Free vibration analysis of cylindrical liquid storage tanks

The circular cylindrical tank, built on grade and usually constructed in steel, aluminum or prestressed concrete, is one of the most common forms of liquid storage vessels. This paper summarizes the results of a comprehensive, computer based, numerical investigation of lateral free vibration of cylindrical liquid storage tanks. An analytical procedure which accurately predicts the fundamental frequencies (corresponding to axial wave number and circumferential wave number both equal to one) of a wide range of cylindrical storage tanks is developed. The procedure is applicable to tanks both completely full and partially full with liquid. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

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.     

主动约束层阻尼圆柱壳的环向占优模态控制

基于作者最近对主动约束层阻尼（ACLD）圆柱壳的建模研究基础,通过数值算例进一步研究了电压分布方式对ACLD圆柱壳减振效果的影响,重点放在控制方式以及驱动电压的施加方案上.大量的数值计算表明,在多种外激励下的ACLD圆柱壳,采用环向占优模态控制方案,具有最佳的振动抑制效果,进而提出了环向占优模态控制策略的概念.     

Jacobi–Ritz method for free vibration analysis of uniform and stepped circular cylindrical shells with arbitrary boundary conditions: A unified formulation

A semi analytical approach is employed to analyze free vibration characteristics of uniform and stepped circular cylindrical shells subject to arbitrary boundary conditions. The analytical model is established on the basis of multi-segment partitioning strategy and Flügge thin shell theory. The admissible displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy arbitrary boundary conditions, the penalty method about the spring technique is adopted. The solutions about free vibration behavior of circular cylindrical shells were obtained by approach of Rayleigh–Ritz. To confirm the reliability and accuracy of this method, convergence study and numerical verifications for circular cylindrical shells subject to different boundary conditions, Jacobi parameters, spring parameters and maximum degree of permissible displacement function are carried out. Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature. In addition, some interesting results about the geometric dimensions are investigated.     

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.     

Performance of the BEM solution in 3D acoustic wave scattering

A fixed cylindrical circular cavity and a cylindrical circular column of fluid of infinite length submerged in a homogeneous fluid medium, and subjected to a pressure point source, for which closed form solutions are known, are used to assess the performance of constant, linear and quadratic boundary elements in the analysis of acoustic scattering.This aim is accomplished by evaluating the error committed by the boundary element method (BEM) for a wide range of frequencies and wave numbers. First, the position of dominant BEM errors in the frequency versus spatial wave number domains are identified and related to the natural modes of vibration of the cylindrical circular inclusion. Then, the errors that occur by using constant, linear and quadratic elements are compared when the inclusion is modelled with the same number of nodes (i.e. maintaining computational cost). Finally, the importance of the position of the nodal points inside discontinuous boundary elements is analysed.     

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.     

Optimization of geometrically imperfect stiffened cylindrical shells under axial compression

A procedure is outlined for optimizing stiffened, thin, circular, cylindrical shells under uniform axial compression against general instability, in the presence of initial geometric imperfection. The procedure consists of two parts (a) optimization on the basis of a linear buckling analysis and perfect geometry, and (b) parametric studies on a reasonable region in the design space surrounding the optimum point (as obtained from part (a)) to assess the effect of initial geometric imperfections. This procedure is demonstrated through two design examples, for which it is concluded, that the presence of initial geometric imperfections does not alter the optimum weight and the corresponding design variables appreciably.     

Symmetry considerations for anisotropic shells

The different types of symmetry exhibited by anisotropic shells for various loadings and boudary conditions are identified, and a simple procedure is presented for exploiting these symmetries in the finite element analysis. Examples are given of anisotropic cylindrical and doubly-curved shells where use of symmetry can significantly reduce the number of independent degrees of freedom in their finite element models.     

Vibration of buckled elastic structures with large rotations by an asymptotic numerical method

A methodological approach based on the finite element and perturbation methods (asymptotic numerical method) has been developed for small vibration analyses of post-buckled shells with large displacements and large rotations. The coupled non-linear static and dynamic problems based on non-linear shells theory are transformed into a sequence of linear problems. Only two linear operators have to be inverted and a large number of terms of the polynomial approximation are numerically computed. The static non-linear response, the load–displacement solution, and the load–frequency dependence are investigated for large amplitudes. The load–frequency curves are obtained for various natural frequencies at any desired load level. A continuation procedure based on Padé approximants is used to get the whole solution. Limit points, bifurcation points and stability zones are analysed. The efficiency of this procedure is tested in some benchmark problems such as rectangular plates, thin and thick cylindrical roofs and deep arches.     

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.     

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.     

