Boundary element analysis of anisotropic Kirchhoff plates

In this paper, the radial integration method is used to obtain a boundary element formulation without any domain integral for general anisotropic plate bending problems. Two integral equations are used and the unknown variables are assumed to be constant along each boundary element. The domain integral which arises from a transversely applied load is exactly transformed into a boundary integral by a radial integration technique. Uniformly and linearly distributed loads are considered. Several computational examples concerning orthotropic and general anisotropic plate bending problems are presented. The results show good agreement with analytical and finite element results available in the literature.     

A reciprocal theorem in generalized thermoelasticity

A reciprocal theorem for initial mixed boundary value problems is obtained in the context of the linearized anisotropic thermoelasticity theory of Green and Lindsay.     

GREEN＇S FUNCTIONS OF TWO－DIMENSIONAL ANISOTROPIC BODY WITH A PARABOLIC BOUNDARY

ＧＲＥＥＮ＇ＳＦＵＮＣＴＩＯＮＳＯＦＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＡＮＩＳＯＴＲＯＰＩＣ ＢＯＤＹ ＷＩＴＨ Ａ ＰＡＲＡＢＯＬＩＣ ＢＯＵＮＤＡＲＹ（胡元太）（赵兴华）ＧＲＥＥＮ＇ＳＦＵＮＣＴＩＯＮＳＯＦＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＡＮＩＳＯＴＲＯＰ?..     

Exact solutions of multi-term fractional difusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multiterm time-fractional difusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial diferential equations are converted into time-fractional ordinary diferential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-difusion problems are given to validate the proposed analytical method.     

Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.     

A combined approach of EFGM and precise algorithm in time domain solving viscoelasticity problems

In this paper, element free Galerkin (EFG) method is combined with a precise algorithm in the time domain for solving viscoelasticity problems. By expanding variables at discretized time intervals, an initial boundary value problem is converted into a series of recurrent boundary value problems which can be conveniently solved by EFG/EFG-FE with a self-adaptive computing process. There is no requirement of iteration for the solution of non-linear cases. Satisfactory numerical results are obtained for both static and dynamical viscoelasticity problems.     

To the Investigation of Plane Wave Propagation in an Elastic Anisotropic Media by a Recursive Operator Method

A solution of the equations of motion of a 3D anisotropic elastic medium without determining the roots of the determinant (secular) equation is obtained by a recursive operator method. A relationship between such solutions and classical solutions is established. The possibility of solving initial–boundary value problems for plane waves is considered. An example and comparative graphs of the solutions are given.     

用子域边界元法研究各向异性材料中的界面裂纹

用子域边界元法研究各向异性材料中的界面裂纹，在边界元公式中，采用了带特征根的基本解，以增量形式的边界积分方程为基础，通过二次等参元及国分之一面力奇异远离散化处理，可以得到各子域的代数方程组，依据凝集技术，可得到仅含有子域公共边界及裂纹边界未知量的求解方程组，通过迭代法，可以寻求到每种载荷作用下的裂纹所处的真实状态，然后，由文献「２」中的方法求解界面裂纹的应力强度因子。结果表明，子域边界方法是正确的     

各向异性平面含斜裂纹的奇异积分方程方法

本文应用平面弹性复变方法，将无限各向异性平面中的任意斜裂纹问题归结为求解一组解析函数边值问题，通过构造适当的积分变换将边值问题转化为奇异积分方程，进而应用Lobotto-Chebyshev数值求积公式，求出该奇异积分方程的数值解，并得到了应力强度因子的近似表达式，最后，给出了一些实例的数值结果，对特例的数值结果与精确结果进行比较，吻合的很好。     

A coupling method of difference with high order accuracy and boundary integral equation for evolutionary equation and its error estimates

In the present paper,a new numerical method for solving initial-boundary valueproblems of evolutionary equations is proposed and studied,combining difference methodwith high accuracy with boundary integral equation method.The numerical approximateschemes for both problems on a bounded or unbounded domain in R~3 are proposed and theirprior error estimates are obtained.     

Global Estimates for Quasilinear Elliptic Equations on Reifenberg Flat Domains

New global regularity estimates are obtained for solutions to a class of quasilinear elliptic boundary value problems. The coefficients are assumed to have small BMO seminorms, and the boundary of the domain is sufficiently flat in the sense of Reifenberg. The main regularity estimates obtained are in weighted Lorentz spaces. Other regularity results in Lorentz–Morrey, Morrey, and Hölder spaces are shown to follow from the main estimates.     

