverse shear deformation

The subspace iteration method used in the buckling options of the shell code FASOR is discussed. Buckling modes of a laminated anisotropic cylindrical shell and a sandwich spherical cap are presented and compared with previously published results.     

圆柱壳在热载荷及微扰外压作用下的分岔

在考虑温度对圆柱壳材料性能影响的基础上,建立了圆柱壳在扰动外压作用下的几何非线性动力控制方程.并采用伽辽金原理及 Melnikov 法研究了圆柱壳在热载荷及微扰外压作用下的分岔,进一步讨论分析了温度、Batdorf 参数等因素对圆柱壳发生混沌运动区域的影响,得出了随温度、Batdorf 参数的增大,混沌运动区域将越来越大的结论.     

Optimization of the crushing characteristics of triangulated aluminum beverage cans

In this study, a cylindrical shell body of the aluminum cans is triangulated and optimized for being folded down easily and safely for recycling. The triangulated cylindrical shell is constructed by a family of triangular surfaces based on one set of helical strips and circles lying on a cylindrical side surface. The intersections of helical strips and circles are used as the vertexes of the triangular surfaces. By changing the helical angle of the strips, the number of the strips, and the number of the circles, various triangulated cylindrical shells with different crushing characteristics can be developed. On the basis of the numerical simulation, the minimization problem of the crushing force of the triangulated cylindrical shells is solved using the crashworthiness maximization technique for tubular structures that combines the techniques of design of experiment, response surface approximation as well as usual mathematical programming.     

A general solution of bending cylindrical shell

In this paper a general solution to the bending problem of cylindrical shells is presented with standard fundamental function. It is practicable in the analysis of the bending problem of cylindrical shells with variable rigidities and reinforced ribs under arbitrary complex loads.     

A finite element study of the effect of the angle between two intersecting cylindrical shells subjected to internal pressure

The results of a study of the critical region of two intersecting cylindrical shells due to internal pressure loading are presented as a function of the angle between the two axes. The investigation was performed using the thin shell element of a three-dimensional finite element program. Three models with the angle between the axes of the two cylindrical shells equal to 30, 60, and 90°, were analyzed. In all of the three models, the diameter ratio of the two shells was 0.5283; the diameter to thickness ratio of the larger or main shell was 44.76, while the same ratio for the smaller or attached shell was 15.487. The results of these analyses show that the stresses in the critical intersection region are least when the two axes are perpendicular to each other; for other angular configurations, the stresses increase as the acute angle between the two axes decrease. This effect of inclination for pressure loading is just opposite of the effect found by authors [1] for external moments. In that case, for in-plane as well as out-ofplane moments, the stresses are larger for normally intersecting shells as compared to other angular configurations.     

Optimal design of underwater stiffened shells

The optimal design parameters of stiffened shells are determined using a rational multicriteria optimization approach. The adopted approach aims at simultaneously minimizing the shell vibration, associated sound radiation, weight of the stiffening rings as well as the cost of the stiffened shell. A finite element model is developed to determine the vibration and noise radiation from cylindrical shells into the surrounding fluid domain. The production cost as well as the life cycle and maintenance costs of the stiffened shells are computed using the Parametric Review of Information for Costing and Evaluation (PRICE) model. A Pareto/min-max multicriteria optimization approach is then utilized to select the optimal dimensions and spacing of the stiffeners. Numerical examples are presented to compare the vibration and noise radiation characteristics of optimally designed stiffened shells with the corresponding characteristics of plain un-stiffened shells. The obtained results emphasis the importance of the adopted multicriteria optimization approach in the design of quiet, low weight and low cost underwater shells which are suitable for various critical applications. Received September 14, 2000 Communicated by J. Sobieski     

Optimization of inelastic cylindrical shells with internal supports

A non-linear programming method is developed for optimization of inelastic cylindrical shells with internal ring supports. The shells under consideration are subjected to internal pressure loading and axial tension. The material of shells is a composite which is considered as an anisotropic inelastic material obeying the yield condition suggested by Lance and Robinson. Taking geometrical non/linearity of the structure into account optimal locations of internal ring supports are determined so that the cost function attains its minimum value. A particular problem of minimization of the mean deflection of the shell with weakened singular cross sections is treated in a greater detail.     

