Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suit- able for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.     

Plane elasticity in sectorial domain and the Hamiltonian system

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Rethinking to finite difference time-step integrations

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HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF MATERIALS(Ⅲ)—FLEXURE AND FREE VIBRATION OF PLATES

The methodology presented in PartⅠis employed to deal with flexure and freevibration of anisotropic plates.     

Finite element analysis for consolidation in interaction between structure and saturated soil foundation

The consolidation analysis of interaction between structure and saturated soil foundation is discussed. With the use of substructure technique, the structure is condensed onto the interface of the soil, and then the consolidation governing equations to describe the interaction between soil and structure are derived, The solution with non-iterative algorithm is proposed in this paper. The pressure Master-Slave relation method is used to deal with the non-permeability conditions on soil boundaries. A numerical example is illustrated. Based on this paper, the interactive consolidation analysis between large structure and soil has been more practical.     

On the computation of the main eigen-pairs of the continuous-time linear quadratic control problem

The degeneration of the eigenvalue equation of the discrete-time linear quadraticcontrol problem to the continuous-time one when△t→0?is given first.When thecontinuous-time n-dimensional eigenvalue equation,which has all the eigenvalues located inthe left half plane,has been reduced from the original2n-dimensional one,the present paperproposes that several of the eigenvalues nearest to the imaginary axis be obtained by thematrix transformation A_e=e~A.All the eigenvalues of A_e are in the unit circle,with theeigenvectors unchanged and the original eigenvaiues can be obtained by a logarithmoperation.And several of the eigenvalues of A_e nearest to the unit circle can be calculated bythe dual subspace iteration method.     

短波近似的保辛算法

WKBJ短波近似是最常用的有效求解方法之一。保守体系的微分方程可用Hamilton体系的方法描述,其特点是保辛。保辛给出保守体系结构最重要的特性。但WKBJ短波近似却未曾考虑保辛的问题。WKBJ近似可用自变量坐标变换,然后再给出其保辛摄动。数值例题展示了本文变换保辛算法的有效性。     

应用四边形十六自由度平板壳单元DKQ16分析板壳结构的稳定性

应用新近开发的四边形十六自由度离散Kirchhoff平板壳单元DKQ16,分析了板壳结构的线性屈曲问题,建立了相应的几何刚度矩阵．通过对几个典型算例的计算与比较,说明了DKQ16单元在板壳结构的稳定性中也有良好的精度．     

基于膜板比拟理论的一个新的四边形薄板单元

平面弹性与板弯曲的相似理论为构造薄板单元提供了一条有效的新途径。由于避开了c1连续性的困难,使得薄板单元的构造变得简单。更为深入地讨论了该相似性理论的应用,并构造了一个新的四节点十六自由度薄板单元。数值结果表明,该单元能通过分片试验,具有良好的收敛性和精度。     

等式约束非线性控制系统的时程精细计算

针对等式约束非线性最优控制问题,通过一阶Taylor级数展开,得到线性化的动力学方程,进而在方程原变量的基础上,引入对偶向量(Lagrange乘子向量),将动力学方程从Lagrange体系引入到了Hamilton体系,在全状态下,从一个新的角度对等式约束非线性控制问题进行了描述,进一步基于时程精细积分理论,对其方程进行了有效的精细求解,并通过算例说明了文中方法的有效性。