圆柱形含能材料热爆炸临界参数计算

根据变分原理,计算了各表面散热条件不同的有限长圆柱含能材料的热爆炸临界参数和临界温度,研究了长径比对热爆炸临界参数和临界温度的影响;计算了各表面散热条件不同的有限长圆柱材料的热爆炸临界参数,得出了Biot数和对热爆炸临界参数和临界温度的作用。计算表明,用变分的方法将求解热爆炸导热方程问题转化为对一个特征值方程求解,求解过程要简单得多,且精度高、速度快。     

热爆炸临界状态的变分特性

本文利用热爆炸的临界状态是其定态方程分岔点的定义,给出了热爆炸临界参数的一个变分原理。泛函J（,）的极大值恰好是点火临界参数i;其极小值则是熄火临界参数e;其鞍点值是转点参数tr。     

正交异性圆柱壳受局部外压的临界力

以往计算正交异性圆柱壳的临界力,多从微分方程组出发,编写较长的计算程序,化费很多机时才能得到结果。本文应用Cheng提出的准确四阶控制方程,把问题归化为解无限行列式的特征值。对于全部受外压,周向波数较多的壳导出了一个临界力公式。1.部分长度承受均布外压壳的临界力(图1) 文献[2]建立了正交异性圆柱壳准确的控制方程(本文使用的符号与[2]相同)     

一种滑动轴承非线性油膜力变分近似计算方法

基于变分原理，在π油膜假设条件下，利用无限长轴承的压力解，给出了滑动轴承非线性油膜力的近似表达式同时在实际轴承参数条件下，对比分析了计算结果及数值解，发现该计算结果具有较高精度．     

含有初始凹陷圆柱壳稳定承载能力的实验研究与数值计算

对含有初始轴对称凹陷的圆柱壳在轴向载荷作用下的稳定承载能力进行了研究。首先,通过实验研究,得到了不同凹陷参数及不同壳长条件下的临界载荷。同时,不考虑凹陷成形过程,仅把凹陷部分当做结构的不规则变化时,对含有凹陷圆柱壳建立三维有限元模型进行稳定性分析。在分析中考虑了初始缺陷(圆柱壳成形加工中的不平直度、椭圆度、初始弯曲等因素引起)幅值f0=0.1t和f0=0.2t(t为壳体壁厚),得到了不同凹陷参数及不同壳长的临界载荷。结果表明:含有凹陷圆柱壳稳定承载能力对初始缺陷不太敏感,即:初始缺陷与凹陷相比,对稳定承载能力的影响极小。数值计算结果与实验结果吻合较好,共同给出了含有初始轴对称凹陷圆柱壳的承载能力随凹陷幅值、长度及圆柱壳长度的变化而改变的规律。     

静力预加载结构冲击屈曲的突变模型

基于突变理论给出静力预加载弹性结构冲击屈曲的准则,并将其用于处理Budian-sky-Hutchinson简单力学模型的冲击屈曲分析和受扭圆柱壳的冲击扭转屈曲分析,给出了临界载荷的求解公式。     

夹层扁球壳的非线性稳定性

基于Reissner假设和变分原理,给出夹层扁球壳在均布压力作用下的大挠度方程,采用修正迭代法求得了夹层扁球壳非线性稳定问题的解析解,得到两类边界条件下临界屈曲载荷的表达式,讨论了几何参数和物理参数对临界屈曲载荷的影响     

非保守稳定问题的有限元法

本文利用Leipholz得到的变分原理,给出一些非保守问题的有限元解。并得到临界荷载。     

复杂载荷作用下圆柱壳的弹塑性动力屈曲研究

对复杂载荷作用下圆柱壳的弹塑性动力屈曲问题进行了研究。基于Hamilton变分原理导出圆柱壳的运动方程 ,本构关系采用增量理论 ,借助增量数值算法求解动力方程组。结果表明 ,均匀径向外压对圆柱壳的轴向冲击的过程或冲击性态有较大的影响 ,并讨论了径向压力与轴向冲击载荷的幅值对结构临界动力屈曲载荷和临界动力失效载荷的影响。     

弹性理论中的临界变分及消除方法

临界变分现象是拉氏乘子法的固有特性，钱伟长应用高阶拉氏乘子消除了临界变分现象。本文将提出一种新的方法－凑合反推法，这种方法摒充了拉氏乘子法，把拉氏乘子所在的项目一个待定函数Ｆ代替。这样构成的泛函，作者称之为试泛函。而待定函数Ｆ的识别类似于拉氏乘子的识别。通过该法可以方便地构造出各种多变量广义变分原理，并且可以消除临界变分现象。     

