径向载荷作用下复合材料圆柱壳的非线性动力屈曲

采用半解析法求解径向阶跃载荷作用下复合材料圆柱壳的非线性动力屈曲。基于一阶剪切变形理论，由Hamilton原理推导出包含横向剪切变形以及几何初缺陷的圆柱壳的非线性动力方程，位移及载荷沿周向采用级数展开，由Galerkin方法得到微分方程组，通过有限差分法求解；根据响应情况，由B—R准则判定屈曲，确定屈曲临界载荷。     

The vibration and stability of symmetrically-laminated composite rectangular plates subjected to in-plane stresses

Consideration is given to the twin problems of the elastic buckling of rectangular, symmetrically-laminated composite plates and of the vibration in the presence of applied in-plane stress of such laminates. First-order shear deformation plate theory provides the mathematical model of plate behaviour and the Rayleigh-Ritz and finite strip methods are used to generate numerical results for laminates of thin and moderately thick geometry, with various combinations of standard plate edge conditions. The applied stresses include uniform shear stress as well as direct stresses, and anisotropic material properties can be included. The presented results demonstrate the accuracy of the numerical methods and highlight the very significant influence that transverse shear and related thickness effects can have in the subject problems.     

Buckling under combined loading of thin,flat-walled structures by a complex finite strip method

A finite strip method is presented for determining the initial buckling stresses of any structure consisting of a series of thin flat isotropic plates rigidly connected together at their longitudinal edges. Each plate may be subjected to a combination of longitudinal and transverse compression, longitudinal in-plane bending, and shear, and it is assumed that the buckling mode, of whatever type, is sinusoidal in the longitudinal direction. Due to the presence of shear, the perturbation forces and displacements which occur at the edges of component plates during buckling are out of phase, and this is accounted for by defining their magnitudes in terms of complex quantities. Stiffness matrices relating the amplitudes of these forces and displacements are derived using an approximate method based upon assumed displacement functions across the width of the plate. It is shown how the method can be used to calculate natural frequencies of prismatic structures, and finally an indication of the accuracy of the method is given together with some illustrative results.     

Effect of in-plane boundary restraints on optimal design of skew laminates under buckling loads

Symmetrically laminated cross-ply and angle-ply skew plates subject to uniaxial buckling loads and various combinations of in-plane boundary restraints are studied using a shear deformable theory. For this purpose a finite element code is developed and applied to a couple of verification problems. The formulation of the parabolic iso-parametric plate element is briefly given and numerical results obtained for the verification problems related to stability analysis and stress diffusion are presented. The effect of in-plane restraints on the non-uniform distribution of in-plane stresses is studied by means of contour graphs. Next the buckling loads are maximized with respect to layer thicknesses in the case of cross-ply laminates and with respect to fiber orientations in the case of angle-ply laminates. The optimization results show that the exclusion of the in-plane restraints, which arise in several engineering applications, may lead to errors in the stability analysis and consequently in the design of laminated plates against buckling.     

The influence of mechanical couplings on the compressive stability of anti-symmetric angle-ply laminates

The compressive stability of anti-symmetric angle-ply laminated plates with particular reference to the degrading influence of membrane–flexural coupling is reported in this paper. The degree of membrane–flexural coupling in the laminated composite plates is varied, essentially, by altering the ply-angle and the number of plies in the laminated stack for a given composite material system. The coupled compressive buckling solutions are determined in the paper using the finite strip method of analysis and the buckling displacement fields of the strip formulation are those which are able to provide zero in-plane normal movement at the edge boundaries of the laminated plates.

Results are given for anti-symmetric angle-ply laminated plates subjected to uniaxial compression and these have been obtained from fully converged finite strip structural models. Validation of the finite strip formulation is indicated in the paper through comparisons with exact solutions where appropriate. Increasing the number of plies in the laminated system is seen to reduce the degree of coupling and the critical stress levels are noted to tend towards the plate orthotropic solutions. The ply-angle corresponding to the optimised buckling stress for any particular laminate is noted in the paper to be influenced by the support boundary conditions at the plates unloaded edges. For any particular laminate the minimum critical buckling stress and corresponding natural half-wavelength of the buckling mode are shown to be highly sensitive to ply-angle variation.

