开孔平板的剪切稳定性实验

对四边简支和四周边受均匀剪切力的矩形薄平板的屈曲失稳,作了实验分析及数值计算.用作者所设计的剪切试验装置,对一组开孔及开孔后加强的薄平板进行了剪切稳定性试验,求得薄平板失稳时的载荷——挠度曲线及失稳波形,由曲线上拐点来确定平板失稳临界载荷,并将实验结果与有限元数值计算结果作了比较.     

剪切变形对FGM圆板轴对称屈曲的影响

基于一阶剪切变形板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中，忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性，得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系，可以直接从已有的较为简单的经典理论的结果，获得一阶板理论下功能梯度材料板的临界屈曲载荷。     

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic-viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.     

基于平板振动精确化方程求解动应力集中问题

基于文献[8]给出的平板弯曲振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究.文中给出了分别基于Mindlin板与精确化板方程在不同参数下圆孔动弯矩集中系数的数值结果,并对结果进行了对比分析和讨论.结果表明:在较低频率和薄板情况下,基于文献[8]的方程与基于Mindlin板理论得到的动弯矩结果是基本一致的;在较高频率和厚板情况下,基于文献[8]的方程与基于Mindlin板理论的动弯矩结果相差较大,最大值超出可达16%.由于文献[8]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此其分析计算结果更精确一些.      

Compressive strength of edge-loaded corrugated board panels

Postbuckling strength of simply supported corrugated board panels subjected to edge compressive loading has been studied experimentally using a specially developed test fixture. Although the load versus out-of-plane displacement response was highly sensitive to the presence of initial imperfections in the panels, the collapse loads did not vary much, which is attributed to the stable postbuckling behavior of the plates. Thin plates collapsed at nearly twice the buckling load, while thick panels collapsed at loads below the elastic critical buckling load. Local buckling of the facing on the concave side of the buckled plate was observed at load levels close to the collapse load. The plate collapse was triggered by compressive failure of the facings that initiated at the unloaded edges. A simplified design analysis was derived based on approximate postbuckling analysis and compared with an existing design formula for corrugated board panels and boxes.     

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young''s moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young''s moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.     

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.     

Hamilton体系下矩形薄板受抛物线压力载荷的屈曲分析

针对四边简支矩形薄板在两对边相向的非线性分布压力下的面内应力分布以及屈曲问题,应用弹性力学的Hamilton体系和Galerkin法进行了研究.基于弹性力学的平面矩形域Hamilton体系,根据辛本征向量展开解法,得到了对应于零本征值和非零本征值的含待定常数的实数型面内应力分布通解.依据必须满足的应力边界条件,导出了矩形薄板在抛物线分布载荷下的面内应力分布.考虑到应力分布表达式的复杂性,用完全的解析方法得到屈曲载荷是不可能的.因此,运用基于虚功原理的Galerkin法,根据四边简支矩形薄板弯曲的位移边界条件,给出了不同长宽比矩形薄板受抛物线分布载荷的屈曲临界载荷.通过与已有文献中DQ法给出的数值计算结果比较,表明了本文求解方法的有效性和正确性.基于所给出的结果,可望为解决矩形薄板在非线性分布载荷下的面内应力分布以及屈曲问题提供一种新的研究方法.     

Nonlinear analysis of a composite panel with a cutout repaired by a bonded tapered composite patch

This study presents a solution method to analyze the geometrically nonlinear response of a patch-repaired flat panel (skin) with a cutout under general loading conditions. The effect of induced stiffening due to tensile loading on the in-plane and, particularly, the out-of-plane behaviors of the patch-repaired skin are investigated. The damage to the skin is represented in the form of a cutout under the patch. The patch with tapered edges is free of external tractions. The skin is subjected to general boundary and loading conditions along its external edge. The solution method provides the transverse shear and normal stresses in the adhesive between the skin and the patch, and in-plane and bending stresses in the patch and skin. Both the patch and skin are made of linearly elastic composite laminates, and the adhesive between them is homogeneous and isotropic, exhibiting a bi-linear elastic behavior. Modified Green’s strain–displacement relations in conjunction with von Karman assumptions are employed in determining the in-plane strains in the skin and patch; however, the transverse shear strains in the adhesive are determined based on the shear-lag theory. The present solution method utilizes the principle of virtual work in conjunction with complex potential functions.     

