拉压不同弹性模量薄板上圆孔的应力分析

采用弹性理论研究了拉压不同弹性模量薄板上圆孔的孔边应力集中问题．采用广义虎克定律推导出了拉压不同弹性模量薄板上圆孔边的应力平衡方程,并联合利用应力函数及边界条件得到了拉压不同弹性模量薄板上圆孔边的应力表达式．算例分析表明,当薄板材料的拉压弹性模量相差较大时,采用经典弹性理论研究薄板上圆孔的孔边应力是不合适的,当经典弹性理论与拉压不同弹性模量弹性理论的计算结果间的差别超过工程允许误差5%时,应该采用拉压不同弹性模量弹性理论进行计算．     

SH波入射时垂直半空间中双相介质界面附近圆孔的动力分析

利用复变函数和Green函数法研究了垂直半空间中双相介质界面附近圆孔对SH波的散射与动应力集中问题。该问题的解答采用镜像法,首先构造出含有圆孔的直角平面区域出平面问题的Green函数,然后利用契合技术,并根据界面处位移连续性条件将解答归结为具有弱奇异性的第一类Fredholm积分方程组的求解,结合散射波的衰减特性,直接离散该方程组,把积分方程组转化为线性代数方程组可得到该问题的数值结果。最后,通过算例分析了圆孔的动应力集中情况。结果表明,与全空间中界面附近圆孔对SH波的散射相比,由于垂直半空间自由边界的存在,孔边动应力集中系数明显增大;另外,入射波由硬介质(波速大)进入到软介质(波速小)时,与均匀介质相比,孔边动应力集中更显著,最不利的参数组合,孔边动应力集中系数几乎提高了一倍,入射波由软介质进入到硬介质时,情况相反。     

弯曲波在含非圆孔洞无限压电薄板中的散射

基于线性压电动力学理论,采用波函数展开法、保角映射以及复变函数,对含非圆孔洞无限大压电薄板弹性波的散射及动应力集中问题进行了分析,给出了其动弯矩集中系数(DMCF)的解析表达式.为说明问题,以PZT-4为例,讨论了外加电场、椭圆孔长短半轴比、椭圆孔倾角以及入射波频率对含圆孔和椭圆孔无限大压电薄板弹性波散射的影响,并分别...     

弯曲波对含多圆孔薄板的散射与动应力集中

采用复变函数法和多极坐标方法,研究了弯曲波对含有多圆孔薄板的散射问题。通过板的弯曲波动方程和内力方程的推导,求出在入射弯曲波条件下该问题的一般解的函数逼近序列和边界条件的表达式。用展开正交函数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。最后,给出了含3圆孔薄板的孔边动应力集中系数的结果,并分析了孔间距和波数对动应力分布的影响。     

含非完整界面的功能梯度压电材料Ⅲ型裂纹问题

本文研究了含非完整界面的功能梯度压电复合材料的Ⅲ型裂纹问题．此裂纹垂直于非完整界面,采用弹簧型力电耦合界面模型模拟非完整界面．界面两侧材料的性质,如弹性模量、压电常数和介电常数均假定呈指数函数形式且沿着裂纹方向变化．运用积分变换法将裂纹面条件转换为奇异积分方程,并使用Gauss-Chebyshev方法对其进行数值求解．根据算例结果讨论了一些退化问题并分析了裂纹尖端强度因子与材料的非均匀系数和非完整界面参数的关系．     

孔洞放电热应力

本文研究介电材料内含空气圆孔在外加均匀电场作用下放电而引起的热应力.首先推导了圆孔放电前的临界电能,然后将复杂的放电效应简化为只存在热效应,并假设临界电能全部转化为热能且沿圆周均匀分布,计算了圆周附近的热应力.最后以聚乙烯材料作为算例,讨论了圆孔尺寸、材料常数等对热应力集中的影响,以及孔洞放电产生的径向应力和环向应力的变化规律.结果表明孔洞放电所引起的热应力集中以孔边的环向应力为主,而且材料放热系数越小,径向应力、环向应力集中程度越明显.     

含孔曲板弹性波散射与动应力分析

基于敞口浅柱壳弹性波动方程及摄动方法，对无限大含孔曲板弹性波散射及动应力问题进行了分析研究，将经典薄板弯曲波动问题的分析解作为本问题的主项，给出了在稳态波下孔洞附近散射波的零阶渐近解。建立了求解含孔曲板弹性波散射与动应力问题的边界积分方程法，利用积分方程法可获得问题的近似分析解。并给出了无限大曲板圆孔附近动应力集中系数的数值结果，且对计算结果进行了分析与讨论。     

具有界面相的球形粒子在无限大基体中的应力集中分析

研究了无限大基体内具有界面相的球形粒子在轴对称载荷作用下的应力场,并与线弹簧界面模型的情形进行了比较,对粒子／界面相以及界面相／基体两个界面的应力集中系数以及粒子内部的应力集中系数进行了分析．研究了应力二轴度、界面相厚度以及三相的模量对应力集中系数的影响．结果表明,对给定的模量和界面相厚度值,存在一个临界应力三轴度值．若应力二轴度小于此临界值,则界面相／基体界面的应力集中系数大于粒子／界面相界面的应力集中系数;否则,前者会小于后者．所做的应力分析可以为颗粒增强复合材料的强韧化设计提供一定参考．     

