Free vibration analysis of circular thin plates with stepped thickness by the DSC element method

Novel formulation is presented by using the discrete singular convolution (DSC) for free vibration analysis of circular thin plates with uniform and stepped thickness. Different from the commonly used ones in literature, regularity conditions are not needed at the circular plate center point to avoid singularity. DSC circular and annular thin plate elements are established. For the DSC circular plate element with radius of R₁, the stiffness equation is first formulated in region [−R₁, R₁] with even number of nodes and then reduced to region [0, R₁] by using either symmetric or anti-symmetric conditions. The proposed DSC circular and annular plate elements are used for obtaining frequencies of uniform/stepped circular thin plates or annular thin plates with different boundary conditions. Comparison of the present DSC results to existing analytic and numerical solutions verifies the proposed formulations. The present research extends the DSC method to free vibration of circular thin plates with stepped thicknesses.     

Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads

Free and forced vibration of composite circular cylindrical shells are investigated based on the first love's approximation theory using the first-order shear deformation shell theory. The boundary conditions (BCs) are considered as clamped-free edges. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The axial compressive load was less than critical buckling loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. The effect of fiber orientation, axial load, and some of the geometric parameters on the time response of the shells has been shown. The results show that dynamic responses are governed primarily by natural period of the structure. The accuracy of the analysis has been examined by comparing results with those available in the literature and experiments.     

Discrete singular convolution method for buckling analysis of rectangular Mindlin plates

The discrete singular convolution (DSC) method is proposed for solving the elastic buckling problem of thick rectangular plates under a uniaxial compressive loading. To allow for the effect of transverse shear deformation in thick plates, the Mindlin plate theory has been adopted. The numerical results are checked against available analytical and other numerical solutions. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.     

扭转作用下有缺陷柱形壳的屈曲和后屈曲性能

分析扭转作用下有缺陷柱形壳的屈曲和后屈曲性能。基于Karman-Donnell-Type非线性微分方程建立计算公式,采用壳屈曲的边界层理论进行分析,以获得能严格满足边界条件的解决方案。采用奇摄动技术,以确定屈曲载荷和后屈曲平衡路径。数值结果显示,目前的理论能对柱形壳的后屈曲性能进行较好评估。同时分析了几何参数对柱形壳的屈曲和后屈曲性能的影响。证实了扭转作用下柱形壳的后屈曲平衡路径并不稳定,并且相对更短的壳体具有更高的后屈曲平衡能力。最后,指出初始缺陷对柱形壳屈曲和后屈曲性能的影响。对具有初始横向挠曲的有缺陷壳体的分析结果显示：即便是非常小的缺陷,也确实会减少屈曲承载力,并使得后屈曲稳定性变差。扭转作用下柱形壳的屈曲和后屈曲性能显示出明显的缺陷敏感性。此外,如果缺陷更大,那么带来的影响也随之会变得更大。     

Static analysis of thick laminated shells with different boundary conditions using GDQ

Equilibrium equations and the associated boundary conditions for doubly curved, relatively deep and thick composite shells are shown. Two First Order Shear Deformation theories (FSDTs) are used. The first one uses plate stiffness parameters for thick shells and the other includes the effect of curvature in the calculation of stiffness parameters. Equilibrium equations are put together with the equations of stress resultants to arrive at a system of seventeen first order differential equations. These equations are solved numerically with the aid of General Differential Quadrature (GDQ) method for isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with six types of different boundary conditions using above mentioned theories. Results obtained using both theories are compared with the available results in literature and those obtained using a three-dimensional (3D) analysis to test the accuracy of the shell theories presented here.     

A triangular conforming element for laminated shells

A 30 degree of freedom (DOF) conforming shell element is developed for laminated composite materials. This element is 10-noded and has a triangular shape. Sander's thin shell theory is used. The element is used to perform both static and dynamic analysis on a composite cylindrical shell. Results obtained by the present element are compared with those available in the literature (exact, experimental, and numerical) for simple support and cantilever boundary conditions. These comparisons show that one can get reasonably accurate results with the present element and good convergence characteristics.     

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.     

Static buckling analysis of thin cylindrical shell with centrally located dent under uniform lateral pressure

One of the common failure modes of thin cylindrical shell subjected to external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the geometrical imperfections present in the cylindrical shell which are very difficult to alleviate during manufacturing process. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the critical buckling pressure of thin cylindrical shells with a centrally located dent is studied using non-linear static finite-element analysis of ANSYS under external pressure with simply supported boundary conditions at the top and bottom edges of the thin cylindrical shell.     