Axisymmetric buckling of transversely isotropic circular and annular plates

This paper presents a general solution of the three-dimensional governing equations for the axisymmetric buckling problem of transversely isotropic media. The solution is expressed by a displacement function that satisfies a homogeneous fourth-order partial differential equation. Using this general solution, the axisymmetric buckling of circular and annular plates is investigated and exact solutions are obtained for appropriate boundary conditions. Numerical results are considered for clamped and simply supported circular and annular plates in comparison with existent results.     

Non-linear axisymmetric static analysis of orthotropic thin annular plates

This investigation deals with the geometrically non-linear axisymmetric static analysis of elastic orthotropic thin annular plates subjected to uniformly distributed and ring loads. Non-linear differential equations in terms of the transverse displacement w and stress function ψ have been employed. Both w and ψ are expanded in finite power series and the orthogonal point collocation method has been used to obtain discretised algebraic equations from the governing differential equations. Results have been presented for annular plates with and without a rigid plug in the hole; simply supported, clamped and free outer edge conditions; three orthotropic parameters β; two annular ratios and two loading conditions. Results have also been presented illustrating the effect of an elastic rotational constraint at the edge and the effect of a prescribed inplane displacement of the edge.     

Three-dimensional stress and free vibration analyses of functionally graded plates with circular holes by the use of the graded finite element method

Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fractions of the constituent materials vary continuously across the plate. The effective properties of the FGM plate are estimated by using the Mori–Tanaka homogenization method. A graded finite element method based on the Rayleigh–Ritz energy formulation is used to solve the problem. Effects of different volume fractions of the materials and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data.     

Axial buckling of perforated plates reinforced with strips and middle tubes

Global buckling of perforated plates reinforced with circumferential strip or short tube is investigated. Effects of the hole radius, width of the strip, thickness and radius of the tube and boundary conditions are studied numerically and experimentally. Axial buckling loads of the holed plates decrease versus the hole radius. By using the strip or tube, the buckling strength increases significantly. In some cases, the stiffened plate has buckling load greater than the perfect plate. Numerical studies showed that the increasing restraints at the boundaries increase the buckling strength in any case and geometry of the plate.     

Stress Concentration Factor in Functionally Graded Plates with Circular Holes Subjected to Anti-plane Shear Loading

Stress concentration factors due to the presence of geometrical discontinuities (circular holes) in functionally graded plates are derived. The material property inhomogeneity is assumed to be in the radial direction originating at the center of the plate. Variable separable closed-form solutions are obtained for the stresses and displacements in functionally graded plates (without and with holes) subjected to anti-plane shear loading. The stresses in functionally graded plates without a hole are not homogeneous as it is in the case of homogeneous plates. Either a stress concentration (more than the applied stress) or dilution (less than the applied stress) occurs depending on whether the modulus increases (hardening graded material) or decreases (softening graded material) away from the center of the graded plate without a hole. A novel definition of the stress concentration factor due to the geometrical discontinuity in functionally graded plates is derived. The effect of the circular hole in functionally graded plates is to magnify (compared to homogeneous plates) the stress concentration when the modulus decreases away from the center of the hole (softening material). Beneficial reduction of the stress concentration factor is achieved in hardening functionally graded materials.     

泡沫金属固支夹芯圆板的大挠度变形分析

论文分析了大挠度情况下固支夹芯圆板在准静态中心荷载作用下的承载能力.提出了考虑芯层强度影响的夹芯结构屈服条件,应用该条件,并基于边界条件和平板的初始变形机制假设夹芯板的速度场,推导了夹芯圆板考虑弯曲和膜力联合作用的大挠度响应,并应用数值算例验证了分析模型的合理性,在此基础上,分析和讨论了面板厚度、芯层厚度和芯层强度对夹芯圆板承载能力的影响.     

