Instability of solution for a class of the third order nonlinear differential equation

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A SUPPLEMENTARY STUDY OF ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE－STRESS CRACK－TIP（I）

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Generalized variational principles for linear elastic materials with voids

In this paper, the idea of variational principles of linear elastic theory is used to establish generalized variational principles for linear elastic materials with voids. The fundamental equations of linear elastic materials with voids used have already been established in Ref. [5].     

有限弹塑性变形的三维组集式本构模型

本文将文[1]中提出的三维组集式弹塑性本构模型推广应用于有限变形分析,导出了全量型和增量型本构关系在初始构形上的拉格朗日(Total Lagrange)形式和瞬时构形上的拉格朗日(Updated Lagrange)形式。文中对晶体单轴拉伸中的宏观剪切带进行了分析。预测结果与实验吻合。从而说明这种本构模型能够模拟有限变形中的几何非线性效应和晶体材料塑性变形中的宏观力学行为。     

A polynomial method for solving the problems for lateral instability of cantilever plates

The present article researches the problems of the lateral instability of cantilever rectangular plates under a concentrated force or a uniformly distributed load respectively.We select the polynomial(2.1)instead of the cosecant function in Ref.[1]as the flexural functions.The minimum critical load obtained here is more exact than the results obtained in Ref.[1]     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITSAPPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

InPartl,anonlineartheoryformultilayersand`"ichshellsundergoingsmallstrainsandmoderaterotatiol1sisgiven-inwhichtranst'ersesheardeformationisconsidered.Thesimplifiedtheoryfortheshellsundergoingmoderateormoderate/smallrotationsisalsoPresented.Theexpressionsi…     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

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NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

A note about Oden’s constitutive variational principle

A remark about some unreasoning things of Oden’s constitutive variationalprinciple described in Ref. [1] is given in this paper. According to Oden’s idea, the other two constitutive variational principles, which are complementary to one another, are developed. An example is performed to demonstrate the application of the constitutive variational principles.     

数值求解Navier—Stokes方程的迎风紧致差分格式

从迎风紧致逼近^[1]出发,提出数值求解可压Navier-Stokes方程的一种高精度的数值方法。利用Steger-Warming的通量分裂技术^[2]将守恒型方程中的流通向量分裂成两部分,在此基础上据风向构造逼近于无粘项的三阶迎风紧致有限差分格式。对方程中的粘性部分采用通常的二阶差分逼近。所建立的差分格式被用来数值求解了三维粘性绕流问题。     

起捞大型物体的水动力计算

提升坠入海底或放置于海底的物体是海洋工程中经常出现的问题。在假设沙质海底具有渗透性但不发生变形的条件下,C.C.Mei等提出了二维物体提升的理论模型以及提升规律的计算公式。本文在同样假设下提出了提升三维物体的计算公式。并且证明,本文所提公式包含了C.C.Mei等的结果。用本文提供的方法可以估计二维计算公式的适用范围。     

The motion of a sphere with weak nutation on a rough horizontal plane

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Refined differential equations of deflections in axial symmetrical bending problems of spherical shell and their singular perturbation solutions

This paper deals with the research of accuracy of differential equations of deflections.The basic idea is as follows.Firstly,considering the boundary effect the meridianmidsurface displacement u=0,thus we derive the deflection differential equations;secondly we accurately prove that by use of the deflection differential equations or theoriginal differential equations the same inner forces solutions are obtained;finally,weaccurately prove that considering the boundary effect the meridian surface displacementu=0 is an exact solution.In this paper we give the singular perturbation solution of thedeflection differential equations.Finally we check the equilibrium condition and prove theinner forces solved by perturbation method and the outer load are fully equilibrated.Itshows that perturbation solution is accurate.On the other hand,it shows again that thedeflection differential equation is an exact equation.The features of the new differential equations are as follows:1.The accuracies of the new differentia     