Some post-buckling results are presented in the paper and these have been determined using the finite element method of analysis. The influence of membrane–flexural coupling is shown to be significant throughout the compressive post-buckling history of the laminated plates. The optimised ply-angle with regard to the critical compressive buckling stress of square simply supported anti-symmetric angle-ply laminates is shown to be less effective in the post-buckling range with regard to post-buckled compressional stiffness.     

Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings

The buckling and postbuckling responses of cylindrical sandwich panels, subjected to non-uniform in-plane loadings are investigates in this paper by analytical method. A fourth and fifth order expansions are used respectively for the transverse and tangential displacement of the core to model the core compressibility effect. The stress distribution within the panels due to the applied non-uniform in-plane edge loadings are determined by prebuckling analysis. The governing partial differential equations describing the buckling and postbuckling behavior of cylindrical sandwich panels are derived using the principle of minimum total potential energy. Galerkin’s method is used to reduce the governing partial differential equations to a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to solve the algebraic equations. Numerical results are presented for both flat and cylindrical sandwich panels subjected to various non-uniform in-plane edge loadings. The sandwich panels used in the present investigation are made up of isotropic and composite materials.     

含界面边裂纹压电材料反平面问题的应力强度因子

研究了含界面边裂纹的不同压电介质组成的复合材料在反平面荷载和平面内电场作用下的电弹场,得到了级数形式的基本解和应力强度因子,最后用边界配置法求解了应力强度因子。结果表明,在外加剪切荷载的作用下,应力强度因子与外加电场无关。     

Finite element evaluation of the boundary conditions for biaxial testing of high strength concrete

This paper represents a numerical investigation, using a non linear finite element approach, to evaluate the different load application platens used in the biaxial testing of concrete. Three methods are evaluated numerically: the dry ordinary solid steel testing platens, the brush platens, and the friction reducing Teflon sheets. The effect of confinement on the displacement field in addition to the stress distribution in the loading direction are presented and discussed. The shear stresses induced in the specimen are evaluated for both uniaxial and biaxial loading conditions. Finally, the buckling capacity of the brush platens is examined. The finite element results indicate that the brush platens provide the most homogeneous displacement fields. The displacement fields are close to those obtained without lateral confinement. In addition, the shear stresses induced in the specimen are the lowest for the brush platens. The current study was used to design brush bearing platens for biaxial testing of high strength concrete. A brush platen with rod dimensions of 5×5 mm cross-section and 75 mm height can be safely used in testing high strength concrete with compressive strength up to 100 MPa with a reasonable factor of safety against buckling of the brush rods.     

On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method

This paper augments bubble functions to the ordinary spline finite strip method in order to calculate the elastic local buckling coefficients of plates and plate structures. The results show that the use of bubble functions improves significantly the convergence of the spline finite strip method in terms of the strip subdivision, and therefore leads to smaller storage requirements for the global stiffness and stability matrices, and faster eigenvalue extraction. Benchmark numerical investigations are presented, including the study of plates with different boundary conditions under uniaxial and biaxial stresses, plates with different aspect ratios under shear, and a stiffened panel under combined shear and compression that has been studied elsewhere. These studies demonstrate that by implementation of the bubble functions, rapid convergence of the solution is obtained. The formulation is ideal for analysing local buckling under a variety of boundary and loading conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations

This paper presents an analytical investigation on the buckling and postbuckling behaviors of thick functionally graded plates resting on elastic foundations and subjected to in-plane compressive, thermal and thermomechanical loads. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The formulations are based on higher order shear deformation plate theory taking into account Von Karman nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. By applying Galerkin method, closed-form relations of buckling loads and postbuckling equilibrium paths for simply supported plates are determined. Analysis is carried out to show the effects of material and geometrical properties, in-plane boundary restraint, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.     

