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。     

基于有限元法的正交各向异性复合材料结构材料参数识别

以大型商用有限元软件ABAQUS为计算平台,提出了正交各向异性复合材料结构材料参数的识别方法。将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有限元计算的相应位移之差的平方和。采用Levenberg-Marquardt方法极小化目标函数,其中灵敏度的计算基于复合材料的有限元离散结构的求解方程对识别的材料参数求导。数值算例表明本文中提出的方法是有效的。在识别参数过程中,参数的初值以及搜索范围的确定对于识别结果有着重要影响。因此必须充分利用材料参数的先验信息。ABAQUS是高效可靠的商用有限元软件,提出的参数识别方法基于这类商用软件,因而该方法有很强的实用性。     

正交各向异性厚板振动分析的边界积分方程法

本文采用正交各向异性厚板静力问题的基本解作为边界积分方程的核函数,利用加权残数法建立了正交各向异性厚板振动分析的边界积分方程。文中详细地讨论了边界积分方程的数值处理过程并给出了若干数值算例以论证本文方法的正确性。      

正交各向异性板动力响应的边界元方法

本文讨论了正交各向异性板动力响应的边界元方法,发展了一种新的求近似基本解的方法,由该方法得到的基本解,给出了弹性薄板诸问题近似基本解的统一形式。应用这个基本解,得到了正交各向异性板和弹性地基板稳态强迫振动的边界元方程。文中的算例表明,本文的方法具有相当高的精度。     

二维正交各向异性结构弹塑性问题的边界元分析

给出了二维正交各向异性结构弹塑性问题的边界元分析方法, 包括相应边界积分方程、内点应力公式、边界元求解格式以及弹塑性应力计算方法。在弹塑性分析中, 引入了Hill-Tsai 屈服准则, 采用初应力法和切向预测径向返回法确定实际应力状态。通过具体算例分析了二维正交各向异性结构的弹塑性应力和塑性区分布情况, 部分数值结果与已有结果进行了比较, 两者基本吻合。结果表明, 本文中给出的边界元法可以有效地用于求解二维正交各向异性结构的弹塑性问题。      

层状正交各向异性材料弹性波导问题的数值计算

研究复合材料弹性波导问题的数值计算方法。将问题导向哈密顿体系,在哈密顿体系中以位移向量和应力向量综合成全状态向量,在杂交体系中建立动力-部分杂交元,导出一套哈密顿体系下新的半解析法。本文中给出了该方法在分层正交各向异性材料的弹性波导问题的数值算例。计算结果展现了该方法在弹性波导问题的应用前景。     

双相压电介质中界面附近圆孔的动态性能分析

采用Green函数法研究界面附近含圆形孔洞的双相压电介质对时间谐和SH波的散射问题。首先利用复变函数的方法构造出适合于本文问题的位移Green函数和电场Green函数。然后利用契合思想，根据界面上的连续性条件建立起求解问题的第一类Fredholm型积分方程，得到了圆孔孔边周向剪应力的动应力集中系数和周向电场强度集中系数的解析表达式。最后作为算例，给出了界面附近圆孔边界的两组集中系数随入射波频率、材料的几何参数和物理参数变化的计算结果图，部分计算结果与已有文献进行了比较。     

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。     

基于修正样条函数分析滑移边界矩形板的自由振动

提出了一种分析滑移边界各向同性和正交各向异性矩形板振动特性的数值方法一双向样条离散法。该方法适用于各种可能组合边界矩形板的自由振动分析；边界包括自由、简支、固定和滑移边界。在x和y方向，板被离散成N和M个等分区间。为适应任意边界，修改N＋3和M＋3维硝样条函数向量的最前和最后三个函数，得到x方向N＋1个点、y方向M＋1个点和x-y方向两个附加点的修正的邱样条函数向量，并以此作为板的位移试函数。在给定边界下，修正的B3样条函数向量对位移、位移的一阶导数和二阶导数都仅保留一个未知系数。基于矩形板的势能泛函导出其特征方程。与有限元法和样条有限条法相比，本文方法具有自由度少、计算效率高和输入数据少等优点。数值计算结果表明，本方法具有高的计算精度。     

SH波入射下正交各向异性双相介质界面附近圆孔的动应力集中

基于复变函数和格林函数的方法，探讨了SH波在具有圆孔的正交各向异性两相介质中的散射，分析了圆孔周围的动态响应规律。首先建立问题的二维解析模型，将全空间分为两个部分：均匀各向同性上半空间以及含圆柱形孔洞的正交各向异性下半空间。采用格林函数法推导出了两半空间界面处各点的格林函数表达式，并引入复变量，构造出了SH波入射下求解区域内位移和应力的表达式。考虑界面的连续性条件，将未定反平面力加载到两个半空间的水平界面上，推导出Fredholm定解积分方程组，用弱奇异积分方程的直接离散方法求解。最终通过算例分析，发现介质的正交各向异性参数、入射波波数、角度以及孔洞埋深等对下半空间圆孔周边的动应力集中系数(DSCF)影响显著。     

