正交各向异性连续板的振动

正交各向异性连续板振动的理论研究对我国多层厂房建设是具有重要的意义。本文给出了正交各向异性连续板振动的介析解,考虑了板的各向异性和附加质量的影响,建立了一系列的公式并编制了各种情况的通用程序。本文所得的计算结果曾与实测进行了比较。与实测较好的符合和本方法比能量法优越是很明显的。     

各向异性板应力强度因子的变分解法

本文在文献的基础上给出了含边缘裂纹各向异性板的应力与位移展开式, 并应用广义变分原理求解含对称中心裂纹、对称边缘裂纹与对称孔边裂纹正交各向异性板的应力强度因子。所得结果的收敛性是令人满意的。同时在各向同性的情况下, 所得结果与文献之结果非常符合。      

正交各向异性和各向同性方板自由振动的三维无网格解

推导了正交各向异性和各向同性弹性体自由振动的三维控制微分方程,利用基于逆复合二次径向基函数的无网格配点法对三维控制微分方程和边界条件进行离散,通过数值算例选取了逆复合二次径向基函数的形状参数,结果表明:形状参数(是x方向的节点数)时计算结果收敛最快。计算了不同边界条件的正交各向异性和各向同性板的固有频率,该文中的结果与文献中的结果具有较好的一致性。     

正交各向异性CFRP材料的本构关系及其在平板撞击模拟中的应用

碳纤维增强树脂基类复合材料通常具有力学性能的正交各向异性,因此在对该类材料的动态力学性能研究中,其本构关系及物态方程必须考虑正交各向异性的修正。从经典的正交各向异性弹性本构方程出发,以某型碳纤维增强酚醛树脂材料为研究对象,引入Tsai-Hill准则描述材料的塑性行为,采用Grüneisen物态方程描述压力与体应变之间的非线性关系,建立了正交各向异性材料的三维弹塑性本构模型。并采用显式有限元方法,对三维条件下平板撞击问题中的应力波传播过程进行了模拟。研究表明,所建立的三维本构模型能够合理呈现出材料的各向异性力学特性。对于靶板中平台压力,由于广义体积模量及正交各向异性修正项的引入,得到的压力相对于各向同性模型偏低。设定飞片以100～3 000 m/s的速度撞击静止靶板,对计算结果的数值分析发现随着飞片速度上升,正交各向异性模型中修正项对压力的贡献减小。最终正交各向异性模型趋近于各向同性模型。     

正交各向异性空心圆柱体中的周向超声导波

周向导波适于大直径管道纵向缺陷的超声无损检测。基于三维弹性理论,采用一种正交多项式法研究正交各向异性无限长管道中的周向导波。为验证方法的正确性与适用性,首先计算了各向同性和横观各向同性管道中的周向导波并与已有数据相比较。其次,计算了单向复合材料中不同纤维增强强度下的频散曲线,论证了纤维增强强度变化对于频散曲线的影响。最后,求解了不同径厚比下正交各向异性管道的周向导波的频散曲线,论述了径厚比的变化对频散曲线的影响。     

瓦楞纸板屁曲临界载荷的一种等效计算方法

为了方便确定屈曲临界载荷,对瓦楞纸板进行合理简化,建立了两种瓦楞纸板的简化模型,并使它们在计算屈曲临界载荷分析方面等效。在有限元分析中,各向同性板模型与正交各向异性板模型相比,减少了建模所需的参数,并可以达到用各向同性板取代瓦楞纸板进行屈曲分析的目的。通过理论计算和有限元分析,结果表明两种简化模型在屈曲临界载荷的分析方面基本等效,误差在5%以内。     

工程中板壳结构的一种实用计算方法

本文采用—维B3样条插值─—半离散法，建立了正交各向异性板壳结构位移和内力的统一计算式。编制的程序适用于两对这简支另两对边任意支承的正交各向异性矩形双曲扁壳、圆柱形扁壳和板；适用于集中、均布、线性荷载或其组合。算例表明该方法能有效地解决板壳的计算。     

考虑横向剪切效应时圆柱型正交各向异性球面扁壳在横向载荷作用下的非线性压屈

本文应用参考文献所介绍的修正迭代法探讨了横向载荷作用下,圆柱型正交各向异性圆底球面扁壳的非线性稳定同题,得出了这一同题的解析解。在求解过程中,本文放弃了经典板壳理论的Kirchhoff假定,从而考虑了横向剪应变对于弯曲变形的影响, 计算结果表明:本文的分析方法和结论是正确的;对于正交各向异性复合材料板壳而言,横向剪切效应是值得注意的。     

直线型正交异性复合材料圆板的大挠度弯曲

本文研究了复合材料直线型正交各向异性圆板的大挠度弯曲问题。首先通过周向刚度分析建立了非轴对称挠曲函数的形式:然后采用伽辽金法求解卡门方程, 其中应力函数是通过求解其非线性协调方程而精确得到的。由此,对周边固支而径向位移约束和自由两种边界条件求解了几种各向异性性质的复合材料园板;并讨论了非轴对称位移项引起的影响。计算结果表明, 非轴对称位移项的影响随着材料正交各向异性强度的增大而更加显著。当材料刚度系数比E₁/E₂=40时, 其对挠度的影响可达17％。      

正交异性蜂窝夹层板动、静力学问题的等效分析方法

本文基于低阶剪切理论, 提出了正交各向异性蜂窝夹层板的一种等效分析方法, 得到等效板的工程常数和密度, 解决了国际上公认的大型有限元通用程序如NA STRAN 等不能直接计算蜂窝夹层板动、静力学问题的难题, 理论验证结果表明, 等效方法具有高精度的近似。     

On stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole

Scale factors (SFs) are widely used in engineering applications to describe the stress concentration factor (SCF) of a finite width isotropic plate with a circular hole and under uniaxial loading. In this paper, these SFs were also found to be valid in an isotropic plate with biaxial loading and an isotropic cylinder with uniaxial loading or internal pressure, if a suitable hole to structure dimension ratio was chosen. The study was further expanded to consider orthotropic plates and cylinders with a center hole and under uniaxial loading. The applicable range of the SFs was given based on the orthotropic material parameters. The influence of the structural dimension on the SCF was also studied. An empirical calculation method for the stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole was proposed and the results agreed well with the FEM simulations. This research work may provide structure engineers a simple and efficient way to estimate the hole effect on plate structures or pressure vessels made of isotropic or orthotropic materials.     