Elastic plates under bending solved by pseudocaustics

The method pf pseudocaustics was applied to the study of out-of-plane bending in elastic plates. It is shown that for bending problems where the loading mode is given, the method determines experimentally the complex potential function at selected points along the boundaries. A conformal mapping of the closed smooth curves of each boundary of the plate on to a unit circle allows the determination of the complex potential ϕ (ζ), expressed in the form of a Laurent series. This in turn yields the complete solution of the bent plate. In order to show the efficiency of the method it was applied to two typical examples of thin infinite plates in cylindrical bending, having either a circular central hole, or a square hole. The experimental results corroborate the theoretical results, thus proving that this combined theoretical and experimental method is suitable for solving elastic problems in applications with high accuracy, where other methods fail to yield satisfactory results.     

Biaxial testing of [O2/±45] s graphite/epoxy plates with holes

An experimental investigation was conducted to study the behavior under biaxial-tensile loading of [O₂/±45] _s graphite/epoxy plates with circular holes and to determine the influence of hole diameter on failure. The specimens were 40-cm×40-cm (16-in.×16-in.) graphite/epoxy plates of [O₂/±45] _s layup. Four hole diameters, 2.54 cm (1.00 in.), 1.91 cm (0.75 in.), 1.27 cm (0.50 in.) and 0.64 cm (0.25 in.), were investigated. Deformations and strains were measured using strain gages and birefringent coatings. Biaxial tension in a 2∶1 ratio was applied by means of four whiffle-tree grip linkages and controlled with a servohydraulic system. Stress and strain redistributions occur around the hole at a stress level corresponding to localized failure around the 67.5-deg location and nonlinear strain response at the 0-deg location. Maximum measured strains at failure on the hole boundary are higher (approximately 0.016) than the highest ultimate strain of the unnotched laminate (0.010). Two basic patterns of failure were observed: (a) horizontal cracking initiating at points off the horizontal axis and accompanied by extensive delamination of the subsurface ±45 deg plies, and (b) vertical cracking along vertical tangents to the hole and accompanied by delamination of the outer 0-deg plies. The strength reduction ratios are lower than corresponding values for uniaxial loading by approximately 16 percent, although the stress-concentration factor under biaxial loading is lower.     

On buckling of cantilever rectangular plates under symmetrical edge loading

The stability of cantilever rectangular plates under the symmetrical edge loading will be studied in this paper by lite varialional calculus. We are going to find out the minimum critical loading for cantilever rectangular plates subjected to various edge loadings symmetrically on a pair of opposite free edges. We’ll discuss the least critical loadings when the buckling of rectangular plates acted on bv a pair of concentrated forces, uniformly distributed loads, locally uniform distributed loads, distributed loads in the form of triangle and a pair of concentrated couples occur respectively.     

采用精确化理论求解厚板任意形开孔动应力集中

摘要：本文基于复变函数与保角映射法,采用平板弯曲振动精确化方程[9],对含任意形开孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解。作为算例,计算了自由边界条件下圆孔和椭圆孔的动弯矩集中系数的数值结果,并对板厚与孔径比对动弯矩分布的影响做了分析研究。结果表明：入射波数、平板厚度和椭圆偏心率等参数对动弯矩的分布都有很大的影响。在较低频率和平板较薄的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布上是基本一致的;在较高频率和平板较厚的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布计算结果相差较大。由于文献[9]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此本文的分析计算结果更精确一些。     

复合材料层合板的二次屈曲和二次分枝点分析

为了研究复合材料层合板的二次分叉特性 ,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层合板在面内载荷作用下的非线性稳定性控制方程组。控制方程组用广义傅立叶级数法进行求解 ,并得到载荷 -挠度曲线。基于分叉理论中的 Lerray-Schaulder定理 ,采用小挠动法 ,直接导出了复合材料层合板的二次失稳方程。研究结果表明 ,非对称层板也可能存在分叉 ,弹性转动支持系数和铺层等因素对二次分叉有很重要的影响。随着弹性系数的增大 ,二次失稳载荷值与初次失稳载荷值之比下降