Buckling response of laminated composite stiffened plates subjected to partial in-plane edge loading

This article presents the buckling analysis of laminated composite stiffened plates subjected to partial in-plane edge loading. The finite element method is used to carry out the analysis. The eight-noded isoparametric degenerated shell element with C⁰ continuity and first-order shear deformation and a compatible three-noded curved beam element are used to model the plate skin and the stiffeners, respectively. The eigen value analysis is carried out to track the buckling load. The convergence study is performed for some specific problems and the results are compared with the available results in the literature. It is observed that the convergence of results is very fast for this finite element model. Effect of different parameters like orientation of fibers, number of layers, and loading types are considered in the present investigation. It is also observed that all these parameters have significant effect on the buckling response of the composite stiffened plate.     

Explicit local buckling analysis of rotationally-restrained orthotropic plates under uniform shear

The explicit closed-form local buckling solution of in-plane shear-loaded orthotropic plates with two opposite edges simply supported and other two opposite edges either both rotationally restrained or one rotationally restrained and the other free is presented. Based on the boundary condition of the other two opposite edges, two types of plates are considered: the RR (both the edges rotationally restrained) and RF (one edge restrained and the other free) plate elements. Different plate buckled shape functions are proposed, and the approximate explicit expressions for the buckling loads are derived using the Rayleigh–Ritz method for the plate with the generic rotationally-restrained (R) boundary conditions which can be reduced to two extreme cases, i.e., simply supported (S) and clamped (C). The accuracy of the derived explicit solutions is verified by comparing the predictions with the existing solutions and numerical finite element analysis, and excellent agreements are obtained. The effects of material and boundary restraining parameters on the local shear buckling behavior of the plate elements are discussed. The derived explicit formulas for the shear buckling loads are straightforward, efficient and reliable for preliminary engineering design and analysis of composite structures under primarily shear-dominant loading conditions.     

Postbuckling analysis of stiffened laminated composite panels,using a higher-order shear deformation theory

The investigation aims at: (i) constructing a modified higher-order shear deformation theory in which Kirchhoff's hypotheses are relaxed, to allow for shear deformations; (ii) validating the present 5-parameter-smeared-laminate theory by comparing the results with exact solutions; and (iii) applying the theory to a specific problem of the postbuckling behavior of a flat stiffened fiber-reinforced laminated composite plate under compression.The first part of this paper is devoted mainly to the derivation of the pertinent displacement field which obviates the need for shear correction factors. The present displacement field compares satisfactorily with the exact solutions for three layered cross-ply laminates. The distinctive feature of the present smeared laminate theory is that the through-the-thickness transverse shear stresses are calculated directly from the constitutive equations without involving any integration of the equilibrium equations.The second part of this paper demonstrates the applicability of the present modified higher-order shear deformation theory to the post-buckling analysis of stiffened laminated panels under compression. to accomplish this, the finite strip method is employed. A C ²-continuity requirement in the displacement field necessitates a modification of the conventional finite strip element technique by introducing higher-order polynomials in the direction normal to that of the stiffener axes. The finite strip formulation is validated by comparing the numerical solutions for buckling problems of the stiffened panels with some typical experimental results.     

Theoretical fatigue–effective notch stresses at spot welds

Notch stress formulae are derived for the application of a notch stress approach to the fatigue assessment of spot welds. A keyhole notch is assumed to describe the edge of the weld spot between the overlapping plates. The stress fields at the keyhole notch under 'singular' and 'non-singular' in-plane loading modes inclusive of the stress concentration factors K _t are derived from the relevant Airy stress functions. The formulae are applied to typical loading cases of spot welds and compared with finite element solutions. Fatigue-effective notch stresses inclusive of fatigue notch factors K _f are calculated by applying the microstructural support hypothesis of Neuber. The notch stresses at the keyhole are also derived for out-of-plane shear loading based on the relevant harmonic stress functions. The multiaxial notch stresses at the weld spot edge are thus completely described.     

