各向异性板孔口补强应力分析

应用复变函数的方法，对于孔口被一圆形弹性环加强的各向异性板，给出了在无限远处任意均布力作用下，环及板内的应力场解；算例表明：随着环宽度的增加，环及板孔周的应力均有所降低；随着环刚度的增加，环内的应力随之增加，但板孔周的应力显著降低。     

集中载荷作用下含椭圆夹杂各向异性板的解法

应用复变函数方法研究了含椭圆夹杂各向异性板在集中载荷作用下的解法，首先将复应力函数在椭圆夹杂与板的接触边界上展开成幂级数，然后代入问题的边界条件，最后得到了幂级数形式的复应力函数的系数的线性方程组，进一步求解可获得板的应力分布。     

各向异性板平面应力问题的一般解析解

根据各向异性矩形板平面应力问题的基本方程精确地求得了位移函数的一般解。一般解包括三角函数和双曲线函数组成的解,还有代数多项式解。前者能满足四个边为任意边界条件问题;后者能满足四个角为任意边界条件等问题。这些边界条件用以决定一般解中的积分常数。因此一般解可用以求解任意边界条件下的平面应力问题。以四边为均匀分布和非均匀分布位移的对称角铺设复合材料板为例进行了计算和分析     

各向异性平面内双边半无限裂纹问题的基本解

应用复变函数的方法，对于含双边半无限裂纹的各向异性平面，给出了其在任意集中力作用下的复应力函数基本解与应力强度因子基本解；结果表明：当外载作用在裂纹表面上时，其应力强度因子与相应各向同性的情形相同     

含多椭圆孔无限大各向异性薄板弯曲问题研究

该文利用各向异性体弹性理论中的复势方法,以Faber 级数和保角映射为工具,对含多椭圆孔无限大各向异性薄板弯曲问题进行分析,得到了含多椭圆孔无限大各向异性薄板弯曲的级数解形式,给出了无限大薄板在受到弯曲载荷时孔边的应力分布,并讨论了孔距、孔的数量、排列方式、椭圆度、材料的各向异性对孔边应力分布的影响,得到了有益的结论.该方法具有计算精度高、收敛速度快、方便快捷等优点.     

无限板内椭圆孔周的应力分析

应用复变函数的方法，对于含有椭圆孔的各向异性板或各向同性板，导出了当椭圆孔周作用任意集中力或分布力时孔周周向应力的解析表达式；其特例与前人结果一致．     

不同孔口形状对含孔复合材料板孔边应力状态影响的研究

对复合材料结构而言,孔口边界条件的建立和处理比金属材料要复杂得多。针对含不同孔形的复合材料板,根据非均质各向异性弹性理论和复变函数理论,通过保角映射方法建立精确的边界条件,解决了某些复杂孔形的边值问题。得到了含圆、矩形和六边形孔复合材料板孔边应力的解析解。并针对不同孔形在受外荷载作用的情况下的应力状态,以及它们对孔边应力集中系数的影响进行了探讨。     

柱状晶Cu-Al-Mn形状记忆合金超弹性各向异性参数研究及数值计算

参考单层板的偏轴工程弹性常数与正轴工程弹性常数的转换关系,进行参数推导,实现了对合金任意角度的超弹性各向异性相关参数的计算。采用有限元用户子程序对合金任意角度下的超弹性应力-应变曲线进行数值模拟。模拟计算结果与实验结果吻合较好,可为柱状晶类组织合金的各向异性性能的模拟计算提供相应指导和参考。      

基于状态空间的能量变分法在板的自然频率求解中的应用

文章从三维弹性力学基本方程出发,由能量变分原理出弹性体的二类变量混合变分方程。引入状态空间,将变分法与状态空间方法相结合,建立正交各向异性体在任意２荷载作用下的弹性力学问题的状态问题。使应力和位移的连续条件得到满意。并导出自由振动方程,给出了任意厚度板的自然频率变分解。     

光弹性贴片法测定复合材料的孔边应力

本文根据复合材料各向异性的特性,对光弹性贴片法测试复合材料板无载孔的孔边应力,作了分析和实验研究.推导出光弹性贴片法测量复合材料孔边应力的基本公式,泊松比失配和贴片增强效应的修正公式.最后,对理论值与测试值进行了比较,符合较好.     

A general method for multiple crack problems in a finite plate

A novel method for the multiple crack problems in a finite plate is proposed in this paper. The basic stress functions of the solution consist of two parts. One is the Fredholm integral equation solution for the crack problem in an infinite plate, and the other is that of the weighted residual method for general plane problems. The combined stress functions are used in the analysis and the boundary conditions on the crack surfaces and the boundary are considered. After the coefficients of the functions have been determined, the stress intensity factors (SIF) at the crack tips can be calculated. Some numerical examples are given and it was observed that when the cracks are very short, the results compare very favorably with the existing results for an infinite plate. Furthermore, the influence of the boundary can be considered. This method can be used for arbitrary multiple crack problems in a finite plate.     

Analysis of an internal crack in a finite anisotropic plate

In this paper the boundary collocation method is presented for computing the stress intensity factors for an internal crack in a finite anisotropic plate. The stress functions are assumed such that they can represent the stress singularity at the crack tips, satisfying not only the governing equations of the anisotropic plate theory in the domain, but also the stress-free conditions on the crack surfaces. Therefore, only the boundary conditions of the plate need to be considered, and they can be satisfied approximately by the Boundary Collocation Method. Numerical examples demonstrated that the proposed method gives satisfactory results compared with the existing solutions.     

