共查询到18条相似文献,搜索用时 140 毫秒
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含内埋矩形脱层复合材料圆柱壳屈曲分析的混合变量条形传递函数方法 总被引:1,自引:0,他引:1
提出了一种分析含内埋矩形脱层正交各向异性圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Mindlin一阶剪切壳理论,通过定义圆柱壳的广义力变量和混合变量,建立了壳的改进混合变量能量泛函;然后,为了便于脱层壳的分区求解,通过引入条形单元,创建了基于混合变量条形传递函数解的含脱层和不合脱层两种超级壳单元;在此基础上,将含内埋矩形脱层的复合材料层合壳划分成两种超级壳单元的组合体,通过各超级壳单元相互之间连接结点处的位移连续和力平衡条件得到脱层壳的屈曲方程;最后由屈曲方程计算含内埋矩形脱层壳的屈曲载荷和屈曲模态。算例分析的结果验证了本方法的正确性,并给出了几种因素对屈曲载荷和屈曲模态的影响。 相似文献
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轴向瞬间阶梯载荷下圆柱壳动力屈曲的双特征参数分析 总被引:3,自引:0,他引:3
对于轴向瞬间阶梯载荷下圆柱壳的弹性非轴对称动力屈曲问题,将临界应力和屈曲惯性项指数参数作为双特征参数求解。由能量转换和守恒准则,导出压缩波阵面上的屈曲变形附加约束条件。失稳控制方程、边界条件和波阵面上的连续条件,连同此附加约束条件构成求解两个特征参数和动力失稳模态的完备定解条件。由伽辽金法得出求解双特征参数问题的数值方法。 相似文献
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圆锥壳自由振动传递函数解 总被引:2,自引:1,他引:2
本文在线性弹性理论基础上,给出了一种求解圆锥薄壳自由振动的渐进传递函数解法,壳体的三个位移分量,外力和边界条件首先沿环向展开的Fourier级数,然后关于时间变量进行Laplace变换,这样就将壳体的控制方程化为一系列含复参数s的变系数常微分方程组,通过定义状态变量。得到了壳体动力学问题的状态空间控制微分方程,引入一小参数,并利用摄动技术就可以得到微分方程的渐进传递函数解,将各于锥段的解进行综合, 相似文献
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旋转壳的数值传递函数方法 总被引:1,自引:0,他引:1
应用数值传递函数方法建立一种用于分析旋转壳静力、动力响应的截锥壳单元,在本方法中,单元的位移在环向展开为Fourier级数的形式,应用薄壳理论可以得到解耦的微分方程,通过Laplace变换可以将方程转化为频域内的常微分方程,将其表示为状态空间形式后,可以应用数值传递函数方法求解,对复杂的系统可以应用与有限元类似的方法,划分多个单元组合求解,文中给出了几种旋转壳的动力、静力问题的数值算例,并与其它方法进行了比较,表明本文方法具有精度高,计算方便等特点。 相似文献
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轴向冲击圆柱壳非弹性响应 总被引:1,自引:0,他引:1
简要论述承受轴向冲击载荷圆柱壳非弹性动屈曲响应的研究进展。采用Karman-Donnell运动方程研究轴向流固冲击载荷作用下的圆柱壳轴对称弹塑性动屈曲问题。本构关系采用增量理论,借助增量数值方法求解动力方程组。研究不同边界条件对屈曲的影响,以及径向外压力在不同边界条件下对屈曲的影响。 相似文献
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复合材料条形域问题混合状态Hamiltonian元的半解析解 总被引:1,自引:0,他引:1
给出了复合材料条形域问题的混合状态Hamilton正则方程及其有效的半解析法。该方法不同于通常的半解析法,需先给出满足规则几何形状和简单边界条件的解析函数,利用Hamilton矩阵的正交性质,采用控制论中的理论与方法后给出复杂几何形状和边界条件的解析函数,这样沿板厚方向就不需引入任何有关位移和应力的人为假设,从而引入了复合材料计算中剪切效应的影响,且发挥了H型方程的传递矩阵法优点,保证了层间位移和应刀的连续,建立了条形梁上下表面相变量之间的关系式,然后利用打靶法进行求解。 相似文献
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基于柱坐标系下的三维弹性力学基本方程,采用状态空间法得到两端固支单层与叠层圆柱厚壳轴对称问题的精确解析解。为严格满足固支端的边界条件,将固支端的边界位移函数作为状态变量引入状态方程,采用增维方法把非齐次状态方程变为齐次状态方程,并通过层合渐近技术将变系数状态矩阵转为常系数矩阵进行求解。所得到的解不仅严格满足三维弹性力学基本方程,而且严格满足固支边界条件,是真正意义上的三维精确解。算例表明,本研究解与有限元解吻合,具有很高的精度,且关于级数项数和分层数具有很好的收敛性。另外,通过圆柱厚壳各力学量沿径向和轴向的精确分布规律分析了厚径比和跨径比变化对位移和应力分布的影响。 相似文献
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层合闭口厚柱壳的温度应力 总被引:2,自引:0,他引:2
基于层合柱壳混合状态方程和边界条件的弱形式,建立了两端固支层合闭口柱壳的温度应力混合方程,给出了任意厚度合闭口柱壳在温度荷载和机械荷载共同作用下的解析解。 相似文献
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Based on unequidistant B-spline function, generalized spline subdomain displacement mode of rotational shell is obtained by taking double-direction interpolation of spline. The elastoplastic constitutive equation of shells is established by using the endochronic theory.According to the initial deflection theory of shells, the elastoplastic stress analysis of cylindrical shells with flat strip geometrical imperfection is studied. Numerical results show that the geometrical imperfection has a great effect on the stress distribution of shells. 相似文献
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黄义 《应用数学和力学(英文版)》1991,12(2):163-180
In this paper,the displacement solution method of the conical shell is presented.Fromthe differential equations in displacement form of conical shell and by introducing adisplacement function,U(s,θ),the differential equations are changed into an eight-ordersoluble partial differential equation about the displacement function U(s,θ)in which thecoefficients are variable.At the same time,the expressions of the displacement and internalforce components of the shell are also given by the displacement function.As special casesof this paper,the displacement function introduced by V.Z.Vlasov in circular cylindricalshell,the basic equation of the cylindrical shell and that of the circular plate are directlyderived.Under the arbitrary loads and boundary conditions,the general bending problem of theconical shell is reduced to finding the displacement function U(s,θ),and the generalsolution of the governing equation is obtained in generalized hypergeometric function,Forthe axisymmetric bending deformation of the 相似文献
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复合材料旋转壳自由振动分析的新方法 总被引:1,自引:0,他引:1
