含初应力复合材料柱壳结构的双稳态特性

为分析初应力对复合材料圆柱壳结构双稳态特性的影响,采用经典板壳理论建立复合材料圆柱壳力学模型,基于层合结构本构关系推导用双参数表达的系统应变能公式;根据最小势能原理得到双稳态产生的条件和稳态时的曲率表达式。利用Abaqus软件构建圆柱壳的有限元模型,通过附加边界弯矩对柱壳稳态跃迁过程进行模拟。理论计算结果与有限元结果的对比验证理论模型的正确性。分析结果表明：当初应力满足一定条件时,复合材料柱壳结构在其变形过程中有2个稳定平衡位置,并且在稳定平衡位置结构都不产生扭转变形;2个稳定平衡位置的曲率方向可以相同或相反,这与无初应力时反对称复合材料柱壳双稳态曲率方向只能相同的情况有区别。     

On post-buckling analysis and experimental correlation of cylindrical composite shells with Reissner-Mindlin-Von Kármán type facet model

In this paper post-buckling analysis of carbon fibre reinforced plastic cylindrical shells under axial compression is considered. Reissner-Mindlin-Von Kármán type shell facet model is used in the computations. The effect of geometric imperfection shape and amplitude on nonlinear analysis results is discussed. Numerical-experimental correlation is performed using the results of experimental buckling tests found in the literature. Results show that bringing the diamond shape geometric imperfection in the model significantly improves the correlation and gives good accuracy in simulating cylindrical shell post-buckling behaviour.     

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.     

Bifurcation and collapse analysis of stringer and ring-stringer stiffened cylindrical shells with cutouts

This paper presents results for cylindrical shell configurations using the STAGS computer program. Discontinuities have been imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements.The cutout problem has been shown to be highly nonlinear for smooth surface shells, but the author has found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following:—comparison between smeared and discrete stiffener theory for linear solutions—numerical finite difference convergence as directed toward buckling determination—collapse load results with the various skin stiffeners.This paper also includes a linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces. Comparisons have been made between a variety of geometric positions considering cutout frame and thickened skin additions. The investigation points toward an optimum positioning.     

Plastic collapse of circular conical shells under uniform external pressure

The article reports on two theoretical investigations and an experimental investigation into the collapse of six circular conical shells under uniform external pressure. Four of the vessels collapsed through plastic non-symmetric bifurcation buckling and one vessel collapsed through plastic axisymmetric buckling. A sixth vessel failed in a mixed mode of plastic non-symmetric bifurcation buckling, combined with plastic axisymmetric buckling. The theoretical and experimental investigations appeared to indicate that there was a link between plastic non-symmetric bifurcation buckling and plastic axisymmetric buckling. The theoretical investigations were via the finite element method and were used to provide a design chart for these vessels.     

Lateral buckling of locally buckled beams using finite element techniques

This paper deals with lateral-torsional buckling of beams which have already buckled locally before the occurrence of overall buckling. Due to the weakening effects of local buckling, the stiffness of the beam is reduced. As a result, overall lateral buckling takes place at a lower load than the member would carry in the absence of local buckling. The effective width concept is used in this investigation to account for the post-buckling strength in the buckled compression plate elements of the beam section. A finite element formulation in conjunction with effective width concept is presented. Due to the nonlinearity involved because of local buckling, an iterative procedure is necessary. Search techniques are used to find the load factor. The method combined with an analysis on nonlinear bending moment distribution can be used to analyze the lateral stability problem of locally buckled continuous structure. In this case, both elastic stiffness matrix and geometric stiffness matrix must be revised at each load level. A computer program has been prepared for an IBM 370/165 computer.     

Buckling and initial post-buckling behavior of thin-walled I columns

The behavior of axially compressed thin-walled I columns after torsional buckling is discussed. At first the state of strain in a column subjected to a large angle of twist is outlined. The considerations are based on the following assumptions: (1) cross section is non-deformable in its own plane, (2) shear deformation is negligible, and (3) strains are small and elastic. The initial post-buckling equilibrium paths are determined by utilizing a perturbation approach. The finite-element and analytical procedure is presented. It has been shown that the point of bifurcation for simply supported, or clamped I column with constant cross section is symmetric and stable. Two examples of I columns of variable cross section are also considered. It is worthwhile noticing that in these examples the critical loads are beyond the limits described by the critical force for column with the minimum and the maximum cross section. The points of bifurcation in these cases are also symmetric and stable. This property of the bifurcation point is very important with regard to the sensitivity to the initial geometrical imperfections. In the case of the unstable point of bifurcation a drastic decrease of the value of the critical loads is possible, which does not hold for stable point.     