A large orthotropic plate with misfit pin under arbitrarily oriented biaxial loading

The problem of misfit (interference or clearance) pin in a large orthotropic plate was solved earlier by the authors for biaxial loading in the principal directions of orthotropy. Here, a more general case of arbitrarily oriented loading is considered. The most important aspect of the problem studied is the partial contact at the pin-hole interface. The solution is obtained by extending the use of ‘inverse technique’ which was successfully applied earlier by the authors to problems of pins in isotropic and orthotropic domains. The loss of symmetry because of the arbitrary orientation of loading makes the problem more complex. Additional parameters are then involved in the inversion of the problem for the solution. Numerical results are presented primarily for a smooth interference fit pin in a typical orthotropic plate.     

Vibration of laminated orthotropic plates using a simplified higher-order deformation theory

Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order plate theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformable plate theory is then used for predicting the natural frequencies of simply-supported isotropic, orthotropic and laminated composite plates. The results obtained for isotropic, orthotropic and laminated plates compare favourably with Reddy's results and other 3D results.     

Stress distribution in orthotropic plates with coupled elastic properties

Summary If the roots of the characteristic equation of the governing differential equation for the stress function of an orthotropic plate under generalized plane stress conditions are equal classical solutions of anisotropic elasticity theory do not hold anymore. The general form of the stress function for such orthotropic materials is discussed and the exact solution is given for the plate with an elliptic opening loaded in tension.Comparison of the stress distribution for the material with distinct characteristic roots indicated that in produces much higher stress concentrations than the model with equal roots. For the latter case solution of any boundary value problem may be obtained very easily through an existing solution for the isotropic material.Given also that there are several problems involving stress concentrations in orthotropic plates as yet unsolved, the analysis presented here might be of considerable help in the, designing of the structure of composite laminates.With 8 Figures     

A BEM-based meshless solution to buckling and vibration problems of orthotropicplates

In this paper a BEM-based meshless solution is presented to buckling and vibration problems of Kirchhoff orthotropic plates with arbitrary shape. The plate is subjected to compressive centrally applied load together with arbitrarily transverse distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting buckling and vibration problems are described by partial differential equations in terms of the deflection. Both problems are solved employing the Analog Equation Method (AEM). According to this method the fourth-order partial differential equation describing the response of the orthotropic plate is converted to an equivalent linear problem for an isotropic plate subjected only to a fictitious load under the same boundary conditions. The AEM is applied to the problem at hand as a boundary-only method by approximating the fictitious load with a radial basis function series. Thus, the method retains all the advantages of the pure BEM using a known simple fundamental solution. Example problems are presented for orthotropic plates, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and its accuracy.     

Anti-plane shear problem for an edge crack in a finite orthotropic plate

The problem of an edge crack in a finite orthotropic plate under anti-plane shear is considered. The boundary collocation method is used to calculate the mode III stress intensity factor (SIF). For the case in which the material is isotropic, the present results agree very well with those obtained by using the integral equation method. Furthermore, the method can be extended readily for general cases with arbitrary geometrical and boundary loading conditions and material properties.     

On Determination of the Stressed State of a Annular Orthotropic Plate

We propose a method of solving a plane problem for thin orthotropic plates using a parameter expansion technique. A solution to the respective isotropic problem serves as a null approximation. For particular materials, the results obtained by this method are shown to agree well with the known solution for an infinite plate with a hole. We study the stressed state of an annular orthotropic plate, derive the stress distribution functions, and compare the results obtained with those available for a similar isotropic plate.     

Free vibration of moving laminated composite plates

Two-dimensional axially moving materials have a wide range of industrial applications such as papers, plastics and composites in producing lines, power transmission and conveyor belts, etc. In many of these instances, the moving material is not isotropic, but is a single-layer orthotropic material or consists of several orthotropic layers.

In this article, free vibration of axially moving symmetrically laminated plates subjected to in-plan forces is studied by classical plate theory. This category includes symmetric cross-ply and angle-ply laminates and anisotropic plates. Firstly, an exact method is developed to analyze vibration of multi-span traveling cross-ply laminates, and then a semi-analytical finite strip method is extended for moving symmetric laminated plates in general, with arbitrary boundary conditions. By the finite strip method intermediate elastic or rigid supports can also be added to the model of the moving plate. The supports may be in the form of point, line or local distributed supports.     

Analytical stress around mode II crack parallel to principle axis in orthotropic composite plate

Stress analyses for orthotropic composite materials containing a through crack under remote shear loads (Mode II) are conducted. By employing the complex theory, a harmonic differential equation was established for the orthotropic plates with axes normal to the three orthogonal planes of material symmetry. An analytical complex function was introduced by following the Westergaard approach. Stress around a mode II crack in the orthotropic composite plate is deduced to have an analytical form. In addition, the analytical solution for a mode II crack was examined in the case of isotropic materials. It demonstrated that the analytical solution obtained is correct for the mode II cracked orthotropic composite plates.