用于正交异性材料构件应变、应力测量的OPCM传感元件研究

介绍了由压电陶瓷和树脂材料构成的正交异性压电复合材料（Orthotropic Piezoelectric Composite Material,简称OPCM）应变传感元件的构造及传感原理，推导了粘贴式和埋入式OPCM传感元件测量正交异性材料构件中应力的传感方程。对受平面应力场的作用的正交异性板的表面应力，应变进行了实测研究，并对测试误差进行了分析。     

1-3型OPCM应变传感元件的传感机理研究

本构造了正交异性压电复合材料（OPCM）应变传感元件。从理论上推导了OPCM传感元件检测平面应变场中任意方向应变的力-电耦合方程,用实验手段对OPCM元件的压电正交异性效应进行了验证。实验证明仅当压电相的极化方向与元件的受力面平行时,OPCM元件具备压电正交异性之特性。     

光弹法实测正交异性双材料界面裂纹断裂参数

采用光弹贴片法实测正交异性双材料界面裂纹尖端区域的应力应变场, 进而求出界面裂纹的断裂力学参量. 将正交异性双材料板加工成拉伸试件,在聚碳酸酯贴片 的单侧表面镀金属铝膜,以提高贴片的反射效率. 沿贴片后的双材料界面预制裂缝,逐渐加 大载荷,得到一系列清晰的等差线条纹图. 利用正交异性双材料界面裂纹尖端应力分量表达 式计算出应力强度因子. 实验表明,光弹贴片法可有效地分析正交异性双材料界面裂纹问题.     

正交异性动态光弹性方法的几个基本问题的研究

文章对适用于动态研究的正交异性光弹性复合材料进行了分析，详细说明了光弹性复合材料中残余双折射的确定方法；基于静态下Ｈｙｅｒ和Ｌｉｕ应力－光性定律，提出了正交异性动态应力－光性定律，并对正交异性材料的动态力学参数及动态光弹性常数给出了实用的标定方法；最后，利用三个单轴压缩试件（０°，９０°及４５°），采用动态应变测量方法，证实了单轴应力状态下正交异性动态应力－光性定律的正确性。     

空间层状正交异性加强结构的计算

本文用曲线坐标系下张量分析的方法导出了空间正交异性薄膜应力单元的刚度矩阵.这种单元可以很好地体现具有空间曲线正交异性性质的材料特征,只需用少量的单元就可计算在工程中遇到的空间层状正交异性加强结构问题.     

正交异性双材料半无限界面裂纹尖端场分析

通过构造含两个实奇异指数的应力函数,利用复合材料断裂复变方法对正交异性双材料界面裂纹进行了研究。在特征方程组的判别式都小于零的情况下,通过求解一类广义重调和方程组边值问题,在双材料工程参数满足适当的条件下,推出了正交异性双材料半无限界面裂纹尖端的应力场和位移场。研究表明:其结果没有振荡奇异性;当上下半平面材料参数相同时,可获得正交异性单材料的应力场。并通过有限元算例进行比较,验证了理论结果的正确性。     

双轴应力状态下正交异性动态光弹性应力——光性定律研究

基于静态下Ｈｙｅｒ和Ｌｉｕ表述的正交异性应力－光性定律，在前文中，提出了正交异性光弹性复合材料的动态应力－光性定律并证明了其在单轴应力状态下的正确性。本文旨在进一步考察在双轴应力状态下正交异性动态应力－光性定律的适用性，采用的方法是对纤维增强光弹性复合材料制作的平板模型施加冲击荷载，加载方向与材料纤维方向分别成０°、９０°及４５°角，同时进行正交异性动态光弹性实验和动态应变测量，另外，对该模型进行相应的各向异性介质时域边界元计算。把动态应变测量推算出的应力分量以及时域边界元计算出的应力分量分别代入正交异性动态应力－光性定律，得到随时间变化的双折射条纹级数历程，将其与正交异性动态光弹性实验的结果进行比较。实验及计算结果表明，在三个加载方向下，由这三种方法得到的双折射条纹级数历程均吻合良好，从而证明了前文提出的正交异性动态应力－光性定律在双轴应力状态下的正确性。     

“论两种不同正交异性楔弹性接触”中应力奇异性

一般楔形体受面力作用时,其应力及位移有时会变为无限大。本文继续[1]的工作,分析均匀正交异性楔和两种不同正交异性复合楔的应力奇异性问题。由于假定了G_(rθ)=((E_rE_θ)/(1/2))/(2(1+(μ_(rθ)μ_(θr))/(1/2)),可用解析法得到应力奇异阶次为γ~(-s)型。对于均匀正交异性楔s只与材料弹性模量比值平方根kl=(E_θ/E_r)/(1/2)有关;对于正交异性复合楔,当k＇=k＇＇,s与复合楔中材料剪切模量比值e(=G_(rθ)~＇/G_(rθ)~＇＇)是无关的。     

