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1.
By means of Fourier integral transformation of generalized fimction, the fimdamental solution for the bending problem of plales on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series.On the basis of the above work, two boundary integral eguations which are suitable to arhitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem. 相似文献
2.
In this paper a boundary integral equation formulation for the Reissner's plates resting on a two-parameter foundation is established. With the aid of the Hormander Operator method, the equations of the corresponding fundamental solutions are converted into a sixth order partial differential equation with a scale function as an unknown. In order to reduce the equation further, two auxiliary functions are introduced. They satisfy a second and a fourth order equation respectively. The expressions of the auxiliary functions can be derived easily. The fundamental solutions of the Reissnei's plates on the two-parameter foundation arc expressed by a linear combination of the auxiliary functions and their derivatives. The boundary integral equations are formulated by the use of the weighted residual procedure. The fundamental solutions obtained are taken as the kernel functions of the boundary integral equations. A few examples are studied. The numerical results show high accuacy and efficiency of the present formulation.This work was supported by the National Natural Science Foundation of China. 相似文献
3.
BOUNDARY INTEGRAL EQUATIONS FOR BENDING PROBLEM OF REISSNER'S PLATES ONTWO-PARAMETER FOUNDATION 总被引:1,自引:0,他引:1
I.IntroductionThickplatesonelastict'oundationarewidelyusedinengineering,suchasthebottomplatesofoffShorestructures,surfaceplatesonrunwayofairportsandfoundationsofhigh-risebuildingsandthelike.Itisextremelydifficulttoobtainanalyticalsolutiontarathickplatewithcomplicatedshapeorcomplicatedboundaryconditiononelasticfoundation.Inrecentyears,theboundaryelementmethod(BEM)hasbeensuccessl'ullyusedtoanalyzethebendingproblemofplatesoneverykindofelasticfoundation(Ref.[l,2.3]).Butthereareonlyfewreferences… 相似文献
4.
Hu Haichang 《Acta Mechanica Sinica》1992,8(2):127-135
A boundary integral representation of plane biharmonic function is established rigorously by the method of unanalytical continuation
in the present paper. In this representation there are two boundary functions and four constants which bear a one to one correspondence
to biharmonic functions. Therefore the set of boundary integral equations with indirect unknowns based on this representation
is equivalent to the original differential equation formulation. 相似文献
5.
IntroductionTheboundaryelementmethod(BEM)providesanattractivealternativefortheanalysisofengineeringproblems.Itsmainadvantagesareeconomicalandparticularlyconvenientforunboundeddomainandstressconcentrationproblems.Theboundaryintegralequation(BIE)isthe… 相似文献
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SOLVINGVIBRATIONPROBLEMOFTHINPLATESUSINGINTEGRALEQUATIONMETHOD¥(许明田,程德林)XuMingtian;ChengDelin(Department.ofMathematicsandPhysi... 相似文献
8.
This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method. 相似文献
9.
IntroductionIt’swell_knownthatthecomplicatedfundamentalsolution[1,2 ]forHelmholtzequationΔu(x) +k2 u(x) =0 (x∈Ω:boundedopenregioninR2 )isu (x,y) =-iH(2 )0 (k x-y ) 4,thusit’snotconvenientfornumericalcomputation .IfapplyingthesimplefundamentalsolutionofLaplaceequationu 0 (x ,y) =-ln|x-y|(2π) ,theexpressionforthesolutionofequationintheclosedregion Ωisc(y)u(y) + ∫Γu(x) u 0 (x,y) nx -u 0 (x ,y) u(x) n dsx =-k2∫Ωu(x)u 0 (x,y)dΩx.Astherightsideappearstheregionalintegrationinclu… 相似文献
10.
This paper studies the free bending vibration of elliptical column partialy submerged in water. It is the first time that we get an exact solution of the function of normal mode of vibretion of column-water couple system and a corresponding frequency equation denoted by limited order determinant. It points out that the effect of water is equivaient to an attached distributive mass. Therefore, the frequency with water is lower than that without water. 相似文献
11.
