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A catastrophic model for vibrational buckling of elastic arches


The authors not only obtain a catastrophic model of vibrational buckling of elastic arches, but also give the critical condition of losing stability.


The stability and convergence of mixed finite element methods are investigated, for an equilibrium problem for thin shallow elastic arches.


Qualitative behavior of buckled nonlinearly elastic arches


Nonlinear boundaryvalue problems of plane bending of elastic arches subjected to uniformly distributed loading are solved numerically by the shooting method.

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The problem of the homogenization of a plane elastic arch is studied by means of the energy method.


We examine an asymptotic expansion of the time dependent displacement field of a solid, threedimensional elastic arch.


On SaintVenant's Principle for a Homogeneous Elastic ArchLike Region


Solutions for the interacting vibrations of a linear elastic arch dam with a linear compressible, threedimensional, irregularly shaped fluidbody are presented.




 This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures. The authors not only obtain a catastrophic model of vibrational buckling of elastic arches, but also give the critical condition of losing stability.  本文是将突变理论应用于工程结构的动力稳定性的一个尝试.作者不仅得到弹性拱振动失稳的突变模型,而且给出发生失稳的条件.  The writer has simply stated the basic concept and formula that are be used to calculate elastic arch by American cultivating Bureau utilizing the form constant and load constant of arch, and has stressed introducing to the skill that the right arch is treated as the left one in the program made in the light of archbeam method. This kind of processing skill is fairly simpler, not only avoid making the program for calculating the right arch, but also having avoided complicated questions brought by calculation... The writer has simply stated the basic concept and formula that are be used to calculate elastic arch by American cultivating Bureau utilizing the form constant and load constant of arch, and has stressed introducing to the skill that the right arch is treated as the left one in the program made in the light of archbeam method. This kind of processing skill is fairly simpler, not only avoid making the program for calculating the right arch, but also having avoided complicated questions brought by calculation of the right arch.  简述了美国垦务局利用拱圈形常数、载常数解算弹性拱的基本概念及公式。另外 ,着重介绍了作者在拱梁分载法程序中解算拱圈时将右拱当作左拱计算的技巧。这种处理方法比较简单 ,既节省了专为右拱计算的程序 ,也避免了右拱公式比较复杂所带来的问题  Based on the extended homogeneous capacity precision integration method,a novel method was presented for solving plane bending problems of elastic arches with arbitrary profile.Firstly,a matrix ordinary differential equation of first order for state vectors of the elastic arch was derived by using the curve beam theory.Secondly,the above equation was homogenized by means of the polynomial approximation,and then the variable coefficients matrix was approximately transformed into the constant coefficients one.Finally,a... Based on the extended homogeneous capacity precision integration method,a novel method was presented for solving plane bending problems of elastic arches with arbitrary profile.Firstly,a matrix ordinary differential equation of first order for state vectors of the elastic arch was derived by using the curve beam theory.Secondly,the above equation was homogenized by means of the polynomial approximation,and then the variable coefficients matrix was approximately transformed into the constant coefficients one.Finally,a semianalytical solution to the problems under consideration was carried out.Numerical results compared with the existing methods show that the method proposed has more superiority than the FEM.  基于齐次扩容精细积分法,提出了求解复杂载荷作用下任意外形弹性拱平面弯曲的一种新方法。首先,利用曲梁理论导出了微弧段状态向量的一阶常微分矩阵方程;然后,借助多项式逼近将该方程齐次化和系数常数化,得到了相应的半解析解,它可以达到任意要求的计算机精度。通过算例结果比较,有力地说明了本文方法的有效性和先进性。  
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