单层球面网壳结构的风振及其参数分析

大跨度网壳结构日趋多样化、大型化、复杂化．风荷载常常起主要甚至决定性作用，风振动力响应特性研究日益受到关注与重视．目前，网壳结构的抗风设计参数取值方法尚不完善，大多沿用高层或高耸结构设计规范．本文讨论了网壳结构风振响应的时程分析计算方法，并利用节点位移风振系数、单元内力风振系数等概念来衡量网壳结构风振特性．对一类K6—6型单层球面网壳结构进行了包括几何参数、结构参数、阻尼比参数、边界约束参数、平均风速参数等多种工况的风振特性参数影响分析，得出该类单层球面网壳结构在上述各种参数工况下风振系数的变化规律，为单层网壳结构抗风设计、防灾分析提供一定参考．     

三向球面空腹网壳稳定性分析

利用非线性有限元法对三向球面空腹网壳稳定性能进行了研究,采用了特征值屈曲分析和非线性屈曲分析两种方法来考查了三向球面空腹网壳的屈曲模态和失稳全过程。通过大规模的几何参数分析得到了不同矢跨比、网壳厚度和不同支承条件下的荷载—位移曲线和极限承载力。最后将三向球面空腹网壳与相同用钢量的单层网壳进行了对比。     

Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion

Buckling and postbuckling behaviors of imperfect cylindrical shell subjected to torsion are investigated. The governing equations are based on the Karman–Donnell-type nonlinear differential equations. A boundary layer theory of shell buckling is applied to obtain the analytic solutions that meet the boundary conditions strictly. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the current theory gives quite good estimates of the postbuckling paths of cylindrical shells. The effects of the geometric parameters on the buckling and postbuckling behaviors of the cylindrical shells are analyzed. It is confirmed that the postbuckling equilibrium paths of cylindrical shells subjected to torsion are unstable and the relatively shorter shells have higher postbuckling equilibrium paths. Finally, the effects of the initial imperfections on the buckling and postbuckling behaviors of the cylindrical shells are clarified. The illustrated results of the imperfect shells with different initial transverse deflections show that extremely small imperfections do indeed reduce the buckling loads and make the postbuckling equilibrium paths be lower. The buckling and postbuckling of cylindrical shells under torsion exhibit obvious imperfect sensitivity. Furthermore, the effects become greater following with the larger imperfections.     

Application of the DSC-Element method to flexural vibration of skew plates with continuous and discontinuous boundaries

This paper generalizes the newly developed DSC-Element method for free vibration analysis of skew plates using the first-order shear deformable plate theory. Basically, the DSC-Element method not only embraces the discrete singular convolution (DSC) delta type wavelet kernel as a trial function with the Ritz principle, but also incorporates the concept of the finite element method. The current approach is novel and flexible as contrast to the global numerical methods in treating the complex kinematic supporting edges. The objective of this paper is to examine the efficiency and validity of the DSC-Element method for oblique plates having large skew angles. Parametric studies for the vibration analysis of skew plates with various skew angles, thickness ratios, aspect ratios and continuous or discontinuous periphery supports are presented as well. The natural frequencies are directly compared and discussed with those reported in the open literature. Some frequency solutions for skew plates with mixed edge conditions are also presented.     

Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections

The effect of localized axisymmetric initial imperfections on the critical load of elastic cylindrical shells subjected to axial compression is studied through analytical modeling. Some classical results regarding sensitivity of shell buckling strength with respect to distributed defects having axisymmetric or asymmetric forms are recalled. Special emphasis is placed after that on the more severe case of localized defects satisfying axial symmetry by displaying an analytical solution to the Von Kármán–Donnell shell equations under specific boundary conditions. The obtained results show that the critical load varies very much with the geometrical parameters of the localized defect. These variations are not monotonic in general. They indicate, however, a clear reduction of the shell critical load for some defects recognized as the most hazardous isolated ones. Reduction of the critical load is found to reach a level which is up to two times lower than that predicted by general distributed defects.     

Large deflection elastoplastic analysis of thin shells

Results are presented and some modifications made to problems posed in an earlier paper by the authors on the extension of the semi-loof element to the analysis of shell structures involving instabilities, snap-through and material nonlinearities. In this paper, by adopting a more refined method for solving problems of plasticity, in conjunction with a subincremental technique, more accurate results are obtained. The second-order Runge-Kutta method employed in this study shows significant improvement in the accuracy of the streesses in the shell as compared to the case when only the simple point-slope method of Euler is used. The detailed computational procedure for elastoplastic analysis of shell problems is presented in a way that can readily be incorporated into standard computer packages. Results obtained for large deflection analysis of plastic shells of different geometries and boundary conditions are compared with the available solutions and show very good agreement.     