功能梯度薄壁圆柱壳的自由振动

研究了由功能梯度材料制成的薄壁圆柱壳的自由振动.采用幂律分布规律描述功能梯度材料沿厚度的梯度性质,根据Donnell壳体理论,导出了功能梯度材料薄壁圆柱壳线性振动的简化控制方程.基于此理论分析了功能梯度圆柱壳的自由振动特性,给出了两端简支功能梯度材料薄壁圆柱壳小挠度固有振动的频率公式.以简支圆柱壳作为算例,与前人结果及有限元法对比验证了该简化功能梯度薄壁圆柱壳理论的正确性,同时讨论了周向波数及梯度指数对其频率的影响.     

Buckling of cylindrical shells under the action of nonuniform external pressure

Over the last few decades, storage tanks have become bigger and thinner. Because of this, the buckling capacity of these cylindrical shells may well be the determining factor of shell thickness. In this paper, the critical buckling load of isotropic and orthotropic cylinders subjected to different types of wind load distributions is investigated. The prebuckling displacements are obtained by using the membrane theory of shell analysis. The principle of minimum potential energy in conjunction with Ritz's approach is used to obtain the stability matrix. The size of the stability matrix in this analysis is (81 × 81). By solving the stability matrix as an eigenvalue problem, the critical pressures are obtained as eigenvalues and the deflection shapes as eigenvectors. In the present study cylindrical shells of various dimensions, which are fixed at the base and free at the top, are investigated. The buckling load curves for isotropic and orthotropic cylinders of various dimensions are given for practical use.     

Determination of realistic worst imperfection for cylindrical shells using surrogate model

Thin-walled cylindrical shells subjected to axial compression are sensitive to initial geometrical imperfections. Firstly, the influence of a single dimple imperfection on the load-carrying capacity of cylindrical shells is investigated by varying the amplitudes, directions and positions of the dimple imperfection. Then a single delta function is introduced to describe the profile of the dimple imperfection in a more general form, which enables to analyze conveniently the effect of the imperfect zone area on the load-carrying capacity of cylindrical shells. Thereafter, a surrogate-based optimization framework of determining the worst realistic imperfection is proposed to study the reduction of the buckling load of cylindrical shells based on a finite number of dimple imperfections. The possible dimple imperfections may be introduced during the service of cylindrical shells. Finally the effectiveness of the present method is demonstrated by an illustrative example.     

Free vibration analysis of circular cylindrical shells

Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

Influence of edge conditions on the modal characteristics of cross-ply laminated shells

The dynamic and static behavior of cross-ply laminated shells are investigated using the third-order shear deformation shell theory of Reddy. The theory is a modification of the Sanders shell theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the shell and does not require shear correction coefficients. The Lévy-type exact solutions for bending, buckling and natural vibration are presented for doubly curved, cylindrical and spherical shells under various boundary conditions.     

Analysis of stresses in internally loaded cylindrical shells

Simply supported cylindrical shells under internal fluid and granular loading are investigated. A Fourier series solution is presented and results are shown for various shell geometries. The accuracy of the results is discussed and a comparison is made with other approximate methods available in the materials handling industry.     

A general finite element model for shells of arbitrary geometry

A finite element formulation is developed for the large displacement analysis of arbitrary shells. Formulation is based on a convected coordinate system and a tensorial approach is followed. The strain-displacement relationships used do not reflect the Kirchhoff hypothesis and Love's approximations. Isoparametric interpolation is used for the discretization of the problem, and the number of nodal points is variable. The numerical examples include the buckling analysis of cylindrical shells as well as two problems to test the convergence and accuracy of the algorithm.     

Optimal design of cylindrical shells

In this paper, two types of problems of the optimal design of cylindrical shells with arbitrary axisymmetrical boundary conditions and distributed load, under the condition of the volume being constant, are discussed. These problems involve the minimax deflection and minimal compliancy of a cylindrical shell. Expressions of the objective function can be obtained by a stepped reduction method. In minimizing the maximum deflection, the position of the maximum deflection from the previous iteration is used as the next one. This procedure converges (Avriel 1976). Several examples are provided to illustrate the method.     

