Positive Solutions of Boundary Value Problems for Second-Order Singular Nonlinear Differential Equations

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｈａｌｌｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｓｉｎｇｕｌａｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ (ＢＶＰ)ｕ″ ｇ(ｔ)ｆ(ｕ) =0 ,　　 0 <ｔ<1 ,αｕ(0 ) -βｕ′(0 ) =0 ,　　γｕ(1 ) δｕ′(1 ) =0 ,(1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,ρ:=βγ αγ αδ>0 ,ｆ∈Ｃ([0 ,∞ ) ,[0 ,∞ ) ) ,ｇｍａｙｂｅｓｉｎｇｕｌａｒａｔｔ=0ａｎｄ/ｏｒｔ=1 .Ｔｈｉｓｐｒｏｂｌｅｍａｒｉｓｅｓｎａｔｕｒａｌｌｙｉｎｔｈｅｓｔｕｄｙｏｆｒａｄｉａｌｌｙｓｙｍｍｅｔ…     

The fractional dimension identification method of critical bifurcated parameters of bearing-rotor system

ＩｎｔｒｏｄｕｃｔｉｏｎＢｉｆｕｒｃａｔｉｏｎａｎｄｆｒａｃｔａｌｔｈｅｏｒｙａｒｅｔｗｏｉｍｐｏｒｔａｎｔｂｒａｎｃｈｅｓｏｆｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅ.Ｔｈｅｂｉｆｕｒｃａｔｉｏｎｉｓ:ｆｏｒｃｏｎｔｉｎｕｏｕｓ＿ｔｉｍｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｘ=ｆ(ｘ,ｔ,α)ｏｒｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｘ｜→ｇ(ｘ,α)(ｗｈｅｒｅｇｉｓｍａｐｇ:Ｒｎ×Ｒ→Ｒｎ),ｗｈｅｎｔｈｅｐａｒａｍｅｔｅｒαｃｈａｎｇｅｓｃｏｎｔｉｎｕｏｕｓｌｙａｎｄｐａｓｓｅｓα0,ｔｈｅｔｏｐｏｌｏｇｉｃ…     

ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＫｂｅａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆａＢａｎａｃｈｓｐａｃｅＸ .ＴｈｅｎａｍａｐｐｉｎｇＴ :Ｋ→ＫｉｓｓａｉｄｔｏｂｅａＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇｉｆ,ｆｏｒｅａｃｈｉｎｔｅｇｅｒｎ≥ 1 ,ｔｈｅｒｅｅｘｉｓｔｓａｃｏｎｓｔａｎｔｋｎ >0ｓｕｃｈｔｈａｔ‖Ｔｎｘ-Ｔｎｙ‖ ≤ｋｎ‖ｘ-ｙ‖　ｆｏｒａｌｌｘ ,ｙ∈Ｋ .ＡＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇＴｉｓｓａｉｄｔｏｂｅｕｎｉｆｏｒｍｌｙｋ＿Ｌｉｐｓｃｈｉｔｚｉａｎｉｆｋｎ =ｋｆｏｒａｌｌｎ ≥ 1 ;ｎｏ…     

POSITIVE SOLUTIONS TO A SINGULAR SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓＴｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｈａｓｂｅｅｎｅｓｔａｂｌｉｓｈｅｄｆｏｒａｎｏｎｌｉｎｅａｒｓｅｃｏｎｄｏｒｄｅｒｔｈｒｅｅ＿ｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｏｆｔｈｅｆｏｒｍ-ｙ″ =Ｑ(ｘ)ｆ(ｙ)　　 ( 0 <ｘ<1 ) ,ｙ( 0 ) =0 ,ｙ( 1 ) =αｙ( η) ( 1 )ｏｎｌｙｖｅｒｙｒｅｃｅｎｔｌｙｉｎ [1 ] .Ｉｔｗａｓａｓｓｕｍｅｄｔｈｅｒｅｔｈａｔ 0 <η <1 ,0 <αη <1 ,Ｑ(ｘ) ∈Ｃ( [0 ,1 ] ;Ｒ+) ,ｆ(ｙ)∈Ｃ…     