Effect of size and orientation of a centrally located dent on the ultimate strength of a thin square steel plate under axial compression

Thin steel plates are widely used in many structural applications because of its high load carrying capacity with less weight. The load carrying capacity of thin plates mainly depends on the imperfections present in them. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the ultimate strength of a thin square plate with a centrally located dent is studied using nonlinear static finite-element analysis, under uni-axial compressive loading with simply supported boundary conditions.     

Control of axi-symmetric vibrations of cylindrical shells using active constrained layer damping

Distributed-parameter modeling of thin cylindrical shells which are fully treated with active constrained layer damping (ACLD) is presented. Hamilton's principle is utilized to develop the shell/ACLD model as well as the associated boundary conditions. A globally stable boundary control strategy is developed to damp out the vibration of the shell/ACLD system. The devised boundary controller is compatible with the operating nature of the ACLD treatments where the strain induced, in the active constraining layer, generates a control force acting at the boundary of the treated shell. As the boundary control strategy is based on a distributed-parameter model of the shell/ACLD system, the classical spillover problems resulting from using “truncated” finite element models is eliminated. Also, such an approach makes the boundary controller capable of controlling all the modes of vibration of the shell/ACLD and guarantees that the total energy norm of the system is continuously decreasing with time. Numerical examples are presented to demonstrate the effectiveness of the ACLD in damping out the vibration of cylindrical shells. Such effectiveness is determined for different control gains and compared with the performance of conventional passive constrained layer damping (PCLD). The results obtained demonstrate the high damping characteristics of the boundary controller particularly over broad frequency bands.     

The prediction of the elastic critical load of submerged elliptical cylindrical shell based on the vibro-acoustic model

Based on the vibro-acoustical model, an effective new approach to nondestructively predict the elastic critical hydrostatic pressure of a submerged elliptical cylindrical shell is presented in this paper. Based on the Goldenveizer–Novozhilov thin shell theory, the vibration equations considering hydrostatic pressures of outer fluid are written in the form of a matrix differential equation which is obtained by using the transfer matrix of the state vector of the shell. The fluid-loading term is represented as the form of Mathieu function. The data of the fundamental natural frequencies of the various elliptical cylindrical shells with different hydrostatic pressure and boundary conditions are obtained by solving the frequency equation using Lagrange interpolation method. The curve of the fundamental natural frequency squared versus hydrostatic pressure is drawn, which is approximately straight line. The elastic critical hydrostatic pressure is therefore obtained while the fundamental natural frequency is assumed to be zero according to the curve. The results obtained by the present approach show good agreement with published results.     

叉筒网壳子结构圆柱面交叉立体桁架系巨型网格结构的稳定性研究

本文针对子结构为单层叉筒网壳的圆柱面交叉立体桁架系巨型网格结构,分析了结构的构成、形体参数、支承方式等;建立了几何非线性力学模型,编制了相应的稳定分析程序;针对本结构的特点,着重研究了结构的稳定性能、失稳形式(局部失稳与整体失稳),以参数分析的形式研究了结构局部失稳与整体失稳的关系,找出了不同跨度结构在整体与局部失稳临界状态某些参数的取值规律,并给出了整体与局部失稳状态的分界曲线,可为该结构形式的工程应用提供参考。     

网格圆柱扁壳的稳定性

本文用将网格壳转化为连续壳的方法建立了网格圆柱扁亮屋盖的稳定平衡微分方程,所得的方程是属于异性圆柱扁壳的方程,并用方法求得简支边界条件的网格圆柱扁壳的临界荷载计算公式。     

Free vibration of a paraboloidal shell of revolution including shear deformation and rotary inertia

The governing strain-displacement and curvature-displacement equations for paraboloidal shells including shear deformation and rotary inertia are solved for free vibration of closed shells. The finite element method is used to obtain three-dimensional frequency of vibration solutions for a variety of boundary conditions, free, fixed and simply supported. Assumptions concerning the circumferential vibrational behavior are incorporated that reduce the analysis to a single coordinate and the element shape function is formulated using the meridional coordinate. The results for frequency of vibration compare favorably with the available literature. Selected results for frequency of vibration are presented in tabular form for several shell parameters, including free, pinned and fixed boundary conditions. Representative mode shapes are plotted for a fixed boundary condition.