On singular perturbation method of perturbed bifurcation problems

In this paper, the general mathematical principle is over-all explained and a new general technique is presented in order to calculate uniformly asymptotic expansions of solutions of the perturbed bifurcation problem (1.6) in the vicinity of y=0, λ=0,δ=0, by means of singular perturbation method. Simultaneously, Newton’s polygon^[4] is generalized. Finally, the calculating results of two examples are given.     

矩形薄板的屈曲状态*

本文根据薄板的广义变分原理,用有限元法对单向受压矩形板的屈曲状态进行了讨论,并用延续算法获得了在不同边界条件下的屈曲状态.     

Elastic instability of an orthotropic elliptic plate

On the basis of von Kármán equations and using the general bifurcation theory,theelastic instability of an orthotropic elliptic plate whose edge is subjected to a uniform planecompression is discussed.Following the well-known Liapunov-Schmidt process theexistance of bifurcation solution at a simple eigenvalue is shown and the asymptoticexpression is obtained by means of the perturbation expansion with a small parameter.Finally,by using the finite element method,the critical loads of the plate are computed andthe post-buckling behavior is analysed.And also the effect of material and geometric parameters on the stability is studied.     

BUCKLING AND POST-BUCKLING OF ANNULAR PLATES UNDER xNON-AXISYMMETRIC PLANE EDGE FORCES

On the basis of both the general theory[1,2]and the finite element method[4]ofperforated thin plates with large deflection,the buckling and post-buckling of annular platesunder non-axisymmetric plane edge forces are studied.     

环面薄膜的膨胀失稳

本文从有限弹性理论出发对超弹性薄膜轴对称大变形问题进行了一般的数学描述.基于本文所导出的基本方程,应用打靶法数值地分析了Mooney-Rivlin型类橡胶环面薄膜的大变形膨胀失稳问题.给出了上、下极限载荷和位移载荷曲线.     

正交各向异性椭圆板的弹性失稳

本文以von Kármán型方程为基础并利用一般分支理论讨论了正交各向异性椭圆板在面内边缘均布压力作用下的弹性失稳.利用Liapunov-Schmidt过程证明了单特征值处分支解的存在性并利用小摄动展开得到了分支解的渐近表达式.最后利用有限单元法计算了正交各向异性椭圆板的临界载荷并进行了板的过屈曲分析,还考察了材料和几何参数对稳定性的影响.     

关于弹性板弯曲变形的Reissner理论

本文根据不完全广义余能原理重新推导了Reissner方程,使应力函数ψ以拉格朗日乘子的方式从变分中自然引出,同时明确了Reissner方程的解的结构.在此基础上提出了一个简化理论,它只需求解一个类似于经典薄板理论的四阶方程,即可得到计及剪力对弯曲变形影响的令人满意的结果.     

VNONLINEAR STABILITY ANALYSIS OF A CLAMPED ROD CARRYING ELECTRIC CURRENT

I.Intr0ducti0nThestabilityanalysisofrodscarryingelectriccurrentsinamagneticfieldhasnoton1ytheimportanttheoreticalvaluebutalsothebackgroundofappIications.lfthecurrentintherodismoderate,wecanneglecttheselffieldeffectsproducedbythecurrentintherodandonlyconsi…     

超弹性矩形板单向拉伸时微孔的增长*

本文研究了含中心微孔的超弹性矩形板在单向拉伸时的有限变形和受力分析.为了考察微孔的存在对矩形板变形和应力的影响,将问题化成一个超弹性环形板的变形和受力分析,并用最小势能原理得到变分近似解.进行了数值计算,分析了微孔的增长情况.     

非线性粘性柱的稳定性和混沌运动

研究了受轴向周期力作用的各向同性简支柱的动力学稳定性。假定粘弹性材料满足Ｌｅａｄｅｒｍａｎ非线性本构关系。导出运动方程为非线性微分－积分方程,并利用Ｇａｌｅｒｋｉｎ方法简化为非线性微分－积分方程。应用平均法进行了稳定性分析,并用数值结果进行验证。数值结果还表明系统可能存在混沌运动。