Thermomechanical postbuckling analysis of symmetric and antisymmetric composite plates with imperfections

In the present paper the postbuckling response of symmetrically and antisymmetrically laminated composite plates subjected to a combination of uniform temperature distribution through the thickness and in-plane compressive edge loading is presented. The structural model is based on a higher-order shear deformation theory incorporating von Karman nonlinear strain displacement relations. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, which are solved using the Newton–Raphson iterative procedure. The critical buckling temperature is obtained from the solution of the linear eigenvalue problem. Postbuckled equilibrium paths are obtained for symmetrically laminated cross-ply, quasi-isotropic and antisymmetric angle-ply composite plates with and without initial geometric imperfections. Modal participation of each mode in the postbuckling deflection is reported using a multi-term Galerkin procedure.     

船体开孔薄板面内剪切屈曲特性研究

船体板材不可避免地存在不同形式的开孔,开孔破坏了结构的连续性,对结构的强度、稳定性具有重要影响,因此研究船体板开孔结构的屈曲特性对保证船舶安全十分重要。在面内载荷作用下,通过画框型剪切夹具、3D全场变形测量-分析系统等对两种不同形式的船体开孔薄板进行剪切屈曲试验,获得了圆形开孔板和方形开孔板的临界屈曲载荷、全场位移/应变信息和拉力-伸长率曲线等;考虑试验夹具的影响,基于Abaqus对不同形式的开孔板进行数值仿真,通过对开孔板进行特征值屈曲分析和非线性屈曲分析,获得了两种不同形式船用开孔薄板的屈曲、后屈曲力学响应信息。通过数值仿真与试验结果的对比研究,验证了数值仿真方法的有效性、准确性。在此基础上,重点剖析载荷-伸长率关系、典型时刻板面全场位移、临界屈曲载荷以及开孔边缘的应力分布响应特征,明确了面积等效情况下圆孔和倒圆角方孔对方形薄板剪切稳定性的影响。为船用薄板面内剪切稳定性的试验和仿真研究以及大型船体结构的设计优化、力学性能评估等提供有益参考。     

Postbuckling response and failure of symmetric laminates under in-plane shear

This paper summarizes a study aimed at understanding the postbuckling behaviour and progressive failure of thin, simply supported symmetric rectangular laminates with various possible in-plane boundary conditions and under the action of in-plane shear loads. First-order shear deformation theory and geometric non-linearity, in the von-Karman sense, is used with a finite-element procedure. The 3D Tsai–Hill criterion is used to predict failure of lamina and the maximum stress criterion is used to predict the onset of delamination at the interface of two adjacent layers. The effect of in-plane boundary conditions, plate lay-ups, plate aspect ratio, fiber orientations and lamina material properties on the load deflection response, buckling load, first-ply failure load, ultimate load and the maximum transverse displacement associated with failure loads is presented.     

Nonlocal buckling and vibration analysis of thick rectangular nanoplates using finite strip method based on refined plate theory

The buckling and vibration of thick rectangular nanoplates is analyzed in this article. A graphene sheet is theoretically assumed and modeled as a nanoplate in this study. The two-variable refined plate theory (RPT) is applied to obtain the differential equations of the nanoplate. The theory accounts for parabolic variation of transverse shear stress through the thickness of the plate without using a shear correction factor. Besides, the analysis is based on the nonlocal theory of elasticity to take the small-scale effects into account. For the first time, the finite strip method (FSM) based on RPT is employed to study the vibration and buckling behavior of nanoplates and graphene sheets. Hamilton’s principle is employed to obtain the differential equations of the nanoplate. The stiffness, stability and mass matrices of the nanoplate are formed using the FSM. The displacement functions of the strips are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. A matrix eigenvalue problem is solved to find the free vibration frequency and buckling load of the nanoplates subjected to different types of in-plane loadings including the uniform and nonuniform uni-axial and biaxial compression. Comparison studies are presented to verify the validity and accuracy of the proposed nonlocal refined finite strip method. Furthermore, a number of examples are presented to investigate the effects of various parameters (e.g., boundary conditions, nonlocal parameter, aspect ratio, type of loading) on the results.