THE PROBLEM OF THE NON-LINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR THIN PLATE WITH VARIABLE THICKNESS

To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.

Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole

The three-dimensional stress concentration factor (SCF) at the edge of elliptical and circular holes in infinite plates under remote tension has been extensively investigated considering the variations of plate thickness, hole dimensions and material properties, such as the Poisson’s coefficient. This study employs three dimensional finite element modeling to numerically investigate the effect of plate width on the behavior of the SCF across the thickness of linear elastic isotropic plates with a through-the-thickness circular hole under remote tension. The problem is governed by two geometric non-dimensional parameters, i.e., the plate half-width to hole radius (W/r) and the plate thickness to hole radius (B/r) ratios. It is shown that for thin plates the value of the SCF is nearly constant throughout the thickness for any plate width. As the plate thickness increases, the point of maximum SCF shifts from the plate middle plane and approaches the free surface. When the ratio of plate half-width to hole radius (W/r) is greater than four, the maximum SCF was observed to approximate the theoretical value determined for infinite plates. When the plate width is reduced, the maximum SCF values significantly increase. A polynomial curve fitting was employed on the numerical results to generate empirical formulas for the maximum and surface SCFs as a function of W/r and B/r. These equations can be applied, with reasonable accuracy, to practical problems of structural strength and fatigue, for instance.

AN INVESTIGATION ON METERIAL PROPERTIESOF NON-HOMOGENEOUS CYLINDRICALLYORTHOTROPIC CIRCULAR PLATES

It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this paper is to verify the effect of radius on the materal properties According to the flat stress-strain relation the values of material properties E E andwhich are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

In this Paper we study the recursive equations under the recursive boundary conditions for W_(nm),nm, v_(nm) and ψ_(nm)(n=0.1.2...N:m=1.2...M. which derivedby the two-variable method ￣[3] in the preceding paper￣[1]. We then solve these problems by using the method of regular perturbation￣[2]. and the uniformly valid asymptotic solution is obtained. Lastly we consider a particular example i. e the bending problems of the axisymmetrical circular plate by using the mixed perurbation method and compare our results with the exact solution found in Ret [ 5 ]. They are similarly coincided.

Bending problems of Non-Homogeneous Cylindrical Orthotropic Circular Plate

In this paper ,the bending problem of the non-homogeneous cylindrical orthotropiccircular plate is described.A general solution for the bending of circular plate underuniformly distributed transverse load is solved.and the exact solution of such circularplate with clamped edges is obtained.

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULA RPLATE（I）

In this paper, ihe probleins of nonlinear unsymmeirucal bending for cylindricallyorthotropic circular plale are sludied by using “ the method of two-variabie”￣[1], and theuniformly valid asympiotic soluiions of Nth-order .lor ε_1 and Mth-order for ε_2 areobiained

UNSYMMETRICAL LARGE DEFORMATION PROBLEM OF ORTHOTROPIC PLATES

Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given .

A generalized plane strain theory for transversely isotropic piezoelectric plates

Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that com- monly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.

圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题（Ⅱ）

本文利用“正则摄动法”［２］研究文献［１］中由“两变量法”［３］所得到的关于Ｗｎｍ，和的递推方程和递推边界条件的求解问题。求得了本问题的一致有效渐近解，最后作为实例，我们利用“混合摄动法”［４］研究了轴对称线性弯曲问题，并将所得结果与文献［５］中给出的精确解相比较，两者基本上是一致的。

正交各向异性板的非对称大变形问题

从各向异性板的基本理论出发 ,推导出正交各向异性圆板的非对称大变形基本方程 ,利用Fourier级数把问题的偏微分方程转化为一组可积分求解的非线性常微分方程 ,并给出利用迭代法求解该问题的基本方法·

