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1.
In this paper, a boundary feedback system of a class of non-uniform undamped Timoshenko beam with both ends free is considered. A linearized three-level difference scheme for the Timoshenko beam equations is derived by the method of reduction of order on uniform meshes. The unique solvability, unconditional stability and convergence of the difference scheme are proved by the discrete energy method. The convergence order in maximum norm is of order two in both space and time. The validity of this theoretical analysis is verified experimentally. 相似文献
2.
Fule Li Kaimei Huang 《高等学校计算数学学报(英文版)》2007,16(3):233-252
In this paper,the numerical approximation of a Timoshenko beam with bound- ary feedback is considered.We derived a linearized three-level difference scheme on uniform meshes by the method of reduction of order for a Timoshenko beam with boundary feedback.It is proved that the scheme is uniquely solvable,unconditionally stable and second order convergent in L_∞norm by using the discrete energy method. A numerical example is presented to verify the theoretical results. 相似文献
3.
G. W. Stewart 《BIT Numerical Mathematics》1980,20(4):526-528
King and Kioustelidis independently proposed a derivative free scheme that permits root finding methods, such as the secant method to preserve high order convergence when the root in question is multiple. In this note it is shown that the scheme can fail to achieve the maximum accuracy that is attainable at a fixed precision of computation.This work was supported in part by the Office of Naval Research under contract No. N00014-76-C-0391. 相似文献
4.
The method of fractional steps for conservation laws 总被引:1,自引:1,他引:0
Summary The stability, accuracy, and convergence of the basic fractional step algorithms are analyzed when these algorithms are used to compute discontinuous solutions of scalar conservation laws. In particular, it is proved that both first order splitting and Strang splitting algorithms always converge to the unique weak solution satisfying the entropy condition. Examples of discontinuous solutions are presented where both Strang-type splitting algorithms are only first order accurate but one of the standard first order algorithms is infinite order accurate. Various aspects of the accuracy, convergence, and correct entropy production are also studied when each split step is discretized via monotone schemes, Lax-Wendroff schemes, and the Glimm scheme.Partially supported by an Alfred Sloan Foundation fellowship and N.S.F. grant MCS-76-10227Sponsored by US Army under contract No. DAA 629-75-0-0024 相似文献
5.
S. I. A. Tirmizi 《Applied Mathematics Letters》1988,1(4):399-402
A fourth-order accurate finite difference method is developed for a class of fourth order nonlinear two-point boundary value problems. The method leads to a pentadiagonal scheme in the linear cases, which often arise in the beam deflection theory. The convergence of the method is tested numerically on examples from the literature. 相似文献
6.
A second order accurate difference scheme for the heat equation with concentrated capacity 总被引:5,自引:0,他引:5
Summary. A numerical solution to the one-dimensional heat equation with concentrated capacity is considered. A second-order accurate difference scheme is derived by the method of reduction of order on non-uniform meshes. The solvability, stability and second order L convergence are proved. A numerical example demonstrates the theoretical results.Mathematics Subject Classification (2000): Primary 65M06, 65M12, 65M15The contract grant sponsor: National Natural Science Foundation of CHINA; The contract grant number:19801007 相似文献
7.
A study on the free vibration analysis of Timoshenko beams is presented here. In order to determine natural frequencies of beams, a thick beam element is developed by using isogeometric approach based on Timoshenko beam theory which allows the transverse shear deformation and rotatory inertia effect. Three refinement schemes such as h-, p- and k-refinement are used in the analysis and the identification of shear locking is also conducted by using numerical examples. From numerical results, the present element can produce very accurate values of natural frequencies and the mode shapes due to exact definition of the geometry. With higher order basis functions, there is no shear locking phenomenon in very thin beam situations. Finally, the benchmark tests described in this study are provided as future reference solutions for Timoshenko beam vibration problem. 相似文献
8.
Zhi‐zhong Sun Lei Zhao Fu‐Le Li 《Numerical Methods for Partial Differential Equations》2007,23(1):1-37
In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that each rod is fixed at one end and is free to expand or contact at the other end. A finite difference scheme is derived by the method of reduction of order on nonuniform mesh. The unique solvability, unconditional stability, and convergence of the difference scheme are proved. The convergence order is of order two in both time and space. The convergence of iterative algorithm for the difference scheme are also discussed. A numerical example is presented to demonstrate the theoretical results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
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11.
Zhonghua Qiao Zhi‐zhong Sun Zhengru Zhang 《Numerical Methods for Partial Differential Equations》2012,28(6):1893-1915
The numerical simulation of the dynamics of the molecular beam epitaxy (MBE) growth is considered in this article. The governing equation is a nonlinear evolutionary equation that is of linear fourth order derivative term and nonlinear second order derivative term in space. The main purpose of this work is to construct and analyze two linearized finite difference schemes for solving the MBE model. The linearized backward Euler difference scheme and the linearized Crank‐Nicolson difference scheme are derived. The unique solvability, unconditional stability and convergence are proved. The linearized Euler scheme is convergent with the convergence order of O(τ + h2) and linearized Crank‐Nicolson scheme is convergent with the convergence order of O(τ2 + h2) in discrete L2‐norm, respectively. Numerical stability with respect to the initial conditions is also obtained for both schemes. Numerical experiments are carried out to demonstrate the theoretical analysis. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
12.
