厚壁圆柱壳的弹性静力分析

本文研究了考虑横向剪切影响的弹性厚壁圆柱壳的静力问题。利用变分原理得到平衡微分方程组和相应的边界条件。将平衡方程组归并成一个高阶微分方程,用数值法求出它的特征根,得到问题的解。     

Nonlinear stability of double-deck reticulated circular shallow spherical shell

Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.     

A modified Hellinger-Reissner variational functional including only two independent variables for large displacement of thin shallow shell

I.IntroductionThemathematicalbasisofthefiniteelementmethodisthevariationalprinciple,andthedevelopmentofthefiniteelementmethodimpelsthevariationalprincipleitselftogetanewdevelopment.ThevariationalprincipIepresentedbyT.H.H.PianandP.Tongistheonethatthecontin…     

The method of transformation of the boundaries for structure the admissible displacements

In this paper the method of transformation of the boundaries for structure the admissible displacements with various boundary conditions is presented. What is called the method of transformation of the boundaries is that, first we transform the actual system into the basic system and additional boundary forces and displacements on the basis of the superposition principle, then apply variational principles to the basic system, finally find the permissible displacement of the actual system by means of the method of transformation of the series.In this paper, we also give mixed energy principles under variation of boundary conditions. The mixed energy principles as the potential and complementary energy principles under variation of boundary conditions are all the chief theoretical fundamental of the method of transformation of the boundaries.Applying the method of transformation of the boundaries, we form the permissible displacements of rectangular plates of plane stress and bending problems with various edge conditions.Because the method of transformation of the boundaries is in progress to follow the variational principles and definite program to form permissible displacements, the difficulty in supposing and piecing together permissible displacements in the Rayleigh-Ritz method will be overcome.     

Numerical modelling of the stability of loaded shells of revolution containing fluid flows

A mixed finite-element algorithm is proposed to study the dynamic behavior of loaded shells of revolution containing a stationary or moving compressible fluid. The behavior of the fluid is described by potential theory, whose equations are reduced to integral form using the Galerkin method. The dynamics of the shell is analyzed with the use of the variational principle of possible displacements, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure exerted on the shell by the fluid. The solution of the problem reduces to the calculation and analysis of the eigenvalues of the coupled system of equations. As an example, the effect of hydrostatic pressure on the dynamic behavior of shells of revolution containing a moving fluid is studied under various boundary conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 185–195, March–April, 2008     

Weak formulation of mixed state equation and boundary value problem of laminated cylindrical shell

IntroductionBasedonthree-dimensionalelasticitytheory,exactsolutionofhomogeneousisotropic,orthotropic,andlaminatedplatesandshellshasbeenstUdiedll]-[61,respeChvely.Butallofabovepapersadoptedrigorousequilibriumandboundarycondihons,andtheirsolutioncanbereliedonlyonspecialtechnique.Thusthosemethodswouldbedifficulttobepopularized.Ref.[7]clarifiedtheimportanceofdriedstateequationofelasticity,andfirStgaveHndltoncanonicalequationbymodifyingHellinger-Reissuervariationalprinciple.AtthesametimeTangL'I…     

轴对称层合圆柱壳混合状态方程的弱形式及其边值问题

从Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，在柱坐标系中，导出圆柱壳轴对称问题的弱形式混合状态方程和边界条件，联用状态空间法给出强厚度叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。     

Non-linear theory of shells

A partially non-linear theory of anisotropic shells of uniform thickness is presented. Variational integrals of the stress equations of motion (26) and boundary conditions (27) consistent with simplified strain-displacement relations (9) are obtained from the Hamilton principle. The displacements and deflection are assumed to vary linearly across the thickness of the shell. The transverse shear and transverse normal strains as well as rotatory inertia and thermal effects are included in the analysis. One special case of the final equations of motion is considered.     

扁球壳的边界元几何非线性分析

本文从壳体位移的三个微分方程出发，采用付立叶积分变换的基本解，利用加权残值法推导了几何非线性边界积分方程。这种基本解的壳体边界元法类似于板的非线性边界元法，各种变量物理意义明确，能方便地处理各种复杂边界条件及有开口情况。文末算例说明本文方法的可行性、收敛性和精确性，并与二变量边界单元法或有限元结果相比较，吻合较好。     

SANDERS薄壳方程的自共轭性

本文对Sanders薄壳方程的自共轭性作了讨论.证明了以下三点: 1.通常的齐次边界条件是简单自共轭边界条件; 2.在简单自共轭边界条件下,Sanders薄壳方程是自共轭的、其蜕化(元矩)方程也是自共轭的; 3.任何薄壳理论,其满足功的互等定理与具有自共轭性所需条件是相同的: 作为6个变形分量的正定二次型的应变能函数存在. 由于Sanders薄壳理论在任意曲线坐标系中成立,故以上结论亦适用于任意曲线坐标系. 本文的讨论为采用Sanders理论对薄壳进行动力分析提供了理论准备.     