The energy generation and transmission in compound elastic cylindrical shells with heavy internal fluid loading—from parametric studies to optimization

The methodology of boundary integral equations is applied for analysis and optimization of the power flows in elastic compound cylindrical shells with heavy internal fluid loading. Two generic model problems are solved and the roles of various physical parameters involved in the problem formulation are assessed. It is shown that the efficiency of an optimization procedure heavily relies on a careful parametric study of wave propagation and correct physical interpretation of its results.     

Optimal shapes of cylindrical concrete water tanks

The optimal wall shapes of circular cylindrical concrete water tanks are treated herein. The tanks have piecewise linearly tapered wall thicknesses. The internal radius and height of the tank are maintained constant while the thickness of the wall is varied along the axis so that the critical bending and hoop stresses attain values as close as possible to their allowable values. For the analysis a procedure which combines the Runge-Kutta method of solution of ordinary differential equations with a numerical minimization method is used. This procedure is then imbedded into a minimization routine to deal with the design problems. The results of the study show that the major saving in material is achieved by one slope itself. While two slopes improve the saving in material for some tanks, it does not seem reasonable to increase the number of slopes beyond two.     

Complex numerical integration procedure for static loading of anisotropic shells of revolution

Through the use of a complex series representation, a complex multi-segment numerical integration procedure is developed which can handle the static analysis of mechanically and thermally loaded branched laminated anisotropic shells of revolution with arbitrary meridional variations in thickness and material properties. In contrast to the real numerical integration treatment of anisotropic shells, the present procedure develops local and global stiffness matrices which require only half the computer storage and which requires significantly less overall computer time. Furthermore, since the overall procedure requires fewer computational steps, an improvement in numerical resolution is also obtained for a given word size machine. To illustrate the procedure several numerical examples are included.     

圆柱壳弹性波超材料分级排列的带隙拓宽方法研究

圆柱壳弹性波超材料的弯曲波带隙拓宽问题限制其满足实际工程中的宽频隔振要求,针对该问题,本文首先研究了基于局域共振机理的圆柱壳弹性波超材料弯曲波带隙特点,研究局域谐振器质量和弹簧劲度系数的关系,然后将周期分级排列的组合方式应用于圆柱壳类弹性波超材料的带隙拓宽中,并利用有限元法进行能带结构和振动传输特性计算.研究结果显示：该方法可实现弯曲波带隙的拓宽;利用组合法构建的轴向周期分级排列圆柱壳弹性波超材料可实现705-1226Hz频率范围内弯曲波的高效衰减,带隙拓宽至分别为单一谐振器的2.55倍,这表明该方法在宽频减振方面具有明显优势,应用前景广阔.     

轴向载荷作用下圆柱壳的屈曲仿真

本文采用非线性有限元方法，在经典刚塑性理论的基础上，考虑了材料非线性、大变形效应对材料的影响，利用大型通用程序LS—DYNA对圆柱壳轴向冲击屈曲过程进行了计算机仿真分析。分析表明，利用非线性有限元数值仿真方法，可以对圆柱壳屈曲这一复杂的力学过程进行真实有效的模拟再现。     

Extended capability for automated design of frame-stiffened,submersible, cylindrical shells

This paper presents a procedure and computer program for the minimum weight design of circular, cylindrical, ‘T’ frame (ring) reinforced, submersible shells where all metal thicknesses may be confined to specified gage thickness values. Using the designer specified parameters defining shell radius shell length, eccentricity, operating depth, design factors of safety, construction materials properties and when used, the specified gage thickness values, the program will generate those values of skin thickness stifiener web and flange thicknesses, stiffener web depth and flange width, and if desired, stiffener spacing that will produce the smallest shell weight to liquid weight displaced ratio.Experience with the program has demonstrated that there is usually little weight penalty associated with the use of discrete metal thickness values when the stiffener spacing can be optimized. This weight penalty can, however, be significant where the number of stiffeners is held fixed.     

考虑横向剪切和转动惯量效应的多层压电层合壳中波的传播

研究了考虑横向剪切及转动惯量效应影响的正交各向异性压电层合壳中的波传播规律。利用Cooper-Naghdi壳体理论建立了波在压电层合壳中传播方程，通过求解特征值得到并讨论了波在压电层合壳中传播特征曲线，分析丁不同的压电层数和厚度比对特征曲线的影响。该方法可用于不同层数、不同厚度、不同母体材料层的壳体中波传播的研究。     

Nonlinear analysis of reinforced concrete cylindrical shells

In this paper, analysis of reinforced concrete cylindrical shells is performed using a strain-based finite element. The shell element employed is bidimensional, cylindrical circular and has four-nodes and five nodal degrees of freedom. The nonlinearities due to concrete cracking and yielding of the steel are taken into account. The constitutive models for the materials employ the smeared cracking concept and a finite element layered approach. Concrete is modeled by a strain-induced orthotropic-elastic model under plane state of stress. A bilinear steel model is used and the stress/reversal with Baushinger effect is included. Examples show the good accuracy provided by this analysis.