Identification of elastic orthotropic material parameters by the scaled boundary finite element method

This paper focuses on a parameter identification algorithm of two-dimensional orthotropic material bodies. The identification inverse problem is formulated as the minimization of an objective function representing differences between the measured displacements and those calculated by using the scaled boundary finite element method (SBFEM). In this novel semi-analytical method, only the boundary is discretized yielding a large reduction of solution unknowns, but no fundamental solution is required. As sufficiently accurate solutions of direct problems are obtained from the SBFEM, the sensitivity coefficients can be calculated conveniently by the finite difference method. The Levenberg–Marquardt method is employed to solve the nonlinear least squares problem attained from the parameter identification problem. Numerical examples are presented at the end to demonstrate the accuracy and efficiency of the proposed technique.     

Stresses around a pin-loaded hole in orthotropic plates with arbitrary loading direction

Lekhnitskii's method of complex stress function is extensively used to solve the pin-loaded circular hole problem in an infinite orthotropic plate. The approach is similar to the one used earlier by the authors, but extended into a more general fashion. The direction of pin-load is arbitrary and the presence of friction is considered.An analytic solution which satisfies the major displacement boundary conditions on the pin-loaded hole has been obtained. Certain parameters are introduced for simplifying the expressions. These formulas can be used for computing the stress distribution around a pin-loaded hole and estimating the effect of direction of the pin-load and the presence of friction. The degree of such an effect depends on the orthotropy of the material. Some numerical results have been calculated and presented in this paper. They are compared with other results available in the literature.     

Wave propagation in fibre reinforced composite plate with circular hole under impact loading

Abstract

In this paper, experimental and numerical methods have been applied to the study of composite dynamics. Dynamic orthotropic photoelasticity is employed in the experimental work and the time domain boundary element method for anisotropic media is adopted for the numerical analysis. A fibre reinforced birefringent composite plate is used to model the semi-infinite orthotropic domain with a circular hole. A rifle bullet was used to exert the impact loading with the loading direction parallel and perpendicular to the fibre direction. In the experiments, the propagation, reflection, and diffraction of the stress wave around the hole were recorded and the results were analysed. The time histories of the stress components were obtained from the same experiments and compared with the results from the corresponding computations carried out using the time domain boundary element method. Some valuable data regarding composite dynamics and associated engineering implications were obtained. The comparative study also demonstrates the applicability and accuracy of the two methods for wave propagation problems in orthotropic media.     

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.     

Cracks emanating from a square hole in rectangular plate in tension

A numerical analysis of cracks emanating from a square hole in a rectangular plate in tension is performed using a hybrid displacement discontinuity method (a boundary element method). Detailed solutions of the stress intensity factors (SIFs) of the plane elastic crack problem are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. By comparing the calculated SIFs of the plane elastic crack problem with those of the centre crack in a rectangular plate in tension, in addition, an amplifying effect of the square hole on the SIFs is found. The numerical results reported here also prove that the boundary element method is simple, yet accurate, for calculating the SIFs of complex crack problems in finite plate.     

Stress analysis of multilayered plates around circular holes

In this paper, a technique to study the 3-dimensional stress state around a circular hole in laminated plates is developed. First, the 3-dimensional elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. This problem was originally solved by Alblas[1]. The reasons for reconsidering it are to introduce a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. Among the additional results of particular interest, one may mention the significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses. Secondly, the elasticity problem for a laminated thick plate, which consists of two bonded dissimilar layers and which contains a circular hole, is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface. Through the expansion of the boundary conditions into Fourier series, the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented, and the stress intensity factors are calculated. It is also observed that, the results compare rather well with those obtained from the finite element method.     

正交各向异性平面问题边界元素法研究

边界元素法是近年来受到国内外广泛重视并得到迅速发展的一种计算方法。本文系统地研究了正交各向异性平面问题边界元素法的有关基本问题,包括基本解,C矩阵、G_ii矩阵和域内应力的表达式等,并在此基础上建立了常值边界元素和线性边界元素的计算公式。所述理论和公式适用于各类边值问题。最后,按本文所述理论和公式计算了含孔正交各向异性板的应力,数值结果与解析解相符甚好。      

Effect of defective holes on crack using the boundary element method

Boundary value problem of a plate with crack and defect such as the circular and/or elliptical holes is a multi-connected domain problem, this kind of problem is suitable for solving by boundary element method with its higher precision. The sub-region method is used in the paper, a center cracked plate subjected to remote tensile and shear loading is studied numerically. The effect of the circular hole on Mode-I and Mode-II stress intensity factors is studied assuming the plane strain condition, the results are more precise than that of using FEM. The effect of the elliptical hole on Mode-I stress intensity factors is studied as well and some significant results are obtained.