On the Boundary Value Problems of Linear Elasticity with Constraints

In this paper classic boundary value problems of linear elastostatics are studied. Displacement, mixed and traction type boundary conditions are considered for an internally constrained, non-homogeneous, anisotropic material. Existence of solutions and constraint stability results are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

A meshfree method for transverse vibrations of anisotropic plates

A meshfree approach, called displacement boundary method, for anisotropic Kirchhoff plate dynamic analysis is presented. This method is deduced from a variational principle, which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables. The discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional. The stiffness and mass matrices obtained for the dynamic model are frequency-independent, symmetric and positive definite and their computation involves boundary integrals of regular kernels only. Due to its features, the final resolving system can be solved with the classical approaches by using standard numerical procedures. To assess the formulation, the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques. The present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach.     

Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions

The problem of formulating minimal conditions on input data that can guarantee the existence and uniqueness of solutions of the boundary value problems describing non-one-dimensional ideal incompressible fluid flow is considered using as an example the initial boundary value problem in a space-time cylinder constructed on a bounded flow domain with the nonpenetration condition on its boundary (which corresponds to fluid flow in a closed vessel). The existence problems are considered only for plane flows, and the uniqueness issues for three-dimensional flows as well. The required conditions are obtained in the form of conditions specifying that the vorticity belongs to definite functional Orlicz spaces. The results are compared with well-known results. Examples are given of admissible types of singularities for which the obtained results are valid, which is a physical interpretation of these results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 130–145, July–August, 2008.     

各向异性位势平面问题的规则化边界元法

基于转化域方程为边界积分方程的极限定理及一个新颖的基本解分解技术, 建立间接变量规则化边界积分方程, 它有效地避免了奇异积分的直接计算. 与已有方法比,该方法不将问题变换为各向同性的问题去处理, 因而无需反演运算, 也有别于Galerkin方法, 无需计算重积分. 可计算任意边界位势梯度, 而不仅限于法向通量. 针对椭圆边界的边值问题, 提交一种精确单元来描述边界几何. 数值算例表明, 所提算法稳定且效率高, 所得数值结果与精确解吻合较好.      

Two theorems on the steady-state conduction in anisotropic body

In this paper, steady-state plane conduction problems are considered. Two theorems are proven on the conductance of non-homogeneous and anisotropic plane conductors. Here, the conductor is a two-dimensional bounded plane domain with a conducting matter having two seperated boundary terminals and two seperated insulated boundary segments. Known theorems referring to homogeneous and isotropic conductors have been extended to non-homogeneous and anisotropic ones. The results of the paper can be directly used in following fields: heat flow, diffusion, irrotational hydraulic flow, flow of electrical current and anti-plane shear deformation. Application of formulae derived is illustrated in the examples of heat flow and anti-plane elastic shear deformation.     

SOME IDENTITY RELATIONS BETWEEN PLANE PROBLEMS FOR VISCO-AND ELASTICITY

I.IntroductionThereareimportantapplicationsfortheor}:ofplanea'iscoelasticit}'Inthefieldsofgeology,miningandconstructingetc.,butformostproblemsofviscoelastici[}'.theirsolutionsareobtainedfromthecorrespondingelasticsolutionsb}'"leansofthecorrespondenceprinc…     

A Legendre wavelet spectral collocation technique resolving anomalies associated with velocity in some boundary layer flows of Walter-B liquid

A Legendre wavelet spectral collocation method is proposed here to solve three boundary layer flow problems of Walter-B fluid namely the stagnation point flow, Blasius flow and Sakiadis flow. In the proposed method, we first transform the boundary value problems into initial value problems using shooting method. We then split the semi infinite domain into subintervals and the governing initial value problems are transformed to system of algebraic equations in each subinterval. The solutions of these algebraic equations yield an approximate solution of the differential equation in each subinterval. The overshoot in the velocity profile associated with the stagnation point and Blasius flows and undershoot in the Sakiadis flow is controlled. Physically realistic solutions are presented for both weakly and strongly viscoelastic parameters. The residual error validates the correctness, convergence and accuracy of the obtained solutions.     

冲击作用下含孔洞纤维增强复合材料平板的动力学实验与数值研究

作为复合材料动力学实验与数值研究的应用实例 ,实验研究采用正交异性动态光弹性方法 ,数值分析运用各向异性介质的时域边界元方法。纤维增强光弹性复合材料平板被用来模拟含孔洞的正交异性半无限域 ,用小口径步枪施加与纤维方向成 0及 90两个方向的冲击载荷 ,在正交异性动态光弹性实验中记录了应力波在孔洞周围的传播、反射与绕射过程 ,此过程被进一步转换成应力分量的变化时程 ,并与相应的时域边界元方法的数值分析结果进行了比较。     

On modeling the aggregate response of laminated thermoelastic media

Sufficient conditions are given that determine when solutions to general boundary value problems for inhomogeneous anisotropic laminated thermoelastic media are approximated, in the average, by solution of constant coefficient equations. These appropriate constant coefficients are computed and shown to be independent of the shape of the body and the loading on the body.