Expansion of Multiple Integrals in Linear Forms

We prove general theorems on expansions of multiple integrals in linear forms in generalized polylogarithms with coefficients that are rational functions.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 683–706.Original Russian Text Copyright ©2005 by S. A. Zlobin.     

New Complexiton Solutions of （2＋1）-Dimensional Nizhnik-Novikov-Veselov Equations

In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.     

New Rational Form Solutions to Coupled Nonlinear Wave Equations

The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.     

????Timoshenko????????????

将理性有限元法引入到Timoshenko梁问题中,提出了一种理性Timoshenko梁单元,克服了 剪切锁死现象. 在推导控制方程时,与传统有限元方法采用Lagrange插值不同, 理性有限元法用Timoshenko梁弯曲问题的基本解逼近单元内部场. 运用该梁单元分析 Timoshenko梁时,无需缩减积分,就能避免剪切锁死,并且极大地提高了计算精度,说明 理性有限元法具有广泛的应用前景.     

结构动力重分析的子结构有理逼近

在基于子结构灵敏度综合的结构动力重分析方法的基础上,应用向量值函数有理逼近,提出了一种新的结构动力重分析方法。子结构方法的应用,有效减少了结构自由度数目,达到了减少计算量的目的。将向量值函数有理逼近应用于截断的Taylor级数,提高了计算精度,扩大了收敛范围,适用于结构作大修改的情形。数值算例表明,所提出的方法对结构参数发生大修改能够有效降低Taylor级数截断的误差,给出高精度的逼近结果。     

Rational finite element method for elastic bending of reissner plates

IntroductionAsawell-establishedandsophisticatednumericalanalysistechniqueforthedifferentialequahons,thefiniteelementmethodwasoriginatedindependentlybythedomesticandtheforeignmechanicalinvestigatorstheyyearsago.ItfoundforthefirsttimewideapplicationsintheelasticstfUctolproblemsandwiththedevelopmentofcomputerextendedinvaryingdegreestOalmostalltheengineeringdisciplinesandmanyscientificandtechnologicalfields.Thisleadstoadramaticbreakthroughforthecurrentcomputationalmathematics.Themathematicalbasis…     

Convenient formulæ for the drag on a prolate ellipsoid moving along its axis of symmetry perpendicular to a plane surface

The drag coefficients for a prolate ellipsoid moving along its axis of symmetry, in the creeping flow regime, either towards or away from a plane surface are calculated. The plane surface may have either a no-slip boundary condition, corresponding to a solid wall, or a perfect slip condition, corresponding to a free surface.First the analytical solutions are employed to obtain exact values for the full range of feasible particle–plane gaps. Next, simple exact formulæ for the asymptotes at small and large gaps are presented. Finally, some convenient approximate formulæ are obtained that may be used across the full range of gaps.