QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

IntroductionIn applications, it is commonly considered that the phenomena of cavity formation,growth and run-through of adjacent cavities occur in materials as precursors to failure. Thesephenomena are mainly due to instability of materials. On the other …     

普叉普适开折的若干动力学性质

从动力学观点出发讨论了具缺陷的音叉问题中出现的模态跃迁现象，解释了板壳等结构由于极值性失稳而引起模态跳跃的动力学机理，最后给出了数值模拟。     

UPWIND LOCAL DIFFERENTIAL QUADRATURE METHOD FOR SOLVING COUPLED VISCOUS FLOW AND HEAT TRANSFER EQUATIONS

The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.     

一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究

研究了一类不可压的广义neo-Hookean材料组成的球体的空穴分岔问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压的neo-Hookean材料,得到了球体内部空穴生成的条件．与均匀各向同性的neo-Hookean球体的情况相比,证明了当摄动参数属于某些区域时,从平凡解局部向左分岔的空穴分岔解上存在一个二次转向分岔点,空穴生成时的临界载荷会比无摄动的材料的临界载荷小．用奇点理论证明了,空穴分岔方程在临界点附近等价于具有单边约束条件的正规形．用最小势能原理分别讨论了空穴分岔解的稳定性和实际稳定的平衡状态．     

Cavity formation at the center of a sphere composed of two compressible hyper-elastic materials

IntroductionHorgan[1] reviewedthecavitatedbifurcationproblemforhyper_elasticmaterials,includinginhomogeneousandanisotropicmaterialsaswellashomogeneousandisotropicmaterials .Forincompressiblematerials,HorganandPence[2 ,3 ] examinedtheeffectofmaterialinhomogeneityontheformationandgrowthofvoidandobtainedananalyticsolutionofthecavitatedbifurcationproblemforasolidspherecomposedoftwoneo_Hookeanmaterials.Thebifurcationmayoccurnotonlytotherightbutalsototheleftforthecomposedsphere .Thestabilitiesofth…     

线性两点边值问题的迭加原理与不变嵌入方法(Ⅰ)

众所周知,常微分方程达值问题的初值方法有两大类。一类是打靶法,一类是不变嵌入法。对线性问题来讲,打靶法是先用求初值问题的数值方法计算出非齐次问题的一个特解和齐次问题的n个线性无关解,然后再进行适当线性组合的一种迭加法。当方程组的雅可比矩阵特征值有绝对值较大的正、负实部时,直接用打靶法将会遇到数值上的     

一类高阶奇点位置确定的数值方法

1.引言 设X是实Hilbert空间,D是X中的开集.F:D×R→X是二次连续可微的非线性算子,R是实数域.考察算子方程: F(x,λ)=0(x,λ)∈D×R.(1.1)如果在(1.1)的解(x_0,λ_0)处F关于x的Frechet导数F_x(x_0,λ_0)是X到X上的线性同胚,则称(x_0,λ_0)是(1.1)的正常解.否则,(1.1)的解称为奇点.对于由正常解组成的连续     

Dynamical Stability of Viscoelastic Column with Fractional Derivative Constitutive Relation

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非线性粘弹性Timoshenko梁动力学行为的分布

本文讨论了有限变形粘弹性Timoshenko梁的动力学行为。首先由Timoshenko梁的理论和分数导数型本构关系给出了梁的控制方程。其次为了便于求解,采用Galerkin方法对系统进行了简化,并比较了1阶和2阶截断系统的动力学性质,它们具有相同的定性性质,说明Galerkin方法的合理性。给出了求解包含分数积分的积分－微分方程的一种新方法,以便求解系统的长时间的解。综合利用非线性动力系统中的经典方法,揭示了梁在有限变形情况下丰富的动力学行为,并分别考察了载荷参数的材料参数对结构的动力学行为的影响。     

具有分数导数本构关系的非线性粘弹性Timoshenko梁动力学行为分析

本文利用分数导数型本构关系建立了在有限变形情况下Timoshenko梁的控制方程并利用Galerkin方法进行简化。然后利用一种存储部分历史数据的分数积分的计算方法对梁的控制方程进行求解。考察了载荷参数和分数导数参数对梁振动的影响,并采用非线性动力学中的各种数值方法,如时程曲线、功率谱、相图、Poincare截面等,揭示了非线性粘弹性Timoshenko梁丰富的动力学行为。