弹性地基上各向异性厚板计算新方法

弹性地基上厚板的弯曲,一直是学者和工程师们十分关切的问题.本文采用分步分析方法,分析了弹性地基上的各向异性厚板和板式筏片基础,使在不需增加基本未知函数个数的情况下就可建立含有横向坐标Z的任意高次项的高阶方程,与现有厚板理论相比,本文所述方法具有基本未知函数少、基本方程易于建立、简单易解、计算结果精度较高等优点.     

基于解析试函数的各向异性材料厚薄通用板单元

该文采用满足Kirchhoff假设的薄板理论,推导了各向异性材料系列解析试函数,并利用该系列解析试函数构造了一个四边形应力杂交板单元。首先,该文从薄板理论的基本方程出发,推导了各向异性材料薄板中面挠度w应满足的特征微分方程。然后,从该方程出发求得w的系列特征通解,由w特征通解可进一步求得广义位移、广义应变和广义应力的解析试函数。同时,根据广义应力利用平衡条件构造了相应的横向剪力解析试函数。最后,根据已有的广义应力和横向剪力解析试函数构造了一个四边形应力杂交板单元ATF-PH4。数值算例表明:上述方法构造出的单元模型有很好的精度、收敛性,且对网格畸变不敏感,同时能较好地解决板单元的厚薄通用性问题。     

Non-uniform eigenstrain induced anti-plane stress field in an elliptic inhomogeneity embedded in anisotropic media with a single plane of symmetry

A closed-form solution is derived for an anti-plane stress field emanating from non-uniform eigenstrains in an elliptic anisotropic inhomogeneity embedded in anisotropic media with one elastic plane of symmetry. The prescribed eigenstrains are characterized by linear functions of the inhomogeneity in Cartesian coordinates. By means of the polynomial conservation theorem, use of complex function method and conformal transformation, explicit expressions for stresses at the interior boundary of the matrix and the strain energy for the elastic inhomogeneity/matrix system are obtained in terms of coefficients in the linear functions. The coefficients are evaluated analytically using the principle of minimum potential energy of the elastic system, leading to the anti-plane stress field. The resulting solution is verified by means of the continuity condition for the shear stress at the interface between the elliptic inhomogeneity and matrix. The present solution is shown to reduce to known results for uniform eigenstrains with illustration by numerical examples.     

On inverse boundary heat-conduction problems for recovery of heat fluxes to anisotropic bodies with nonlinear heat-transfer characteristics

A closed method is proposed for recovering heat fluxes to anisotropic bodies under conditions of aero-gasdynamic heating from experimental temperature data at spatial-temporal nodes. The thermal protection of a body is made of anisotropic materials with components of thermal-conductivity tensor, which are dependent of temperature, i.e., are nonlinear. The method is based on approximating a spatial dependence of a heat flux by a linear combination of basis functions with sought coefficients (parameters), which are found by minimization of a quadratic functional of the residual (the discrepancy between experimental and theoretical temperature values) using the implicit method of gradient descent, as well as on constructing and numerically solving problems for the determination of sensitivity coefficients. To increase the degree of correctness of an inverse problem, along with a main functional, the regularizing functionals have been constructed and utilized on the basis of smoothness requirements for spatial functions of heat fluxes to have continuous first and second derivatives, which allowed heat fluxes with the coupled heat transfer to be recovered in the form of arbitrary functions: monotonic, nonmonotonic, having extrema, inflection points, etc. Numerous results of recovering heat fluxes to anisotropic bodies are obtained and discussed, with the regularization parameter being selected for every case.     

Forced Vibration Analysis of Functionally Graded Anisotropic Nanoplates Resting on Winkler/Pasternak-Foundation

This study investigates the forced vibration of functionally graded hexagonal nano-size plates for the first time. A quasi-three-dimensional (3D) plate theory including stretching effect is used to model the anisotropic plate as a continuum one where smallscale effects are considered based on nonlocal strain gradient theory. Also, the plate is assumed on a Pasternak foundation in which normal and transverse shear loads are taken into account. The governing equations of motion are obtained via the Hamiltonian principles which are solved using analytical based methods by means of Navier’s approximation. The influences of the exponential factor, nonlocal parameter, strain gradient parameter, Pasternak foundation coefficients, length-to-thickness, and length-to-width ratios on the dynamic response of the nanoplates are examined. In addition, the accuracy of an isotropic approximate instead of the anisotropic model is studied. The dynamic behavior of the system shows that mechanical mathematics-based models may get better results considering the anisotropic model because the dynamic response can cause prominent differences (up to 17%) between isotropic approximation and anisotropic model.     

A correspondence principle for laminated plates

The problem of determining the stress distribution within a plate laminated of any number of isotropic plies is considered. The general method of approach is via the three-dimensional theory of elasticity. The laminated plate is regarded as a material continuum characterized by material property functions which possess finite jumps across material interfaces. The stress field is supposed to be induced by boundary tractions applied to the edges and to one lateral face, and by temperature, the plate being stress-free in the reference state. The continuity conditions across material interfaces are automatically satisfied by a method of formulation previously reported in [1].It is shown that the problem involves the determination of four continuous stress functions which may have discontinuous normal derivatives at material interfaces. In the case in which the number of laminations increases without limit, a Correspondence Principle is derived which relates the stress field in the laminated plate to the stress field in a ‘corresponding’ homogeneous, anisotropic plate subjected to the same loading. Numerical results are exhibited which show that the maximum strain error obtained by applying the Correspondence Principle to a plate with as few as three plies is less than 1 per cent.     

Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.