An analogue rotated vector field of polynomial system

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ·ＤｅｆｉｎｉｔｉｏｎｏｆＡｎａｌｏｇｕｅＲｏｔａｔｅｄＶｅｃｔｏｒＳｕｐｐｏｓｉｎｇｔｈａｔａｌｉｍｉｔｃｙｃｌｅｉｓｌｏｃａｔｅｄｉｎａｒｏｔａｔｅｄｖｅｃｔｏｒｆｉｅｌｄｏｆｐｏｌｙｎｏｍｉａｌｓｙｓｔｅｍｔｈａｔｄｅｐｅｎｄｓｏｎａｐａｒａｍｅｔｅｒα,ａｎｄｗｈｅｎαｍｏｎｏｔｏｎｏｕｓｌｙｃｈａｎｇｅｓ,ｔｈｉｓｌｉｍｉｔｃｙｃｌｅｗｉｌｌｍｏｎｏｔｏｎｏｕｓｌｙｅｘｐａｎｄ(ｏｒｒｅｄｕｃｅ)ｗｉｔｈｔｈｅα.Ｂｕｔｍｏｒｅｔｈａｎｏｎｅｎｅｉｇｈｂｏｕｒｉｎ…     

A class of parabolic hemivariational inequalities

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｎｏｐｅｎｂｏｕｎｄｅｄｄｏｍａｉｎｏｆＲＮ,Ｑ=Ω× (0 ,Ｔ) ,0 <Ｔ<∞ ,2 ≤ｐ<∞ ,(1 /ｐ) (1 /ｐ′) =1 .Ｆｏｒｃｏｎｖｅｎｉｅｎｃｅ ,ｗｅｓｅｔＶ =Ｗ1,ｐ0 (Ω) ,Ｖ′=Ｗ- 1,ｐ′(Ω)ｉｎｔｈｅｓｅｑｕｅｌ.ＴｈｅｎＶｉｓａｒｅａｌｒｅｆｌｅｘｉｖｅＢａｎａｃｈｓｐａｃｅｄｅｎｓｅｌｙａｎｄｃｏｍｐａｃｔｌｙｉｍｂｅｄｄｅｄｉｎｔｏＬｐ(Ω) .ＴｈｅｎｏｒｍｏｆａｎｙＢａｎａｃｈｓｐａｃｅＢｉｓｄｅｎｏｔｅｄｂｙ‖·‖Ｂ.ＴｈｅｐａｉｒｉｎｇｂｅｔｗｅｅｎＢａｎ…     

BLOCK H-MATRICES AND SPECTRUM OF BLOCK MATRICES

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＡ ∈Ｃｎ ,ｎ,ａｎｄｂｅｐａｒｔｉｔｉｏｎｅｄａｓｆｏｌｌｏｗｓ:Ａ =Ａ11Ａ12 …Ａ1ｋＡ2 1Ａ2 2 …Ａ2ｋ…………Ａｋ1Ａｋ2 …Ａｋｋ,( 1 )ｗｈｅｒｅＡｉｉ∈Ｃｎｉ,ｎｉ,1 ≤ｉ≤ｋ ,∑ｋｉ=1ｎｉ=ｎ ,Ａｉｉ( 1 ≤ｉ≤ｋ)ａｒｅｎｏｎｓｉｎｇｕｌａｒ.Ｉｎｍｏｓｔｐｒａｃｔｉｃａｌａｐｐｌｉｃａｔｉｏｎｓ,ｔｈｅｍａｔｒｉｃｅｓＡｉｊａｒｅｓｐａｒｓｅａｎｄｍａｎｙｏｆｔｈｅｂｌｏｃｋｍａｔｒｉｃｅｓａｒｅｚｅｒｏ .Ｄｅｆｉｎｉｔｉｏｎ 1　ＩｆＢ =(ｂｉｊ) =(‖Ａｉｊ‖ ) ｋ×…     

GLOBAL ATTRACTIVITY FOR A CLASS OF NONLINEARDELAY DIFFERENCE EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｇｌｏｂａｌａｔｔｒａｃｔｉｖｉｔｙｏｆｔｈｅｎｏｎｌｉｎｅａｒｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｘｎ+ａｎｘｎ+ｆ(ｎ ,∑0ｓ=-ｋ ｑｓ,ｎｘｓ+ｎ) =0　 (ｎ=0 ,1 ,2 ,… ) . ( 1 )ＴｈｅｉｎｉｔｉａｌｖａｌｕｅｏｆＥｑ .( 1 )ｉｓｘｓ =φｓ　 (ｓ=-ｋ ,-ｋ+ 1 ,… ,-1 ,0 ) . ( 2 )Ｉｎｔｈｅｓｅｑｕｅｌ,ｗｅａｌｗａｙｓｓｕｐｐｏｓｅｔｈａｔＤ1) ａｎ ｉｓａｎｏｎｎｅｇａｔｉｖｅｒｅａｌｓｅｑｕｅｎｃｅ ,0 ≤ａｎ <1ａｎｄｋｉｓａｐｏｓｉｔｉｖｅ…     

New scalar-type equilibrium equations of the general space force system

ＩｎｔｒｏｄｕｃｔｉｏｎＬｉｋｅｔｈｅｃｏｐｌａｎａｒｆｏｒｃｅｓｙｓｔｅｍ ,ａｎｙｇｅｎｅｒａｌｓｐａｃｅｆｏｒｃｅｓｙｓｔｅｍＦｉ(ｉ =1 ,2 ,… ,ｎ)ｃａｎｂｅｒｅｄｕｃｅｄｔｏａｐｏｉｎｔＯａｎｄｒｅｐｌａｃｅｄｂｙａｐｒｉｎｃｉｐａｌｖｅｃｔｏｒＲａｎｄａｐｒｉｎｃｉｐａｌｍｏｍｅｎｔＬ0 .Ｓｏｔｈａｔｔｈｅｖｅｃｔｏｒ＿ｔｙｐｅｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｆｏｒｅｑｕｉｌｉｂｒｉｕｍｏｆｔｈｅｇｉｖｅｎｆｏｒｃｅｓｙｓｔｅｍａｒｅＲ =0 ,　Ｌ0 =0 . (1 )…     

ON THE CRITICAL POINTS OF THE MAP F_p:X→‖AXB-C‖_p~p

1　ＰｒｅｌｉｍｉｎａｒｉｅｓＬｅｔＨｂｅａＨｉｌｂｅｒｔｓｐａｃｅ,ａｎｄＬ(Ｈ) ,ｂｅｔｈｅｓｐａｃｅｏｆａｌｌｔｈｅｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｏｎＨ ,ａｎｏｐｅｒａｔｏｒＴ- ｉｓｓａｉｄｔｏｂｅａｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｏｆｔｈｅｏｐｅｒａｔｏｒＴｉｆＴＴ- Ｔ =Ｔ .ＡｎｏｐｅｒａｔｏｒＴｉｎＬ(Ｈ)ｈａｓａｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｉｆａｎｄｏｎｌｙｉｆｔｈｅｒａｎｇｅｏｆＴ ,ｄｅｎｏｔｅｄｒａｎ(Ｔ) ,ｉｓｃｌｏｓｅｄ[1].ＲＰｅｎｒｏｓｅ[1]ｓｈｏｗｅｄｔ…     

Approximate Methods for the Linear and Nonlinear Analysis of Plates and Shallow Shells

Abstract

Berger's equations for the large amplitude deformation of membranes are used to produce a simple approximate expression for the large amplitude deflection of plates. The deformation of shallow shells is also considered and two approximate methods are outlined. Several important problems are discussed, the obtained solution being in good agreement with both experimental data and other approximate results. The main advantage of this technique is its ease of application, as it requires comparatively little computational work. A simple approximate formula for computing the fundamental frequency of a vibrating shallow shell is also presented and is shown to yield very accurate values in the case of a shallow dome and a rectangular panel.     

一般夹层旋转壳在轴对称变形下的大挠度方程

应用最小势能原理建立了具有不同质不等厚薄表层和软夹心的一般夹层旋转壳在轴对称变形下的非线性理论,得到了一组相对简单的夹层壳大挠度方程和边界条件。在分析壳体的变形时,将表层视作薄膜,假设夹心沿厚度方向不可压缩且只能承受横向剪应力,参考面的法线在变形时保持为直线。为便于实际应用,给出几种特殊壳体情况下的大挠度方程。     

NON-SYMMETRICAL LARGE DEFORMATION OFA SHALLOW THIN CONICAL SHELL

I.IntroductionItisimportanttoresearchnon-symmetricalquestionsofshallowcollicalshellsintheoryoronapplication.Asonekindofpressurevessel'sparts,shallowconicalshellsareverycommonlyusedillellgineerillgpractice,becausethedifficultyofmanul\lctul.illgthemis'small.AlthotlghwelookupmanyChineseandtbreignperiodicalswhicharctlblctobefound,wehavenotyeth'ulldarticlesanddocumentsfornon-symmetricalandnolllinearquestionsofshitllowconictllshells.Oval'rccelltyears,ProlbssorWangXinzhiandhiscolleagueshavedonealot…     

Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitude-frequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.     

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 shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining 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].     

Analysis for the thermoelastic bending of a functionally graded material cylindrical shell

An analytic study for thermoelastic bending of a functionally graded material (FGM) cylindrical shell subjected to a uniform transverse mechanical load and non-uniform thermal loads is presented. Based on the classical linear shell theory, the equations with the radial deflection and horizontal displacement are derived out. An arbitrary material property of the FGM cylindrical shell is assumed to vary through the thickness of the cylindrical shell, and exact solution of the problem is obtained by using an analytic method. For the FGM cylindrical shell with fixed and simply supported boundary conditions, the effects of mechanical load, thermal load and the power law exponent on the deformation of the FGM cylindrical shell are analyzed and discussed.     

Nonlinear vibration analysis of geometrically nonlinear shell structures

The nonlinear vibration analysis of a geometrically nonlinear shell structure is investigated in this study. In general, when the shell structure is subjected to excessive loadings, the large deformation of the shell structures must be considered, and the governing equation of the shell structure becomes nonlinear since the stiffness matrix of the governing equation is related to the deflection. Therefore, the natural frequency of the shell structure is varied with respect to the time which is quite different from that of the linear structures. In order to solve the nonlinearity of the governing equations of the shell structures, the well known Newton-Raphson iteration procedure in conjunction with Newmark scheme is adopted to perform the frequency analysis of the nonlinear-shell structures. Incidentally, the natural frequencies for various curvatures of the shell structures are also investigated from the practical engineering point of view.     

功能梯度截顶圆锥壳的热弹性弯曲精确解

研究了功能梯度材料截顶圆锥壳在横向机械载荷与非均匀热载荷同时作用下的变形问题. 基 于经典线性壳体理论推导出了以横向剪力和中面转角为基本未知量的功能梯度薄圆锥壳轴对 称变形的混合型控制方程. 假设功能梯度圆锥壳的材料性质为沿厚度方向按照幂函数 连续变化的形式. 然后采用解析方法求解，得到了问题的精确解. 分别就两端简支和两端固 支边界条件，给出了圆锥壳的变形随其载荷、材料参数等变化的特征关系曲线，重点分析和 讨论了载荷参数与材料梯度变化参数对变形的影响.     

基于拟应变法的壳单元大变形分析及在冲击动力问题中的应用

为了简便有效地解决板壳结构的大变形问题，本文针对八节点相对自由度壳单元进行研究。该单元的位移场由壳的中面节点位移和上表面节点的相对位移组成，不带有转动变量。所有的研究都是基于完全的三维位移、应力、应变场。采用拟应变法，对应变场另行假设，能够改善该单元在大变形情况下的计算精度。通过引入Wilson非协调模式，构造了大变形情况下的拟应变场表达式，给出了该单元用于解决非线性动力分析问题的有限元求解方程。通过算例表明，本文针对相对自由度壳单元提出的方法及推导的公式，能够解决冲击动力问题中的大变形问题。     

简支梯形底扁球壳弯曲问题的准格林函数方法

以简支梯形底扁球壳的弯曲问题为例,详细阐明了准格林函数方法的思想.即利用问题的基本解和边界方程构造一个准格林函数,这个函数满足了问题的齐次边界条件,采用格林公式将简支扁球壳弯曲问题的控制微分方程化为两个互相耦合的第二类Fredholm积分方程.边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的边界方程...