Collapse of long, noncircular, cylindrical shells under pure bending

This paper describes an extension of a method developed in a previous paper to determine the moment carrying capacity of elastoplastic noncircular cylindrical shells with infinite length by the finite element method. As a result of the shape change in the cross section of a shell during deformation, the bending moment reaches a global maximum value and then decreases as the bending curvature further increases. The shell would consequently collapse at the maximum moment. However, a bifurcation buckling may occur before the maximum moment can be developed. This bifurcation buckling could induce collapse of the shell under a moment less than the maximum. Determination of the likelihood that the bifurcation buckling would generate shell collapse may be made from the initial post-buckling behavior. An initial post-buckling analysis based on the J₂ deformation theory of plasticity has been developed in this paper. The finite element method with one spatial variable is used to locate the bifurcation point as well as to analyze the initial post-buckling behavior. Numerical examples of cylindrical shells with various cross-sectional shapes are shown. In particular, for a shell of square cross section, the moment at the bifurcation is much lower than the maximum value; however, the initial post-buckling analysis reveals that the state of equilibrium is still stable. Deep post-buckling analysis is required to determine the moment carrying capacity of a shell with such cross section.     

Computation of lower-bound elastic buckling loads using general-purpose finite element codes

This paper investigates ways to have a computational implementation of a lower bound approach for the buckling of imperfection-sensitive shells using general purpose finite element codes. This approach was developed by Croll and others, and has been mainly employed by developing special purpose programs or analytical solutions. However, it is felt that this limits the possibilities of the user, and this shortcoming is addressed in the paper. First, the formulation is presented in a way to highlight what computations can be done following a reduced energy approach. Then, a methodology is implemented in conjunction with a general purpose program to compute the lower bound buckling load for cylindrical shells with different geometric configurations under uniform pressure. The accuracy of the procedure and the difficulties in the implementation, depending on the finite element chosen for the discretization are shown. Results demonstrate that the proposed reduced energy model can predict the lower bound load for cylindrical shells under uniform pressure distributions.     

Postbuckling of multilayer cylindrical and spherical shell panels reinforced with graphene platelet by isogeometric analysis

The present work fills a gap on the postbuckling behavior of multilayer functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and spherical shell panels resting on elastic foundations subjected to central pinching forces and pressure loadings. Based on a higher-order shear deformation theory and the von Kármán’s nonlinear strain–displacement relations, the governing equations of the FG-GPLRC cylindrical and spherical shell panels are established by the principle of virtual work. The non-uniform rational B-spline (NURBS) based isogeometric analysis (IGA), the modified arc-length method and the Newton’s iteration method are employed synthetically to obtain nonlinear load–deflection curves for the panels numerically. Several comparative examples are performed to test reliability and accuracy of IGA and arc-length method in present formulation and programming implementation. Parametric investigations are carried out to illustrate the effects of dispersion type of the graphene platelet (GPL), weight fraction of the GPL, thickness of the panel, radius of the panel and parameters of elastic foundation on the load–deflection curves of the FG-GPLRC shell panels. Some complex load–deflection curves of the FG-GPLRC cylindrical and spherical shell panels resting on elastic foundations may be useful for future references.

     

Vibration of thin cylindrical shells based on a mixed finite element formulation

A Hellinger-Reissner functional for thin circular cylindrical shells is presented. A mixed finite element formulation is developed from this functional, which is free from line integrals and relaxed continuity terms. This element is applied to the problem of vibration of rectangular cylindrical shells. Bilinear trial functions are used for all field variables. The element satisfies the compatibility and completeness requirements. The numerical results obtained in this work show that convergence is quite rapid and monotonic for a much smaller number of degrees of freedom than other finite element formulations.     

A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problems

This paper has two main objectives. First to describe a very simple facet triangular plate and shell finite element called TRUMP which includes, if required, transverse shear deformation and is based on physical lumping ideas with a simple mechanical interpretation [ 1,2,4,5 ]. Second to give an account of some non-trivial numerical examples of large deflection and post-buckling of shells. There are two types of non-linear structural problems which give rise to particularly delicate numerical experimentation. They are those involving deflections of the order of the structural dimensions, such as three-dimensional elastica, and the instability phenomena of the type leading to dynamic snapthrough, e.g. in cylindrical panels. To tackle such problems using a highly sophisticated shell element such as SHEBA is neither easy nor inexpensive. It is shown that the TRUMP element with only 18 displacement and rotation degrees of freedom is relatively economical to use and yet capable of engineering accuracy. The paper makes use of the theory of simplified geometrical stiffness based on the natural mode method which has been described fully in previous publications [1,2].