An exact finite strip for the initial postbuckling analysis of channel section struts

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of channel section struts. The presented method provides an efficient and extremely accurate buckling solution. The Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and mode shapes for the channel section struts. The investigation of buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. Through the solution of the Von-Karman’s compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. All the displacement functions are then substituted in the total strain energy expressions. The theorem of minimum total potential energy is subsequently applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial post-buckling behavior of some representative channel sections for which the results were also obtained through the application of a semi-energy finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.     

Instability of short stiffened composite cylindrical shells under bending with prebuckling displacements

This paper presents results for buckling of a stiffened cylindrical shell with cutouts and both isotropic and composite shells without cutouts acting under end bending moments. The STAGS-C program has been used in the analysis.     

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.     

Nonlinear finite element analysis of shell structures using the semi-loof element

The Semi-Loof Shell element originally developed by Irons [2] for linear elastic analysis of thin shell structures is formulated to include large deflection and plastic deformation effects. In this paper the details of the finite element formulation of the problem using total Lagrangian coordinate systems are presented and different element matrices are given. For plastic materials following the Prandtl-Reuss flow rule with isotropic strain hardening a multi-layer approach using a subincremental technique is employed. Numerical results on the performance of the element for a variety of applications are presented. These computer studies include complete load-deflection curves into the post-buckling range and comparisons are made with other existing results. Current experience with the element indicates that it is a reliable and competitive element for nonlinear analysis of shells of general geometry.     

Stiffness analysis of locally-buckled thin-walled continuous beams

A direct iterative numerical method is presented for predicting the post-local-buckling response of thin-walled continuous structures. Nonlinearities due to local buckling and non-linear material properties are accounted for by the nonlinear moment-curvature relations of the section derived with the aid of effective width concept. Since the effective width of the compression element decreases as the stress borne by the element edge increases, the effective flexural rigidity of the cross-section varies along the member length depending upon the magnitude of the moment at the section. In the post-buckling range, the member is treated as a nonprismatic section. For continuous thin-walled structures, it is further complicated by the fact that the bending moment distribution throughout the structure and the member stiffnesses are interdependent. The proposed direct iterative solution scheme includes a stiffness matrix method of analysis in conjunction with a numerical integration procedure for evaluating the member stiffnesses. The method is employed to analyze continuous beams in the post-buckling range. Using the moment distribution of an elastic prismatic continuous beam based on the nonbuckling analysis as a first approximation, it has been found that the iterative solution scheme converges rapidly.An excellent agreement has been obtained between the results based on the method presented and from an earlier study for continuous beams. The stiffness formulation is direct and is well suited for the analysis of continuous thin-walled structures.     

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].     

Buckling of pressure loaded rings and shells by the finite element method

The correct formulations for solving nonlinear structural problems by the finite element method have now been established. Numerous investigators have given the derivation for the solution of problems by the incremental tangent stiffness method and total formulation methods. These derivations have been applied to many problems and the results have been shown to be quite accurate for the problems that have been selected. However there is one area of application that has received practically no attention. This is in the investigation of the buckling strength of pressure loaded rings and shells. The effect of pressure loading where the loading changes direction as the structure deforms has been included in several previous derivations, by what is known as the load stiffness matrix, but to the author's knowledge no one has investigated problems where this effect has been included in the solution procedure. For rings and some buckling modes of shells, the results can be in error by as much as 50%.This paper will describe an iterative process for solving the nonlinear equilibrium equations and correcting the loads to include the effect of changing geometry at each load level. This approach is different from the classical eigenvalue or bifurcation method. Several case studies will be described which were performed on ring and shell problems. The geometry of these example problems were axisymmetric and in order to apply a nonlinear collapse analysis, the structure had to be perturbed out of its axisymmetric pattern into a buckling pattern. Imperfect geometry and very small concentrated loads were used to cause this perturbation and this will be described in the paper. The sensitivity of the computed collapse pressure to the finite element mesh gradation will be discussed. A comparison will be made between results obtained by including the effect of following pressure load and those obtained by not including this effect.     

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.     

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.     

On load interaction in the non linear buckling analysis of cylindrical shells

The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite element discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction problems considered.     

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.     

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigen mode of the panel.In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths.The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.