共查询到19条相似文献,搜索用时 218 毫秒
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给出了正交各向异性平面热弹性问题的边界积分方程、内点应力公式和常单元离散化时计算奇异积分的解析式,计算了正交各向异性板的热应力强度因子,结果表明了文中所导公式的正确性 相似文献
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正交各向异性平面问题应力强度因子的边界元分析 总被引:2,自引:0,他引:2
本文给出了正交各向异性平面弹性问题的边界元方程,导出了常单元离散化时求系数的解析式。作为数值算例,计算了正交各向异性板的应力强度因子。结果表明,本文所导出公式的正确性。 相似文献
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无单元法是一种新出现的数值方法。本文对无单元法的数学基础—滑动最小二乘法进行了详细的研究,推导了无单元法的形函数,并对一些关键问题,如权函数的选取,正交基函数,边界条件,数值实现方法等得出了研究结论。用无单元法研究了正交各向异性板的自由振动问题,由动力学变分原理和滑动最小二乘法导出了正交各向异性板的无单元法质量矩阵和刚度矩阵,编制了相应的计算程序,通过计算实例验证了该方法的有效性。 相似文献
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正交异性光弹性应力分离的边界元法 总被引:1,自引:0,他引:1
本文对平面正交各向异性复合材料模型引入正应力线性和及边界上正应力线性和流的概念,提出从应力相容方程出发.用边界元法计算正交异性光弹性模型内任一点的正应力线性和位的方法,再与正交异性光弹性法中所给出的应力同的关系结合,即可进行正交异性光弹性应力的分离.最后,对边界元方法的精度进行了讨论. 相似文献
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研制了一种适用于二维正交各向异性位势问题的高阶单元(线性单元和二次单元)快速多极边界元法. 在快速多极边界元法中, 源点对于远场区域的积分采用快速多极展开式计算, 而对于近场区域的积分则直接进行计算. 高阶单元的使用使得近场积分, 尤其是奇异积分和几乎奇异积分的计算更加复杂. 通过引入复数表达对其进行简化, 若边界采用线性单元插值, 近场积分可直接解析计算; 若采用二次单元插值, 则给出一个半解析算法计算近场积分. 高阶单元奇异积分和几乎奇异积分计算难题的解决, 使得高阶单元快速多极边界元法不仅能够计算一般结构, 也能被应用于超薄体结构, 拓宽了高阶单元快速多极边界元法的适用范围. 数值算例表明, 若计算精度一定, 高阶单元快速多极边界元法较常值单元快速多极边界元法使用的单元数量显著减少, 且高阶单元快速多极边界元法计算时间与自由度数量成线性关系, 其计算效率仍处于$O(N)$量级, 因此高阶单元快速多极边界元法可更加高效求解大规模问题. 相似文献
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正交各向异性厚板的边界元解法 总被引:1,自引:1,他引:1
本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。 相似文献
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Roberta Santoro 《European Journal of Mechanics - A/Solids》2011,30(6):924-939
In this paper the numerical technique, labelled Line Element-less Method (LEM), is employed to provide approximate solutions of the coupled flexure-torsion De Saint Venant problem for orthotropic beams having simply and multiply-connected cross-section. The analysis is accomplished with a suitable transformation of coordinates which allows to take full advantage of the theory of analytic complex functions as in the isotropic case.A boundary value problem is formulated with respect to a novel complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. This potential function is analytic in all the transformed domain and then expanded in the double-ended Laurent series involving harmonic polynomials.The solution is provided employing an element-free weak form procedure imposing that the squared net flux of the shear stress across the border is minimum with respect to the series coefficients.Numerical implementation of the LEM results in system of linear algebraic equations involving symmetric and positive-definite matrices. All the integrals are transferred into the boundary without requiring any discretization neither in the domain nor in the contour.The technique provides the evaluation of the shear stress field at any interior point as shown by some numerical applications worked out to illustrate the efficiency and the accuracy of the developed method to handle shear stress problems in presence of orthotropic material. 相似文献
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采用格林公式和基本解推导出直接边界积分方程来求解渗流问题.边界积分方程数值离散基于格林元方法(Green element methond),改进了原方法中压力和压力导数的求解方法,命名为混合边界元方法(Mixed boundary element method).相较于格林元类方法,该方法显式考虑了求解节点的外法向流量值和压力值,并使求得的数值解在求解区域上能够连续,符合实际的物理过程,在不增加额外未知数的情况下提高了计算精度.分析了不同网格类型对模拟计算结果的影响,并对稳定渗流问题、非稳定(瞬态)渗流问题和非稳态问题进行了实例计算,结果显示改进方法提高了计算精度,并对各类渗流问题有较好的适应性. 相似文献
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The solution of Laplace's equation for a wide range of spatial domains and boundary conditions is a valuable asset in the study of potential theory. Recently, classical analytic series techniques based on separation of variables have been modified to solve Laplace's equation with both irregular and free boundaries. Computationally the free boundary problem is reduced to an iterative sequence of curve-fitting exercises. At each iteration the series coefficients for a known boundary problem are evaluated numerically. In this paper a new interpolation approach is presented for the estimation of the series coefficients. It has the advantages of providing a conceptually simpler view of the series technique and of estimating the series coefficients significantly faster than alternative approaches. Owing to the choice of basis functions in the truncated series solution, rigorous estimates of the error in the approximation are immediately available. A free boundary problem from steady hillside seepage with irregular boundaries will be used to illustrate the new technique. 相似文献