两种不同正交异性楔的弹性接触

本文给出了满足圆柱型正交异性体相容方程的应力函数,称为广义Airy应力函数。应用该应力函数还找到了用两种不同材料(皆为均匀、正交异性)组成的复合楔形体,在表面分布荷载作用下,应力和位移的一般解析式。式中含有的两个参数k租e分别表示材料的正交异性和不同介质特性。当命k=1或e=1或k=1、e=1等等。可得到关于材料特性有六种不同类型组合的一般解析式。文中给出的实例,精确地满足所有条件。     

含共线双半无限裂纹的正交异性复合材料板平面弹性问题的解析解

运用广义复变函数方法,通过构造适当的广义保角映射研究了含有共线双半无限裂纹的正交异性复合材料板的平面弹性问题,得出了部分裂纹面上受均匀面内载荷时应力场与两裂纹尖端处应力强度因子的解析解。结果表明:应力场的大小不仅与材料的几何构型及外载荷有关,还与材料的弹性常数有关,这是正交异性复合材料不同于各向同性材料的显著特征;两裂纹尖端处应力强度因子的大小只与材料的几何构型及外载荷有关;当两裂纹尖端的距离趋于无穷大时,所得到的解析解可退化为已有的正交异性复合材料板中半无限裂纹问题的解,通过将其与已有文献中的结果进行对比,验证了本文解析解的正确性。并通过数值算例分析了裂纹面上的受载长度、两裂纹尖端的距离对应力强度因子的影响规律以及两裂纹之间的相互作用。     

The OPCM strain gauges for strain and stress measurement of orthotropic material structures

The orthotropic mechanical sensor of piezoelectric composite material made from piezoelectric ceramic and resin materials and their sensing mechanism are presented. The sensing equations of the adhered-and embedded-type sensing units are deduced, which are used to detect the stresses in orthotropic material structures. The surface strain of the orthogonal plate is measured under the action of the planar stress field, and the error is analyzed. Supported by the National Natural Science Foundation (No. 59635640), the Science Foundation of Jiangsu Education Committe (99KJD130001) and the Science Foundation of Jiangsu Province (BK99116).     

Axial buckling of an orthotropic circular cylinder: Application to orthogrid concept

A novel re-defining of the orthotropic material properties in terms of a so-called associated geometric mean isotropic (GMI) material is used to develop a thorough buckling analysis of an axially-loaded orthotropic circular cylinder. A membrane prebuckling condition is assumed and an expression for the buckling stress is derived in terms of cylinder geometry, orthotropic material properties, and the number of waves in the buckling deformation pattern in the axial and circumferential directions. By assuming the number of waves in each direction are real-valued variables, as opposed to integers, conditions which result in stationary values of the buckling stress are sought, and once found, examined for their character as regards representing minima, maxima, or saddle points. Three quite different buckling characteristics are predicted, the particulars depending on the shear modulus of the orthotropic material relative to that of the associated GMI material. It is shown that if the shear modulus of the orthotropic material is greater than the shear modulus of the associated GMI material, the cylinder buckles into a unique axisymmetric deformation pattern. If the shear modulus of the orthotropic material is less than the shear modulus of the associated GMI material, the cylinder buckles into a unique nonaxisymmetric deformation pattern. If the shear modulus of the orthotropic material is exactly equal to the shear modulus of the associated GMI material (this is the situation for an isotropic cylinder), the cylinder can buckle into either axisymmetric or nonaxisymmetric deformation patterns. Moreover it is shown that, in this case, there exists a number of deformation patterns, all at essentially the same stress level. Closed-form lower-bound expressions for the buckling stress are developed using the adopted notation, the value of the shear modulus relative to the shear modulus of the GMI material determining which expression is applicable. The results of this analysis are applied to a circular cylinder constructed of a lattice structure consisting of helical and circumferential ribs, a so-called orthogrid lattice cylinder, where it is assumed that the ribs of the lattice structure are dense enough to be able to represent the elastic properties of the lattice with an equivalent homogenized orthotropic material. An isogrid cylinder, where the helical rib angle is 30° relative to the axial direction, is a special case. The orthotropic cylinder analysis is reformulated in terms of the material properties of the ribs and the angle of the helical ribs. For this situation the isogrid case is the GMI material, and the rib angle determines whether the shear modulus of the equivalent orthotropic material is greater than or less than the GMI material. This translates into the character of the buckling deformations depending directly on the rib angle.     