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL I： GENERALIZED VARIATIONAL THEORETICAL MODELING

Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.     

Free vibrations of multilayered doubly curved shells based on a mixed variational approach and global piecewise-smooth functions

This paper presents the extension of a two-dimensional model that, recently appeared in literature, deals with freely vibrating laminated plates. The extension takes into account the corresponding theory describing the dynamic of freely vibrating multilayered doubly curved shells. The relevant governing differential equations, associated boundary conditions and constitutive equations are derived from one of Reissner’s mixed variational theorems. Both the governing differential equations and the related boundary conditions are presented in terms of resultant stresses and displacements. In spite of the multi-layer nature of the shell, the theory is developed as if the shell were virtually made of a single layer. This choice does not limit the performances of the model, which are comparable to the corresponding three-dimensional theory. This ability is accomplished by an appropriate global expansion of the relevant kinetic and stress quantities, through the thickness of the multilayered shell. The mentioned expansion is realized by a novel selection of global piecewise-smooth functions. Numerical tests illustrate the performance of the model with respect to several elements subjected to a class of simply supported boundary conditions: plates, circular cylindrical shells, spherical and saddle-shape laminates. The model is first tested by comparing its resulting eigen-parameters, with those few existing of exact or approximate three-dimensional models and, finally, new results are provided for several geometrical and material characteristics for plates and shells.     

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL-Ⅰ: GENERALIZED VARIATIONAL THEORETICAL MODELING

Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which axe coincident with the ones in literature.     

圆锥壳结构自振特性的多项式解

本文研究了圆锥壳结构自振特性的多项式解。文中利用Hamilton原理,采用Love薄壳简化假设,设位移为不受边界条件限制的多项式解,通过求解能量法的特征方程得到结构的自然频率。文中给出了数值算例。与有限元模拟得到的结果比较,吻合得非常好。     

基于区域分解的环肋圆柱壳-圆锥壳组合结构振动分析

提出了一种区域分解法来分析不同边界条件下环肋骨圆柱壳-圆锥壳组合结构的振动特性.首先把组合壳体分解为自由的圆柱壳、圆锥壳段;视环肋骨为离散元件,根据肋骨与圆柱壳段之间的变形协调条件,将肋骨的动能和应变能附加于圆柱壳段能量泛函中.然后基于分区广义变分和最小二乘加权残值法将所有分区界面的位移协调方程引入到组合壳体的能量泛函中.圆柱壳段、圆锥壳段位移变量的周向和轴向分量分别采用Fourier级数和Chebyshev多项式展开.以自由-自由、自由-固支和固支-固支边界条件的环肋骨组合壳体为例,采用区域分解法分析了其自由振动及在不同激励下的振动响应.通过与有限元软件ANSYS结果进行对比,发现两种方法计算结果非常吻合,验证了区域分解方法的计算精度和高效性.     

A generalized variational principle of composite shallow shells and its application to the folded shell

In this paper, a generalized variational principle of elastodynamics in composite shallow shells with edge beams is presented, and its equivalence to corresponding basic equations, ridge conditions and boundary conditions is proved. Then this variational principle is applied to the folded shell structure. By means of double series, the approximate analytical solutions for statics and dynamics under common boundary conditions are obtained. The comparison of our results with FEM computations and experiments shows the analytical solutions have good convergence and their accuracy is quite satisfactory.     

拉压性能不同材料厚壁圆筒和厚壁球壳的极限压力分析

本文用广义双剪应力强度理论对拉压性能不同的材料制成的厚壁圆筒和厚壁球壳进行了弹塑性应力分析，得出与拉压比有关的弹性极限内压力、塑性极限内压力、弹塑性区的应力以及弹塑性内压力与弹塑性半径之间的关系式．     

夹层扁球壳的非线性稳定性

基于Reissner假设和变分原理,给出夹层扁球壳在均布压力作用下的大挠度方程,采用修正迭代法求得了夹层扁球壳非线性稳定问题的解析解,得到两类边界条件下临界屈曲载荷的表达式,讨论了几何参数和物理参数对临界屈曲载荷的影响     

A polar theory for vibrations of thin elastic shells

In relation to a polar continuum, this paper presents a 2-D shear deformable theory for the high frequency vibrations of a thin elastic shell. To begin with, the 3-D fundamental equations of the micropolar elastic continuum are expressed as the Euler–Lagrange equations of a unified variational principle. Next, the kinematic variables of the shell are represented by the power series expansions in its thickness coordinate, and then, they are used to establish the 2-D theory by means of the variational principle. The 2-D theory is derived in invariant variational and differential forms and governs all the types of vibrations of the functionally graded micropolar shell. Lastly, the uniqueness is investigated in solutions of the initial mixed boundary value problems defined by the 2-D theory, and some of special cases are indicated in the theory.