正交各向异性孔板的材料参数识别

结合优化技术和边界元分析,针对正交各向异性孔板进行了材料参数的识别。材料参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与边界元计算相应的位移之差的平方和。采用Levenberg-Marquardt方法解极小化目标函数的问题,其中灵敏度的计算是基于离散的边界元代数矩阵方程对识别材料参数的求导。数值算例中,首先把边界元计算正交各向异性圆孔方板位移的结果与解析解进行比较,两者符合良好;然后采用本文提出的方法识别正交各向异性圆孔方板的材料参数。数值算例表明本文提出的方法是有效的。

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。

不同荷载作用下圆孔板孔边及孔口附近应力场的仿真分析

建立了基于弹性理论及复变函数理论的计算模型。利用所建立的计算模型对孔边应力场进行了分析,同时也对孔口附近的各应力分量进行了较为全面的计算,得到了一些有益的结论。对孔边各应力分量进行了比较,同时也对距孔边不同距离时的应力场进行了比较。另外,通过施加不同的荷载,对孔边的应力场以及距孔边不同距离时的应力场的影响进行了研究。

正交各向异性复合材料孔板性能参数识别测点的最优布置

基于静态位移的测量和边界元分析,性能参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与边界元计算的位移之差的平方和。求解此优化问题采用Levenberg-Marquardt算法。通过该算法适定性的分析,提出了考虑诸多因素综合影响的优化测点布置的方法。该方法的有效性得到了数值算例的验证,算例结果表明测点布置对正交各向异性复合材料孔板性能参数识别的结果有较大的影响。提出的方法可以找出测点的最优布置,得到令人满意的识别结果。

有限厚中心圆孔板的最大三维应力集中

应用有限元法对有限厚中心圆孔板的三维应力集中进行了分析。分析发现,当板厚是孔半径的2.4倍时,出现最大应力集中,若此时采用总厚度与其相等的系列分层板来代替整板,将有效地降低三维应力集中;对于厚板,最大应力集中总是出现在离自由表面1.2倍孔半径的位置。分析得到最大三维应力集中系数与相应平面解之间的近似关系;在缺口系数的基础上,研究了三维应力集中对疲劳强度的影响,并给出一个三维应力集中对疲劳强度的影响系数。

圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题（Ⅰ）

本文利用“两变量法”￣［１］研究了圆柱型正交各向异性圆形薄板在非均布横向载荷作用下的非线性非对称弯曲问题，并得到在周边为可移夹支条件下的本问题的一致有效渐近解。

小孔法测量正交各向异性材料残余应力

讨论了小孔法测量正交各向异性材料残余应力。以正交各向异性无限大板孔边应力场解析解为基础，导出了释放应变矩阵计算表达式，并用一个算例验证了该计算式的正确性。

倾斜地表下深埋隧道受力弹性分析

本文通过对倾斜地表重力作用下岩石的应力分析，把相对隧道截面埋置较深的圆形隧道问题看作弹性力学中无限板圆孔来处理，在计算方面采用分解叠加的等效原则把工程中遇到的复杂应力转化为简单应力，求解出一般条件下平面应变解析表达式。避免了繁杂运算，并且详细地讨论了影响隧道围岩应力分布的各项因素。

开孔有限平板应力集中问题的有限元分析

针对中心带有圆孔的有限宽平板的应力集中问题,利用软件ABAQUS对其进行有限元分析。定义了孔边应力集中系数K和描述板宽与孔径相对尺度的特征参数ξ,研究得到了反映不同板宽下孔边应力集中程度的ξ-K关系曲线图,并将其与无限大板宽情形下的解析解进行比较,给出解析解的适用范围。在此基础上,数值分析了不同形状的椭圆孔口应力集中问题,并对椭圆尖端奇异性进行简要讨论。

海洋结构薄板弹性屈曲的群孔效应

针对含孔洞板结构,重点考虑非均匀孔洞分布,采用有限元方法对小变形结构的极限承载能力进行计算,得到孔洞数量、面积、位置、分布等因素对屈曲临界应力的影响规律。结果表明:孔洞分布不仅会改变有效承载面积并使承载能力变化,局部结构还会进入不同承载状态,使板结构承载性能产生非单调变化,即孔洞对板结构屈曲应力的影响具有一定的"群孔"效应。