王左辉 《应用数学和力学(英文版)》1993,14(8):767-776
In this paper,the nonsingular fundamental solutions are obtained from Fourierseries under some given conditions.These solutions can be taken as the kernels ofintegral equation.So a new boundary element method is presented,with which allkinds of thin-plate bending problems can’be solved,even with complicated loadings andsinuous boundaries.The calculation is much simpler and more accurate. 相似文献
12.
Research on the companion solution for a thin plate in the meshless local boundary integral equation method 总被引:1,自引:1,他引:0
The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method ( GFEM ), boundary element method (BEM) and element free Galerkin method (EFGM), and is a truly meshless method possessing wide prospects in engineeringapplications. The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem. 相似文献
13.
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain. 相似文献
14.
弹性体的正则方程和加筋板的固有频率分析 总被引:8,自引:0,他引:8
应用弹性力学的Hamilton正则方程理论和其半解析法,为整体加筋板的固有频率分析提出了一种新颖的数学模型. 采用同一种平面元素离散板和加强筋,并分别建立板和加强筋的线性方程组. 考虑到板和加强筋连接界面上应力和位移的连续性,联立板和加强筋的方程得到全结构的方程组和求解固有频率的特征方程. 主要优越性表现为:结构的旋转惯性、剪切变形等都得到了考虑,且不限制结构的板厚度和加强筋的高度. 多个数值实例的收敛分析和结果证明了方法是可靠的. 该方法很容易被修改用来分析加筋壳、加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳问题. 相似文献
15.
Zhu Jiaming 《应用数学和力学(英文版)》1995,16(6):593-601
The analytical solution for the bending problem of the rectangular plates on an elastic foundation is investigated by using
the Stockes' transformation of a double variables function. The numerical results for the rectangular plates with free edges
on the elastic foundations under a concentrated force are given in the example.
First Received Dec. 14 1993 相似文献
16.
Leonid K. Antanovskii 《Meccanica》1991,26(2-3):59-65
In this paper planar viscous flows with a free boundary are further studied using the quasisteady approximation [1]. The introduction of the bianalytical stress-stream function provides an opportunity to adopt the theory of analytical functions. The mode of construction of the Fredholm boundary integral equations is here proposed through the explicit solutions of two Hilbert problems for holomorphic functions with the application of the conformal mappings. The stabiligy of the equilibrium of the annulus liquid layer is investigated by way of example.
Sommario Si prosegue lo studio di flussi piani viscosi con frontiera libera applicando l'approssimazione quasistazionaria [1]. L'introduzione della funzione stress-stream bianalitica consente l'uso della teoria delle funzioni olomorfe. La costruzione delle equazioni integrali di Fredholm al contorno proposta qui si basa sulla risoluzione esplicita di due problemi di Hilbert per funzioni analitiche mediante applicazione della tecnica delle trasformazioni conformi. Come esempio si studia la stabilità dell'equilibrio di uno strato liquido anulare.相似文献
17.
压电介质边界元法及奇异性处理 总被引:1,自引:0,他引:1
本文从压电材料的基本方程出发,利用功的互等原理推导了边界积分方程,并详细地讨论了边界元的计算步骤,利用等参变换,着重研究了在边界元计算中基本解的奇异性问题,对各种情况讨论了系数矩阵H和G的算法,并给出院具体的表达式,作为算例,选取了均匀薄板和开孔薄板PZY-4压电材料,计算结果表明,本文提出的边界元的计算格式和奇异性的处理方法相当有效。 相似文献
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19.
A scheme is developed for analysing the interaction between a foundation and a nonlinear rock and soil medium, in which the
foundation is considered as a linear elastic body and a typical boundary integral equation method (BIEM) is employed. On the
basis of taking the nonlinear properties of the medium into account, a perturbation BIEM is developed. The fundamental equations
for the nonlinear coupling analysis are formulated, and typical problems are solved and discussed by the present method. 相似文献
20.
Equivalent Boundary Integral Equations with indirect unknowns for thin elastic plate bending theory 总被引:4,自引:0,他引:4
Zhang Yao-ming Associate Professor Doctor Sun Huan-chun Yang Jia-xin 《应用数学和力学(英文版)》2000,21(11):1246-1255
Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent
to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and
is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect
unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.
Paper from SUN Huan-chun, Member of Editorial Commitee, AMM
Biography: ZHANG Yao-ming (1962-) 相似文献