A consistent flexibility matrix is presented for a large displacement equilibrium-based Timoshenko beam–column element. This development is an improvement and extension to Neuenhofer–Filippou [1] (1998. ASCE J. Struct. Eng. 124, 704–711) for geometrically nonlinear Euler–Bernoulli force-based beam element. In order to find weak form compatibility and strong form equilibrium equations of the beam, the Hellinger–Reissner potential is expressed. During the formulation process, an extended displacement interpolation technique named curvature/shearing based displacement interpolation (CSBDI) is proposed for the strain–displacement relationship. Finally, the extended CSBDI technique is validated for geometric nonlinear examples and accuracy of the method is investigated concluding improved convergence rates with respect to the general finite element formulation. Also it is seen that the use of force based formulation removes shear locking effects. The results demonstrate considerable accuracy even in presence of high axial loading in comparison with the displacement based approach. 相似文献
13.
A finite difference scheme for solving the Timoshenko beam equations with boundary feedback 总被引:2,自引:0,他引:2
In this study, we derive a finite difference for a Timoshenko beam with boundary feedback by the method of reduction of order on uniform meshes. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable and second order convergent in L∞ norm. Numerical results demonstrate the theoretical results. 相似文献
14.
As a promising strategy to adjust the order in the variable-order BDF algorithm, a time filtered backward Euler scheme is investigated for the molecular beam
epitaxial equation with slope selection. The temporal second-order convergence in
the $L^2$ norm is established under a convergence-solvability-stability (CSS)-consistent
time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order to that for solvability and
stability (in certain norms) as the small interface parameter $ε → 0^+.$ Similar to the
backward Euler scheme, the time filtered backward Euler scheme preserves some
physical properties of the original problem at the discrete levels, including the volume conservation, the energy dissipation law and $L^2$ norm boundedness. Numerical
tests are included to support the theoretical results. 相似文献
15.
李福乐 《数学的实践与认识》2011,41(12)
对一类半线性变系数抛物型方程初边值问题建立了紧差分格式,用能量分析方法证明了差分格式解的存在唯一性、关于初值的无条件稳定性和在L_∞范数下阶数为O(τ~2+h~4)的收敛性,最后给出的数值算例验证了理论结果. 相似文献
16.
This work deals with a study of the vibrational properties of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs) under the actions of moving load. Timoshenko and Euler-Bernoulli beam theories are used to evaluate dynamic characteristics of the beam. The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The primary contribution of the present work deals with the global elastic properties of nano-structured composite beams. The system of equations of motion is derived by using Hamilton’s principle under the assumptions of the Timoshenko beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. In order to evaluate time response of the system, Newmark method is also used. Numerical results are presented in both tabular and graphical forms to figure out the effects of various material distributions, carbon nanotube orientations, velocity of the moving load, shear deformation, slenderness ratios and boundary conditions on the dynamic characteristics of the beam. The results show that the above mentioned effects play very important role on the dynamic behavior of the beam and it is believed that new results are presented for dynamics of FG nano-structure beams under moving loads which are of interest to the scientific and engineering community in the area of FGM nano-structures. 相似文献
17.
1.IntroductionTheTimoshenkobeammodelisgivenbywherethebeamisconsidereddamped,drepresentsthebeamthicknessandI~[0,1].000istherotationofverticalfibersinthebeamandw(x)istheverticaldisplacementofthebeam'scenterline(underaverticalloadgivenbyg(x)).Analogoust... 相似文献
18.
Qing-xuYan Hui-chaoZou De-xingFeng 《应用数学学报(英文版)》2003,19(2):239-246
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control actiondecays exponentially or in negative power of time t as t→∞. 相似文献
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20.
This paper studies the stress and displacement distributions of continuously varying thickness multi-span beams simply supported at two ends and under static loads. The intermediate supports of the beam may be elastic and/or rigid in one or two directions. On the basis of the two-dimensional plane elasticity theory, the general solution of stress function, which exactly satisfies the governing differential equations and the simply supported boundary conditions, is deduced. In the present analysis, the reaction forces of the intermediate supports are regarded as the unknown external forces acting on the lower surface of the beam under consideration. The unknown coefficients in the solutions are determined by using the Fourier sinusoidal series expansions to the boundary conditions on the upper and lower surfaces of the beam and using the linear relations between reaction forces and displacements of the beam at intermediate supports. The solution obtained is exact and excellent convergence has been confirmed. Comparing the numerical results obtained from the proposed method to those obtained from the Euler beam theory, the Timoshenko beam theory and those obtained from the commercial finite element software ANSYS, high accuracy of the present method is demonstrated. 相似文献