The Method of Multiple Scales Applied to the Nonlinear Stability Problem of a Truncated Shallow Spherical Shell of Variable Thickness with the Large Geometrical Parameter

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关于大几何参数的开顶扁球壳屈曲问题的奇摄动*

本文利用修正多重尺度法研究了大几何参数的具有刚性中心的边缘铰接的开顶扁球壳,在复合载荷作用下的非线性稳定问题。求得了扁壳几何参数h值较大时,本问题的一致有效的渐近解。     

Singular perturbation solutions of the nonlinear stability of a truncated shallow shperical shell under linear distributed loads along the interior edge

Using a singular perturbation method,the nonlinear stability of a truncated shallow,spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper.When the geometrical parameter k is large,the uniformly valid asymptotic solutions are obtained.     

多重尺度法应用于变厚度开顶扁球壳在复合载荷下的非线性稳定问题

利用改进多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳,在复合载荷作用下的非线性稳定问题,求得了扁壳几何参数k值较大时,本问题的一致有效的渐近解,并进行了余项误差估计。     

大几何参数的变厚度开顶扁薄壳的非线性屈曲问题的奇摄动解

该文利用修正多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳，在均布载荷作用下的非线性稳定问题．求得了扁壳几何参数k值较大时，本问题的一致有效的渐进解，并进行了余项误差估计．     

Singular perturbation of nonlinear vector boundary value problem

In this paper we study the perturbed boundary value problem of the form dx/dt=f(x,y,t;ε), εdy/dt=g(x,y,t;ε), a_1(ε)x(0,ε)+a_2(ε)y(0,ε)=a(ε) b_1(ε)x(1,ε)+εb_2(ε)y(1,ε)=β(ε)in whichx,f,β∈E~m, y,g,a∈E~n, 0<ε(?)1and a_1(ε), a_2(ε), b_2(ε)and b_2(ε) are matrices of the appropriate size. Under the condition that g_y(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.     

Asymptotic properties of solutions of nonlinear vector initial value problem on the infinite interval

In this paper we study initial value problems on the infinite interval:where x, f∈E~m, y, g∈E~n,εare real small positive parameters, 0≤t<+∞. Oncondition that g_y(t) is nonsingular and under other assumptions, we have proved that thereare serial (k+m~*)-dimensional manifolds{S_R(e)}∈E~(m+n)such that (I.I)degeneratesregularly provided(ξ(e), η(e))∈S_R(e). Besides, the R-order asymptotic expansions ofsolutions are constructed, and their errors are estimated.     

在边缘线布载荷作用下开顶扁球壳的非线性稳定问题的奇摄动解

本文利用奇异摄动方法计算了在内边缘线布载荷作用下无刚性中心的开顶扁球壳的非线性稳定问题,得到了几何参数k值较大时本问题的一致有效的渐近解.     

THE SINGULAR PERTURBATION METHOD APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A SHALLOW SPHERICAL SHELL(Ⅱ)

In this paper we consider the nonlinear stability of a thin elastic circular shallowspherical shell under the action of uniform normal pressure with a clamped edge.When thegeometrical parameter k is large,the uniformly valid asymptotic solutions are obtained bymeans of the singular perturbation method.In addition,we give the analytic formula fordetermining the centre deflection and the critical load,and the stability curve is also derived.This paper is a continuation of the author’s previous paper[11].     

无穷区域上非线性向量方程初值问题的解的渐近性质

本文研究无穷域上的初值问题:其中x,f∈Em,y,g∈En,实的小参数ε>0,0≤t<+∞,在g_r(t)是非奇异的和其它适当的假设下,证明了存在一系列k+m*维流形{S_R(ε)}∈Em+n,使得如果(ξ(ε),η(ε))∈S_R(ε),方程(1.1)是正则退化的,并作出了解的R阶渐近展开式及其余项估计。