径向非均匀压电介质中圆孔对SH波的散射

利用复变函数理论对SH波作用下含圆孔径向非均匀压电介质的反平面动力特性进行了研究。压电介质的密度沿径向按幂函数形式变化,但压电参数、弹性参数、介电参数均为常数。利用变量替换法将非均匀压电介质的变系数波动方程组转化为标准的Helmholtz方程组,得到了满足边界条件的波函数解析表达式。通过数值算例分析了入射角度、入射波频率、幂次等对应力集中系数和电场强度集中系数的影响,并与已有文献进行比较。结果表明,某些参数组合下,动应力集中系数与电场强度集中系数均随幂次增大而增大。     

无限大板开孔弹性波的散射及动应力集中

采用弹性平板理论及复变函数理论，对含孔无限大平板弹性波的散射及动应力集中问题进行了分析研究，建立了求解平板开孔动应力集中问题的复变函数方法。若同时采用映射变换，就为求解平板开任意形状孔的动应力集中问题提供了一种规范而有效的方法。为说明问题，本文给出了平板开圆孔及椭圆孔动应力集中因子的数值结果。     

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.     

Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate

The aim of this work is to present an analytical solution to reduce the stress concentration factor (SCF) around a circular hole in an isotropic homogeneous plate subjected to far-field uniaxial loading. In this paper the elastic response of an inhomogeneous annular ring made of functionally graded material (FGM), inserted around a hole of a homogeneous plate, is studied. By assuming that Young’s modulus varies in the radial direction with power law and that Poisson’s ratio is constant, the governing differential equations for plane stress conditions are obtained. Using stress function a general solution in explicit closed form is presented and the SCF investigated to highlight the inhomogeneity effects. Furthermore, the explicit solution for an inner homogeneous ring, with different properties with respect to those of the plate, is explicitly obtained and numerical results are compared between homogeneous ring and FGM ring.     

Stress analysis of a functional graded material plate with a circular hole

This paper is to study the two-dimensional stress distribution of a functional graded material plate (FGMP) with a circular hole under arbitrary constant loads. With using the method of piece-wise homogeneous layers, the stress distribution of the functional graded material plate having radial arbitrary elastic properties is derived based on the theory of the complex variable functions. As examples, numerical results are presented for the FGMPs having given radial Young’s modulus or Poisson’s ratio. It is shown that the stress is greatly reduced as the radial Young’s modulus increased, but it is less influenced by the variation of the Poisson’s ratio. Moreover, it is also found that the stress level varies when the radial Young’s modulus increased in different ways. Thus, it can be concluded that the stress around the circular hole in the FGMP can be effectively reduced by choosing the proper change ways of the radial elastic properties.     

含功能梯度材料加强环的任意几何形状孔附近应力集中分析

基于复变函数理论,结合保角变换技术研究含功能梯度材料（FGM）加强环的任意几何形状孔附近应力集中。采用分层均匀化方法,给出了远场均布载荷作用下材料参数沿孔周法线方向任意变化的FGM加强环内的复势函数解。通过数值算例,详细讨论了加强环内杨氏模量不同变化规律对三角形、正方形、矩形等各种几何形状孔附近应力分布的影响。结果表明：通过在孔周衬入FGM加强环并合理选择加强环内材料参数的递变规律,可以有效缓解各种几何形状孔附近的应力集中。同时通过一些特例与已有文献比对验证了本文结果的正确性。     

Stress in elastic plates reinforced by fibres lying in concentric circles

We Consider fibre-reinforced elastic plates with the reinforcement continuously distributed in concentric circles ; such a material is locally transversely isotropic, with the circumferential direction as the preferred direction. For an annulus bounded by concentric circles, the exact solution of the traction boundary value problem is obtained. When the extension modulus in the fibre direction is large compared to other extension and shear moduli, the material is strongly anisotropic. For this case a simpler approximate solution is obtained by treating the material as inextensible in the fibre direction. It is shown that the exact solution reduces to the inextensible solution in the appropriate limit. The inextensible theory predicts the occurrence of stress concentration layers in which the direct stress is infinite ; for materials with small but finite extensibility these layers correspond to thin regions of high stress and high stress gradient. A boundary layer theory is developed for these regions. For a typical carbon fibre-resin composite, the combined boundary layer and inextensible solutions give an excellent approximation to the exact solution. The theory is applied to the problem of an isotropic plate, under uniform stress at infinity, containing a circular hole which is strengthened by the addition of an annulus of fibre-reinforced material.     

Dynamic stress analysis of a functionally graded material plate with a circular hole

This paper is to study the two-dimensional dynamic stress of a functionally graded material (FGM) plate with a circular hole under plane compressional waves at infinity. With using the method of piece-wise homogeneous layers, the dynamic stress distribution of the FGM plate having radial arbitrary material parameters is derived based on the complex variable method. As examples, numerical results are presented for the FGM plate having given radial shear modulus, density and Poisson’s ratio. It is found that the dynamic stress around the circular hole in the FGM plate can be effectively reduced by choosing the proper change ways of the radial material parameters for different frequency incident wave.     

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.     

用能量法研究双模量大挠度圆板的轴对称弯曲

双模量圆板在外载荷作用下发生轴对称弯曲变形时,会形成各向同性的拉伸区和压缩区.此种情况下,可把双模量圆板看成两种各向同性材料组成的层合板,采用弹性理论建立了双模量圆板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量圆板的中性面位置.在此基础上,采用能量法研究了双模量大挠度圆板轴对称弯曲变形问题,将该方法计算结...     

DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT

The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy.