GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｌｌｏｗｓ[1,2 ]ｉｓａｓｈｅｌｌｏｆｒｅｖｏｌｕｔｉｏｎｗｉｔｈｗｒｉｎｋｌｅｄｍｅｒｉｄｉａｎ ,ｕｓｕａｌｌｙｎａｍｅｄａｆｔｅｒｉｔｓｍｅｒｉｄｉｏｎａｌｓｈａｐｅｉｎａｐｅｒｉｏｄｏｒｉｔｓｐｒｏｆｉｌｅｏｆａｃｏｎｖｏｌｕｔｉｏｎ ,ｓｕｃｈａｓΩ＿ｓｈａｐｅｄｂｅｌｌｏｗｓ,Ｃ＿ｓｈａｐｅｄｂｅｌｌｏｗｓ,Ｕ＿ｓｈａｐｅｄｂｅｌｌｏｗｓａｎｄｓｏｏｎ .Ｔｈｅｙａｒｅｗｉｄｅｌｙｕｓｅｄｉｎｍａｎｙｆｉｅｌｄｓ,ｆｏｒｅｘａｍｐｌｅ ,ｔｈｅｅｌａｓｔｉｃｓｅｎｓｅ…     

Electromagnetic tomography (EMT): Theoretical analysis of the forward problem

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｔｈｅｍｉｄ＿1 980’ｓ,ａｔｏｍｏｇｒａｐｈｉｃｉｍａｇｉｎｇｔｅｃｈｎｉｑｕｅｓｕｉｔｅｄｔｏｉｎｄｕｓｔｒｉａｌｐｒｏｃｅｓｓｄｅｔｅｃｔｉｏｎ ,ＰｒｏｃｅｓｓＴｏｍｏｇｒａｐｈｙ[1],ｗａｓｒａｐｉｄｌｙｄｅｖｅｌｏｐｅｄｉｎｔｈｅＵＫ ,ＵＳＡ ,ｅｔｃ .ｗｉｔｈｓｕｃｃｅｓｓｆｕｌａｐｐｌｉｃａｔｉｏｎｓｏｆＣＴｔｅｃｈｎｉｑｕｅｔｏｍｅｄｉｃａｌｄｉａｇｎｏｓｉｓ .Ｉｎｐａｒｔｉｃｕｌａｒ,ａｓａｎｅｗｍｅｍｂｅｒｗｉｔｈｉｎｔｈｅｆａｍｉｌｙｏｆｔｈｅ…     

Qualitative Analysis for a Class of Second-order Nonlinear System with Delay

Ｕｐｔｏｎｏｗ ,ｔｈｅｑｕａｌｉｔａｔｉｖｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｅｃｏｎｄ＿ｏｒｄｅｒｎｏｎｌｉｎｅａｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓａｎｄｔｈｅｉｒａｐｐｌｉｃａｔｉｏｎｓｈａｖｅｂｅｅｎｄｉｓｃｕｓｓｅｄｅｘｔｅｎｓｉｖｅｌｙｉｎｌｉｔｅｒａｔｕｒｅ.ＷｅｒｅｆｅｒｔｏｔｈｅＲｅｆｓ .[1 -8] .Ｃｏｎｖｅｒｓｅｌｙ ,ｔｈｅｄｉｓｃｕｓｓｉｏｎｆｏｒｔｈｅｑｕａｌｉｔａｔｉｖｅｂｅｈａｖｉｏｒｏｆｔｈｅｄｅｌａｙｓｙｓｔｅｍｉｓｌｅｓｓ .Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔ…     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅳ)-CALCULATION FOR U-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＵ＿ｓｈａｐｅｄｂｅｌｌｏｗｓａｒｅｕｓｕａｌｌｙｓｅｅｎｉｎｔｈｅｐｉｐｅｌｉｎｅｓｙｓｔｅｍ (Ｆｉｇ .1) ,ｗｈｉｃｈａｒｅｕｓｅｄｔｏｃｏｍｐｅｎｓａｔｅｆｏｒｔｈｅａｘｉａｌｍｏｖｅｍｅｎｔ,ｔｈｅｒｏｔａｔｉｏｎａｎｄｔｈｅｄｅｆｌｅｃｔｉｏｎｏｆｔｈｅｐｉｐｅｌｉｎｅｓｄｕｅｔｏｔｈｅｔｈｅｒｍａｌａｃｔｉｏｎ ,ｔｈｅｂａｓｅｕｎｅｑｕａｌｓｅｔｔｌｅｍｅｎｔｓａｎｄｔｈｅｉｎｓｔａｌｌａｔｉｏｎｅｒｒｏｒｓ.Ｔｈｅａｘｉｓｙｍｍｅｔｒｉｃａｌｄｅｆｏｒｍａｔｉｏ…     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＣ＿ｓｈａｐｅｄｂｅｌｌｏｗｓｏｒｒｅｆｅｒｒｅｄｔｏａｓｓｅｍｉ＿ｃｉｒｃｌｅｂｅｌｌｏｗｓａｒｅｗｉｔｈｃｏｍｐｌｅｘｃｏｎｆｉｇｕｒａｔｉｏｎ(Ｆｉｇ .1) .Ａｔｔｈｅｃｏｎｃａｖｅａｎｄｃｏｎｖｅｘｊｏｉｎｔｓｏｆｔｈｅｓｈｅｌｌ,ｆｏｒｅｘａｍｐｌｅａｔｐｏｉｎｔＣ ,ｔｈｅｌａｔｉｔｕｄｅａｎｇｌｅψｉｎｃｒｅａｓｅｓｂｙ 180°ａｂｒｕｐｔｌｙ .Ｓｏｉｔｉｓｔｈｅｋｅｙｔｏｃａｌｃｕｌａｔｉｏｎｆｏｒｂｅｌｌｏｗｓｔｈａｔｍａｋｉｎｇｕｐｓｏｌｕｔｉｏｎｓｅｘａｃｔ…     

On monotone iterative method for initial value problems of nonlinear second-order integro-differential equations in Banach spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｐａｐｅｒ[1],Ｄ.Ｇｕｏｅｓｔａｂｌｉｓｈｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｅｘｔｒｅｍｅｓｏｌｕｔｉｏｎｓｏｆｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｆｉｒｓｔ＿ｏｒｄｅｒｉｎｔｅｇｒｏ＿ｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆＶｏｌｔｅｒｒａｔｙｐｅｉｎＢａｎａｃｈｓｐａｃｅｓ.Ｎｏｗ,ｗｅｃｏｎｓｉｄｅｒｔｈｅＩＶＰｆｏｒｓｅｃｏｎｄ＿ｏｒｄｅｒｉｎｔｅｇｒｏ＿ｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎａｒｅａｌＢａｎａｃｈｓｐａｃｅＥ:ｕ″=Ｆ(ｔ,ｕ,…     

SIMILARITY REDUCTIONS FOR THE NONLINEAR EVOLUTION EQUATION ARISING IN THE FERMI-PASTA-ULAM PROBLEM

ＩｎｔｒｏｄｕｃｔｉｏｎＦｅｒｍｉ,ＰａｓｔａａｎｄＵｌａｍ[1]ｐｒｅｓｅｎｔｅｄａｗｅｌｌ＿ｋｎｏｗｎｐｒｏｂｌｅｍｗｈｙｓｏｌｉｄｓｈａｄｆｉｎｉｔｅｈｅａｔｃｏｎｄｕｃｔｉｖｉｔｙ ,ｗｈｉｃｈｗａｓｃａｌｌｅｄｔｈｅＦｅｒｍｉ＿Ｐａｓｔａ＿Ｕｌａｍ(ＦＰＵ)ｐｒｏｂｌｅｍ .Ｔｈｅｓｏｌｉｄｉｓｍｏｄｅｌｌｅｄｂｙａｏｎｅ＿ｄｉｍｅｎｓｉｏｎａｌｌａｔｔｉｃｅ ,ａｓｅｔｏｆｍａｓｓｅｓｃｏｕｐｌｅｄｂｙｓｔｒｉｎｇ .Ｔｈｅｅｑｕａｔｉｏｎｓｇｏｖｅｒｎｉｎｇｔｈｅｄｙｎａｍｉｃｓｏｆｔｈｉｓｌａ…     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

RESEARCH ON THE EFFECT OF CYLINDER PARTICLES ON THE TURBULENT PROPERTIES IN PARTICULATE FLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｗｏ＿ｐｈａｓｅｆｌｏｗｗｉｔｈｃｙｌｉｎｄｅｒｐａｒｔｉｃｌｅｓｉｓａｄｉｆｆｉｃｕｌｔｍａｔｔｅｒｉｎｔｈｅｏｒｅｔｉｃａｌｒｅｓｅａｒｃｈｏｆｍｕｌｔｉｐｈａｓｅｆｌｏｗａｎｄｎｏｎ＿Ｎｅｗｔｏｎｉａｎｆｌｏｗ ,ｓｏｉｔｉｓａｃａｄｅｍｉｃａｌｌｙｖａｌｕａｂｌｅｔｏｓｔｕｄｙｉｔ.Ｍｅａｎｗｈｉｌｅ ,ｓｕｃｈｆｌｏｗｓｈａｖｅａｂｒｏａｄｂａｃｋｇｒｏｕｎｄｉｎｉｎｄｕｓｔｒｙ .Ｉｎｔｈｅｍａｔｅｒｉａｌｓｃｉｅｎｃｅ,ｔｈｅｍｏｌｄｉｎｇａｎｄｐｒｏｃｅｓ…     

Weighted Solution of Small-Deflection Buckling Equation of Thin Shell

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｎ＿ｗａｌｌｅｄｓｈｅｌｌｈａｓｍａｎｙａｐｐｌｉａｎｃｅｓｉｎｅｎｇｉｎｅｅｒｉｎｇｓｕｃｈａｓｕｎｄｅｒｇｒｏｕｎｄｐｉｐｅ,ｏｕｔｅｒｓｈｅｌｌｏｆｓｕｂｍａｒｉｎｅｗｈｉｃｈａｒｅｕｓｕａｌｌｙｓｕｂｊｅｃｔｅｄｔｏｅｘｔｅｒｎａｌｐｒｅｓｓｕｒｅ .Ｗｈｅｎｄｅｓｉｇｎｉｎｇｔｈｏｓｅｓｔｒｕｃｔｕｒｅｓｗｅｓｈｏｕｌｄｃｏｎｓｉｄｅｒｎｏｔｏｎｌｙｔｈｅｓｔｒｅｎｇｔｈｐｒｏｂｌｅｍｉｎｓｅｒｖｉｃｅ ,ｂｕｔａｌｓｏｔｈｅｂｕｃｋｌｉｎｇｐｒｏｂｌｅｍｕｎ…     

Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells

ＩｎｔｒｏｄｕｃｔｉｏｎＥｑｕａｔｉｏｎｓｆｏｒｃｉｒｃｕｌａｒｒｉｎｇｓｈｅｌｌｓａｒｅｄｉｆｆｉｃｕｌｔｔｏｓｏｌｖｅ．Ｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｉｓｐｒｏｂｌｅｍｓｔａｒｔｅｄａｔｔｈｅｂｅｇｉｎｎｉｎｇｏｆｔｈｉｓｃｅｎｔｕｒｙ．Ｉｎｔｈｅｌａｔｅ１９７０ｓａｎｄｅａｒｌｙ１９８０ｓ,Ｗ．Ｚ．Ｃｈｉｅｎ（１９７９,１９８０,１９８１）［１～３］ｒｅｂｕｉｌｔｔｈｅｃｏｍｐｌｅｘｅｑｕａｔｉｏｎｓｏｆａｘｉｓ＿ｓｙｍｍｅｔｒｉｃａｌｌｙｌｏａｄｅｄｒｉｎｇｓｈｅｌｌｓｐｒｅｓｅｎｔｅｄ…     

用初参数法解C型波纹管在子午面内整体弯曲

波纹管是一种呈波纹状的管形薄壁结构,作为弹性敏感元件、密封元件和位移补偿器,在现代工业、国防和民用设备中的应用日益广泛.波纹管的计算,特别是在非轴对称受力和变形方面亟待完善.本文讨论了C型波纹管在子午面内整体弯曲的应力分布和端面角位移.从柔性圆环壳在子午面内整体弯曲的复变量方程出发,化边值问题为初值问题,用S.Gill法,得到了该波纹管的数值解,适用于0＜α＜1的范围.通过3个例子,将本文的数值解和已有的细环壳一般解(解析解)作了比较.结果表明,两者基本一致,并且,当环壳较细(α较小)时,两种计算结果更为接近.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｑｕａｔｉｏｎｓａｎｄｔｈｅｓｏｌｕｔｉｏｎｐｒｏｃｅｄｕｒｅｓｏｆｔｈｅｆｉｎｉｔｅ＿ｅｌｅｍｅｎｔ＿ｄｉｓｐｌａｃｅｍｅｎｔ＿ｐｅｒｔｕｒｂａｔｉｏｎｍｅｔｈｏｄ (ＦＥＤＰＭ)ｆｏｒｔｈｅｇｅｏｍｅｔｒｉｃｎｏｎｌｉｎｅａｒｂｅｈａｖｉｏｒｓｏｆｓｈｅｌｌｓｏｆｒｅｖｏｌｕｔｉｏｎｓｕｂｊｅｃｔｅｄｔｏｐｕｒｅｂｅｎｄｉｎｇｍｏｍｅｎｔｓｏｒｌａｔｅｒａｌｆｏｒｃｅｓｉｎｏｎｅｏｆｔｈｅｉｒｍｅｒｉｄｉｏｎａｌｐｌａｎｅｓｗｅｒｅｐｒｅｓｅｎｔｅｄｉｎ (Ⅰ ) .…     

The bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads

On the basis of the stepped reduction method suggested in [1], we investigate the problem of the bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads. The general solution of this problem is obtained so that it can be used for the calculations of strength and rigidity of practical problems such as arch, tunnel etc. In order to examine results of this paper and explain the application of this new method, an example is brought out at the end of this paper. Circular ring and arch are commonly used structures in engineering. Timoshenko, S.^[2], Barber, J. R.^[3], Tsumura Rimitsu^[4] et al. have studied these problems of bending, but, so far as we know, it has been solely restricted to the general solution of homogeneous uniform cross section ring. The only known solution for the problems with variable cross section ones has been solely restricted to the solution of special case of flexural rigidity in linear function of coordinates. On account of fundamental equations of the non-homogeneous variable cross section problem being variable coefficients, it is very difficult to solve them. In this paper, we use the stepped reduction method suggested in [1] to transform the variable coefficient differential equation into equivalent constant coefficient one. After introducing virtual internal forces, we obtain general solution of an elastic circular ring with non-homogeneity and variable cross section under the actions of arbitrary loads.     

薄板理论的正交关系及其变分原理

利用平面弹性与板弯曲的相似性理论，将弹性力学新正交关系中构造对偶向量的思路推广到 各向同性薄板弹性弯曲问题，由混合变量求解法直接得到对偶微分方程并推导了对应的变分 原理. 所导出的对偶微分矩阵具有主对角子矩阵为零矩阵的特点. 发现了两个独立的、对称 的正交关系，利用薄板弹性弯曲理论的积分形式证明了这种正交关系的成立. 在恰当选择对 偶向量后，弹性力学的新正交关系可以推广到各向同性薄板弹性弯曲理论.     

微结构非局部效应的多重性模型及在微梁弯曲中的应用

基于Eringen非局部弹性理论,直接利用逐次逼近法推导了非局部应力场的精确表达,该精确的非局部应力可具体表示为一个无穷级数的形式. 然后以微梁的横向弯曲和纯弯曲变形为例,建立平衡方程并求解及分析了挠度受非局部效应的影响. 结果表明：根据所取非局部小尺度参数大小的不同,非局部微梁的弯曲挠度可低于也可以高于经典力学下的挠度,非局部效应的增大可提高亦可降低结构的抗弯刚度. 本文结果证明了Wang以及Lim等人分别提出的两种相反的非局部模型的各自正确性. 同时首次发现,弯曲挠度随着非局部效应的增大而上下波动且存在若干跳跃点,挠度是非局部小尺度参数的非单调函数,研究同时给出了一种确定材料非局部常数的建议途径.     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega-shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non-homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non-homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

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