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A. Ya. Grigorenko O. V. Vovkodav S. N. Yaremchenko 《International Applied Mechanics》2012,48(1):80-93
The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed.
Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on
spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells
with variable thickness is studied 相似文献
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《International Journal of Solids and Structures》2007,44(11-12):3638-3645
Two-dimensional plane wave propagation in an orthotropic micropolar elastic solid is studied. There exist three types of coupled waves in xy-plane, whose velocities depend upon the angle of propagation and material parameters. A problem on reflection of these plane waves from a stress-free boundary is considered. The reflection coefficients of various reflected waves are computed numerically for a particular model of the solid. The effects of anisotropy upon the velocities and reflection coefficients are depicted graphically for different angles of propagation. 相似文献
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I.IntroductionTheengineeringstructuresareoftells,'1>:'rectcdtotheactionofthestochasticloadingthatvarieswiththetime,forexample,theengineeringstructuresactedonbytheearthquake,theoceanstructuresactedonbydynamicpressure,andthevehiclesofthetransportationinflue… 相似文献
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Summary A boundary value problem for two semi-infinite anisotropic spaces with mixed boundary conditions at the interface is considered.
Assuming that the displacements are independent of the coordinate x
3, stresses and derivatives of displacement jumps are expressed via a sectionally holomorphic vector function. By means of
these relations the problem for an interface crack with an artificial contact zone in an orthotropic bimaterial is reduced
to a combined Dirichlet-Riemann problem which is solved analytically. As a particular case of this solution, the contact zone
model (in Comninou's sense) is derived. A simple transcendental equation and an asymptotic formula for the determination of
the real contact zone length are obtained. The classical interface crack model with oscillating singularities at the crack
tips is derived from the obtained solution as well. Analytical relations between fracture mechanical parameters of different
models are found, and recommendations concerning their implementation are given. The dependencies of the contact zone lengths
on material properties and external load coefficients are illustrated in graphical form. The practical applicability of the
obtained results is demonstrated by means of a FEM analysis of a finite-sized orthotropic bimaterial with an interface crack.
Received 19 October 1998; accepted for publication 13 November 1998 相似文献
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《International Journal of Solids and Structures》2007,44(10):3575-3593
This paper deals with an elastic orthotropic inhomogeneity problem due to non-uniform eigenstrains. The specific form of the distribution of eigenstrains is assumed to be a linear function in Cartesian coordinates of the points of the inhomogeneity. Based on the polynomial conservation theorem, the induced stress field inside the inhomogeneity which is also linear, is determined by the evaluation of 10 unknown real coefficients. These coefficients are derived analytically based on the principle of minimum potential energy of the elastic inhomogeneity/matrix system together with the complex function method and conformal transformation. The resulting stress field in the inhomogeneity is verified using the continuity conditions for the normal and shear stresses on the boundary. In addition, the present analytic solution can be reduced to known results for the case of uniform eigenstrain. 相似文献