A thin cylindrical shell finite element based on a mixed formulation

A specialized functional for thin cylindrical shells derived from the Washizu-Hu variational principle using considerations of relaxed continuity requirements is presented. A mixed formulation for a cylindrical thin shell finite element is developed from this functional. The assumed fields for displacements and stress resultants are bilinear functions in the longitudinal and circunferential directions.The agreement between the present results and those obtained in previous formulations is good if the comparison is based on the precision related to the number of variables involved in the problem.     

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.     

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiffened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.     

Numerically integrated triangular element for doubly curved thin shells

A doubly curved triangular finite element for the analysis of thin shells with nonzero Gaussian curvature is developed by numerical integration. The element, though nonconforming in bending, is found to give good results when applied to cylindrical and spherical shell problems.     

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.     

A conical shell finite element

In the analysis of rocket and missiles structures one frequently encounters cylindrical and cornica' shells. A simple finite element which fits the above configuration is obviously a conical shell finite element. In this paper stiffness matrix for a conical shell finite element is derived using Novozhilov's strain-displacement relations for a conical shell. Numerical integration is carried out to ge. the stiffness matrix. The element has 28 degrees-of-freedom and is nonconforming. An eigenvalue analysis of the stiffness matrix showed that it contains all the rigid body modes (six in this case) adequately, which is one of the convergence criteria. An advantage of this element is that a cylindrical shell, an annular segment flat plate, a rectangular flat plate elements can easily be obtained as degenerate cases. The effectiveness of this element is shown through a variety of numerical examples pertaining to annular plate, cylindrical shell and conical shell problems. Comparison of the present solution is made with the existing ones wherever possible. The comparison shows that the present element is superior in some respects to the existing elements     

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.     

A three-dimensional state space finite element solution for laminated composite cylindrical shells

On the basis of the theory of three-dimensional elasticity, this paper presents a state space finite element solution for stress analysis of cross-ply laminated composite shells. This is a continuation of the authors’ previously published work on laminated plates [Compos. Struct. 57 (1–4) (2002) 117; Comput. Methods Appl. Mech. Engrg. 191 (37–38) (2002) 4259]. Once again a state space formulation is introduced to solve for through-thickness stress distributions, while the traditional finite elements are used to approximate the in-surface variations of state variables. A three-dimensional laminated shell element is established in an arbitrary orthogonal curvilinear coordinate system, while the application of the element is shown by calculating stresses in laminated cylindrical shells. Compared with the traditional finite element method, the new solution provides accurate continuous through-thickness distributions of both displacements and transverse stresses.     

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

A modified Hellinger-Reissner functional for thin shells of revolution is presented. A mixed finite element formulation is developed from this functional which is free from line integrals and relaxed continuity terms. This formulation is applied to the problem of free vibration of spherical and conical shells. Bilinear trial functions are used for all field variables. The quadrilateral curved elements here presented satisfy the C⁰ continuity requirement of the functional. In all the results obtained the accuracy is quite good even for a reasonable     

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.     

Effect of bolt load on the deformation of a taper hub flange

This paper presents an investigation to study the effect of bolt load on the displacement and stress pattern of a taper hub flange. The flange is analysed both by finite difference and finite element methods. Novozhilov's self-consistent shell theory is applied in deriving the equations of equilibrium in the three dimensions. The axial displacements are important in any flange design with regard to the leakage characteristics of such a joint hence the preference to the above theory. The tapered hub is approximated by a series of consecutive stepped cylindrical shells. While applying the finite difference method, the flange ring is suitably modelled using the concept of branching of shells. In this work one such flange is analysed and the results of finite difference and finite element methods are found to be in agreement.     

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.     

Finite element analysis of bimodulus composite stiffened thin shells of revolution

This paper is a sequel to the work published by the first and third authors[l] on stiffened laminated shells of revolution made of unimodular materials (materials having identical properties in tension and compression). A finite element analysis of laminated bimodulus composite thin shells of revolution, reinforced by laminated bimodulus composite stiffeners is reported herein. A 48 dot doubly curved quadrilateral laminated anisotropic shell of revolution finite element and it's two compatible 16 dof stiffener finite elements namely: (i) a laminated anisotropic parallel circle stiffener element (PCSE) and (ii) a laminated anisotropic meridional stiffener element (MSE) have been used iteratively.The constitutive relationship of each layer is assumed to depend on whether the fiberdirection strain is tensile or compressive. The true state of strain or stress is realized when the locations of the neutral surfaces in the shell and the stiffeners remain unaltered (to a specified accuracy) between two successive iterations. The solutions for static loading of a stiffened plate, a stiffened cylindrical shell. and a stiffened spherical shell, all made of bimodulus composite materials, have been presented.     

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     

Free flexural vibration behavior of laminated angle-ply elliptical cylindrical shells

This paper deals with the free flexural vibration characteristics of anisotropic laminated angle-ply elliptical cylindrical shells using finite element approach. The formulation is based on first-order shear deformation theory. The present model accounts for in-plane and rotary inertia effects. A detailed study is carried out to highlight the effects of shell geometry, cross-sectional properties, lap-up and ply-angle on the natural frequencies pertaining to different types of modes of vibrations of non-circular shell structures.     

Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE).These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.     

Frequency response of shell-plate combinations

Natural frequencies of cylindrical shells with a circular plate attached at arbitrary locations are determined for various boundary conditions and L/D ratios. The semi-analytical finite element method is used for the analysis. A conical shell element with four degrees of freedom per node and two nodes per element is used. For clamped-clamped and simply-supported boundary conditions the plate is attached at the center of the shell. For a clamped-free boundary condition the plate is at the free end of the shell. The effects of plate thickness and L/D ratio of the shell on the frequencies of the shell-plate combination are investigated.     

Large deflection analysis of plates and shells by discrete energy method

The discrete energy method—a special form of finite difference energy approach—is presented as a suitable alternative to the finite element method for the large deflection elastic analysis of plates and shallow shells of constant thickness. Strain displacement relations are derived for the calculation of various linear and nonlinear element stiffness matrices for two types of elements into which the structure is discretized for considering separately energy due to extension and bending and energy due to shear and twisting. Large deflection analyses of plates with various edge and loading conditions and of a shallow cylindrical shell are carried out using the proposed method and the results compared with finite element solutions. The computational efforts required are also indicated.     

Natural vibrations and stability of a stationary or rotating circular cylindrical shell containing a rotating fluid

The finite element method is applied to analyze a stationary or rotating cylindrical shell containing a co-rotating compressible fluid. The motion of the rotating fluid is described in the framework of the potential theory. The behavior of shells is analyzed using the classical shell theory. It has been found that the loss of stability in the stationary shells occurs in the form of a flutter. It has been shown that in the case of rotating shells the loss of stability is prevented by taking into account the initial circumferential tension caused by the centrifugal forces.     

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.