大转动曲边柱壳非线性3-D动力学建模及分析

对曲边柱壳受轴向非均匀内压作用下的大转动几何非线性3-D动力学行为进行了研究.基于Nayfeh and Pai[1]非线性壳体理论,给出了考虑几何非线性的3-D混合型（含内力与位移）动力学模型.为了克服该强非线性模型难以求解的问题,依据分析获得的结构静动态变形关系,采用Lagrange方程推导建立了基于结构静态解的曲边柱壳多自由度3-D动力学方程,并对其进行了线性化与降阶处理,结合差分法获得了一套高效的求解算法.与LS-DYNA有限元结果的吻合,验证了本文方法的正确性.最后分析了单元数和计算时间步分别对有限元模型和本文方法的影响,发现求解精度随着计算时间步的减小不断提高直至趋于稳定.同时对采用本文方法获得的曲边柱壳动态变形模式的分析表明:结构动态响应与其所受内压载荷沿轴向的分布形式关系紧密,可以通过改变或者设计内压轴向分布形式来影响以及控制结构的动态变形模式,从而应用于曲边柱壳结构设计及优化的工程实际中.     

轴对称激励下力变厚度圆柱壳与液体的耦联振动

利用文献[1]的结果，研究了液体中的变厚度圆柱壳在轴对称激励力下的强迫振动问题，从基本微分方程出发，导出了问题的级数解，最后通过实例计算说明了该方法的应用。     

关于三维光弹性几个基本问题的讨论

本文讨论下面几个问题:三维光弹性基本方程;特征量(包括特征方向及特征位相差)与应力分量之间的关系;光弹性基本方程的解。这些问题都是已解决的问题,本文的目的,一是改进解决方法使之简易直接,再是对于改进方法中所依据的物理概念使之更加明确,这样就使这些复杂问题变得易于接受。     

Fibre-reinforced composites with fibre-bending stiffness under azimuthal shear – Comparison of simulation results with analytical solutions

In Ref. [1], Spencer and Soldatos proposed an enhanced modelling approach for fibre-reinforced composites which accounts for the fibre-bending stiffness in addition to the directional dependency induced by the fibres. Although analytical solutions for simple geometries have been derived over the past years, often subject to specific assumptions such as small deformation kinematics, the application to more general and non-academic boundary value problems is desirable. Motivated by the latter, the numerical solution of the general system of partial differential equations by means of a multi-field finite element approach is proposed in Ref. [2] and the principal model properties are studied for a specific form of the elastic energy potential. In the present contribution a comparison of the numerical solution by means of the multi-field finite element approach against the analytical solution is presented for the azimuthal shear deformation of a tube-like structure. To this end, the general deformation pattern and especially the distribution of the stress and couple stress tensor are taken into account. We find that, although the analytical solution is derived subject to the assumption of small deformations, whereas the numerical solution is based on the finite strain counterpart of the theory, the simulation results are quasi identical, which verifies the numerical framework proposed.     

Is the suppression of short waves by a swell a three-dimensional effect?

We consider the phenomenon of suppression of short waves by a long wave, observed by Mitsuyasu in 1966. The recently proposed [1] essentially 3-D explanation of this phenomenon is reviewed and compared with more traditional 2-D explanations. Several physical implications of this 3-D explanation are suggested and the experimental verification is discussed.     

Supplementary study on anisotropic plastic stress fields at a stationary plane-stress crack-tip

The results in Ref.[1]are not suitable for the cases of a≥2 .For this reason,we use the method in Ref.[1]to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of a=2 and a>2 .As an example,we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of modeⅠand modeⅡplane-stress cracks for the case of a=2.     

A Variational Approach for the 2-Dimensional Semi-Geostrophic Shallow Water Equations

Existence of weak solutions to the 3-D semi-geostrophic equations with rigid boundaries was proved by Benamou and Brenier [3], using Monge transport theory. This paper extends the results to a free surface boundary condition, which is more physically appropriate. This extension is at present for the 2-D shallow water case only. In addition, we establish stronger time regularity than was possible in [3]. Accepted October 9, 2000?Published online February 14, 2001