On the asymptotic crack-tip stress fields in nonlocal orthotropic elasticity

The crack-tip stress fields in orthotropic bodies are derived within the framework of Eringen’s nonlocal elasticity via the Green’s function method. The modified Bessel function of second kind and order zero is considered as the nonlocal kernel. We demonstrate that if the localisation residuals are neglected, as originally proposed by Eringen, the asymptotic stress tensor and its normal derivative are continuous across the crack. We prove that the stresses attained at the crack tip are finite in nonlocal orthotropic continua for all the three fracture modes (I, II and III). The relative magnitudes of the stress components depend on the material orthotropy. Moreover, non-zero self-balanced tractions exist on the crack edges for both isotropic and orthotropic continua. The special case of a mode I Griffith crack in a nonlocal and orthotropic material is studied, with the inclusion of the T-stress term.     

Non-linear least-squares solution to the moiré hole method problem in orthotropic materials. Part II: Material elastic constants

This is the second of two papers dealing with inverse problems arising from the hole method problem in orthotropic materials. Two inverse problems are of interest in this second paper: one relates to the use of the hole method as a means of separation of stresses; the other deals with using it for orthotropic material elastic constant identification. The problem of separation of stresses is posed and briefly discussed, but the orthotropic material identification problem is addressed, fully showing how to obtain the five orthotropic elastic constants, four of which are independent, when knowing the applied stresses and examining the isothetics or moiré fringes around a through hole in a biaxially loaded thin wood plate.     

The effect of material and geometry on the non-linear vibrations of orthotropic circular cylindrical shells

The extensive use of circular cylindrical shells in modern industrial applications has made their analysis an important research area in applied mechanics. In spite of a large number of papers on cylindrical shells, just a small number of these works is related to the analysis of orthotropic shells. However several modern and natural materials display orthotropic properties and also densely stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of both material properties and geometry on the non-linear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied. Donnell׳s non-linear shallow shell theory is used to model the shell and a modal solution with six degrees of freedom is used to describe the lateral displacements of the shell. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge–Kutta method. The obtained results show that the material properties and geometric relations have a significant influence on the instability loads and resonance curves of the orthotropic shell.     

Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations

In this study, the torsional vibration and stability problems of functionally graded (FG) orthotropic cylindrical shells in the elastic medium, using the Galerkin method was investigated. Pasternak model is used to describe the reaction of the elastic medium on the cylindrical shell. Mixed boundary conditions are considered. The material properties and density of the orthotropic cylindrical shell are assumed to vary exponentially in the thickness direction. The basic equations of the FG orthotropic cylindrical shell under the torsional load resting on the Pasternak-type elastic foundation are derived. The expressions for the critical torsional load and dimensionless torsional frequency parameter of the FG orthotropic cylindrical shell resting on elastic foundations are obtained. The effects of variations of shell parameters, the exponential factor characterizing the degree of material gradient, orthotropy, foundation stiffness and shear subgrade modulus of the foundation on the critical torsional load and dimensionless torsional frequency parameter are examined.     

Dependence of stress intensity factors on elastic constants for cracks in an orthotropic bimaterial with a thin film

An interface crack and a subinterface crack in an orthotropic bimaterial structure consisting of a thin film and a half plane substrate are analyzed. The orthotropic bimaterial structure is subjected to compressive load and bending moment per unit thickness. Complete expressions of stress intensity factors for the two cracks are obtained based on the path independence of the J integral, apart from one dimensionless parameter undetermined each. The dependence of the dimensionless parameters on material constants is examined. A reduction of the number of necessary material parameters for the parameters is made based upon the modified Stroh formalism. The explicit dependence of the dimensionless parameters on one orthotropic parameter for the film is determined by using the orthotropy rescaling technique. Variations of the dimensionless parameters with the other material parameters are also obtained through numerical computations.     

Affine transformations of the equations of the linear theory of elasticity

This paper deals with the general formulas of affine transformations that preserve invariance of the static equations of the linear theory of elasticity in the case of arbitrary anisotropic materials. The invariance of the equations with respect to affine transformations allows one to model a given anisotropic material by another material. All anisotropic materials are divided into classes of mutually congruent materials. The congruency conditions are obtained for orthotropic and isotropic materials and for orthotropic and transversely isotropic materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 124–134, July–August, 2006.