提出了一种半解析区域分解法来分析任意边界条件的复合材料层合旋转壳自由振动. 沿壳体旋转轴线将壳体分解为一些自由的层合壳段, 视位移边界界面为一种特殊的分区界面;采用分区广义变分和最小二乘加权残值法将壳体所有分区界面上的位移协调方程引入到壳体的能量泛函中, 使层合壳的振动分析问题归结为无约束泛函变分问题. 层合壳段位移变量采用Fourier 级数和Chebyshev 多项式展开. 以不同边界条件的层合圆柱壳、圆锥壳及球壳为例, 采用区域分解法分析了其自由振动, 并将计算结果与其他文献值进行了对比. 算例表明, 该方法具有高效率、高精度和收敛性好等优点. 相似文献
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A. M. Zenkour 《Archive of Applied Mechanics (Ingenieur Archiv)》2004,74(3-4):262-276
Summary The static and dynamic responses of anisotropic spherical shells under a uniformly distributed transverse load are investigated.
Analytical solutions using the mixed variational formulation are presented for spherical shells subjected to various boundary
conditions. Numerical results of a refined mixed first-order shear deformation theory for natural frequencies, critical buckling,
center deflections and stresses are compared with those obtained using the classical shell theory. A variety of simply-supported
and clamped boundary conditions are considered and comparisons with the existing literature are made. The sample numerical
results presented herein for global structural behaviour of monoclinic spherical shells should serve as references for future
comparisons. 相似文献
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A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to
dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous
ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function
was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties
of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained.
The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral
transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically
isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic
cylindrical shell that is fixed at the internal surface.
Contributed by Ding Hao-jiang
Foundation item: the National Natural Science Foundation of China (10172075)
Biography: Ding Hao-jiang (1934-) 相似文献
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We discuss the non-linear theory of thin shells expressed in terms of displacements of the shell reference surface as the only independent field variables. The formulation is based on the principle of virtual work postulated for the reference surface. In our approach: (1) the vector equilibrium equations are represented through components in the deformed contravariant surface base, and using the compatibility conditions the resulting tangential equilibrium equations are additionally simplified, (2) at the shell boundary the new scalar function of displacement derivatives is defined and new sets of four work-conjugate static and geometric boundary conditions are derived, as well as (3) for prescribed shell geometry all non-linear shell relations are generated automatically by two packages set up in Mathematica. The displacement boundary value problem and the associated homogeneous shell buckling problem are generated exactly without using any additional approximations following from errors of the constitutive equations. Both problems are extremely complex and available only in the computer memory. Such an approach allows us to account also for those a few supposedly small terms which may be critical for finding the correct buckling load of shells sensitive to imperfections. This approach is used in the accompanying paper by Opoka and Pietraszkiewicz [Opoka, S., Pietraszkiewicz, W., 2009. On refined analysis of bifurcation buckling for the axially compressed circular cylinder. International Journal of Solids and Structures, 46, 3111–3123.] to perform the refined numerical analysis of bifurcation buckling for the axially compressed circular cylinder. 相似文献
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G. P. Gulgazaryan 《International Applied Mechanics》2008,44(5):534-554
The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations
for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary
conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is
proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip
plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical
shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure
to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as
an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008. 相似文献