BCKLUND TRANSFORMATION, NONLINEAR SUPERPOSITION FORMULAE AND INFINITE CONSERVED LAWS OF BENJAMIN EQUATION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＲｅｆ.[1 ]ｐｏｉｎｔｅｄｏｕｔｔｈａｔｓｏｍｅｔｙｐｉｃａｌｎｏｎｌｉｎｅａｒｗａｖｅｅｑｕａｔｉｏｎｓｐｏｓｓｅｓｓｅｄｆｉｖｅｃｏｍｍｏｎｆａｃｔｏｒｓ,ｗｈｉｃｈｗｅｒｅｗｉｔｈｓｏｌｉｔａｒｙｓｏｌｕｔｉｏｎｓ,ｉｎｆｉｎｉｔｅｃｏｎｓｅｒｖｅｄｌａｗｓ,ｅｘａｃｔｌｙｓｏｌｖａｂｌｅｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎｓｂｙｔｈｅｕｓｅｏｆｉｎｖｅｒｓｅｓｃａｔｔｅｒｉｎｇｍｅｔｈｏｄ .Ｂ ｃｋｌｕｎｄｔｒａｎｓｆｏｒｍａｔｉｏｎｓ,ｂｅｉｎｇｒｅｄｕｃｅｄｔｏ…     

Practical computation of normal forms of?the?Bogdanov�CTakens bifurcation

In this paper, we study the Bogdanov?CTakens (double-zero) bifurcations for any autonomous ODEs system, and derive simple computational formulae for both critical normal forms and generic norm forms. These formulae involve only coefficients of the Taylor expansions of its right-hand sides at the equilibrium. They are equally suitable for both numerical and symbolic evaluations and conveniently allow us to classify codimension 2 Bogdanov?CTakens bifurcations. Furthermore, we can use them to check whether there exist the original parameters such that a system presents the Bogdanov?CTakens bifurcation, and compute the corresponding bifurcation curves with high precision. Two known models are used as test examples to demonstrate the advantages of this method.     

Integral transform analysis of natural convection in porous enclosures

A hybrid numerical-analytical solution for steady-state natural convection in a porous cavity is proposed, based on application of the ideas in the generalized integral transform technique. The integral transformation process reduces the original coupled partial differential equations, for temperature and stream function, into an infinite system of non-linear ordinary differential equations for the transformed potentials, which is adaptively truncated and numerically solved through well-established algorithms. The approach is applied to a vertical rectangular enclosure subjected to uniform internal heat generation. The convergence characteristics of the explicit inversion formulae are illustrated and critical comparisons with previously reported purely numerical solutions are performed.     

Remarks of some problems for rectangular thin plates with free edges on elastic foundations

For the bending,stability and vibrations of rectangular thin plates with free edges onelastic foundations,in this paper we give a flexural function which exactly satisfies not onlyall the boundary conditions on free edges but also the conditions at free corner points.Applying energy variation principle,we give equations defining parameters in flexuralfunction,stability equation,frequency equation,and general formulae of minimum criticalforce and minimum eigenfrequency as well.     

Waves in Nonlocal Elastic Solid with Voids

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter (\(\tau \)) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.     

On the Solution of an Elliptical Inhomogeneity in Plane Elasticity by the Equivalent Inclusion Method

Stress analysis of an elliptical inhomogeneity in an infinite isotropic elastic plane is a classical elasticity problem, which is usually solved by means of the complex variable formulation. In this work, we demonstrate that an alternative method of solution for such a problem, via the equivalent inclusion method, may be more convenient and straightforward without recourse to complex potentials or curvilinear coordinates. The explicit analytical solution can be derived through simple algebraic manipulation, although the longitudinal eigenstrain component should be handled with care in the case of plane strain. Since the exterior Eshelby tensor for an elliptical inclusion is available in closed-form, the present study provides a full field stress solution expressed in Cartesian coordinates. Furthermore, the in-plane stress components are represented in terms of Dundurs’ parameters. The solution methodology and the convenient formulae of the stress concentration may be of practical use to the engineers in developing benchmarks for design evaluation.     

Theoretical solution for the cross-flow heat exchanger

The theory of the cross-flow heat exchanger first was treated by Nußelt [1, 2] on the base of heat balances for the two interacting fluids over an exchanging area element. This leads to a partial differential equation. But the solution was an infinite row which could not be expressed in a compact formula. In this paper it will be shown that a compact formula for the infinite row is possible. All temperatures of the interacting fluids, for example the local fluid temperatures and the mean outlet temperatures as well as the local temperature difference and the mean temperature difference over the complete exchanger are now being available in simple formulae which have the form of an infinite sum. The summation has to be stopped at a finite value with a negligible deviation. As all variables in the formulae are dimensionless, normalized diagrams are developed which are generally valid and give a good overview over a wide range of exchanger conditions.     

BACKLUND TRANSFORMATION, NONLINEAR SUPERPOSITION FORMULAE AND INFINITE CONSERVED LAWS OF BENJAMIN EQUATION

Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.     

Bäcklund Transformation, Nonlinear Superposition Formulae and Infinite Conserved Laws of Benjamin Equation

Bäcklund transformation, exact solitary wave solutions, nonlinear supperposition formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.     

Singular perturbation analysis of the buckling of circular cylindrical shells

This paper deals with the buckling of thin cylindrical shells with very large Batdorf parameters under external pressure. We first perform a simplified analysis from which we obtain explicit formulae for the critical load. An asymptotic analysis is carried out with a view to determining the effects of the boundary conditions on the critical loads and buckling shapes. The inverse of the Batdorf parameter is the convenient small parameter of the analysis. Among the whole set of boundary conditions, the axial boundary conditions are found to be have crucially important at the first order. This analysis also shows the existence of boundary layers in which the remaining boundary conditions are only significant at the second order, at the very most.