基于混合变量条形传递函数方法的圆柱壳屈曲分析

提出了一种分析交各向异性圆柱壳和阶梯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Fluegge薄壳理论，通过定义广义位移变量和对应的广义力变量，建立了圆柱壳混合变量能量泛函；然后通过引入条形单元，定义混合状态变量和采用传递函数方法对超级壳单元求解，得到具有多种边界条件圆柱壳屈曲问题的半解析解；最后通过位移连续和力平衡条件，可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。     

The R-function method used to solve nonlinear bending problems for orthotropic shallow shells on an elastic foundation

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied     

Three-dimensional free vibration analysis of rotating laminated conical shells: layerwise differential quadrature (LW-DQ) method

This paper focuses on the free vibration analysis of thick, rotating laminated composite conical shells with different boundary conditions based on the three-dimensional theory, using the layerwise differential quadrature method (LW-DQM). The equations of motion are derived applying the Hamilton’s principle. In order to accurately account for the thickness effects, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equation applying the DQM in the meridional direction. This study demonstrates the applicability, accuracy, stability and the fast rate of convergence of the present method, for free vibration analyses of rotating thick laminated conical shells. The presented results are compared with those of other shell theories obtained using conventional methods and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell and excellent agreements are achieved.     

Nonlinear bending of corrugated diaphragm with large boundary corrugation under compound load

IntroductionCorrugateddiaphragmisatypeofelasticthinshells .Itsdesignisverycomplicatedbecauseoftoomanyparametersthatinfluenceeachother.Inanumberofinstrumentsmeasuringdisplacements,corrugateddiaphragmissubjectedtoelasticdisplacementthatisatleastthesameorderasitsthickness,sothatitisnecessarytousegeometricalnonlineartheoryofthinshellstoanalyze.Sofarasweknow ,inmostcases,investigatorsdiscussedonlytheproblemofcorrugateddiaphragmwithuniformanddensecorrugationsundertheactionofaunique(uniformlyorconcen…     

VIBRO-ACOUSTIC BEHAVIOR OF SUBMERGED CYLINDRICAL SHELLS: ANALYTICAL FORMULATION AND NUMERICAL MODEL

We propose both an analytical formulation and a numerical model to study the hydroelastic or vibroacoustic behaviour of cylindrical thin shells immersed in an unbounded, inviscid and heavy fluid. The analytical solution allows us to calculate the dynamic response and the pressure radiated in the far field by a baffled cylinder. This formulation uses the truncated modal basis of the dry structure to expand the displacements of the submerged shell. The analytical model is used as a reference in order to validate a numerical model which couples the finite element method (FEM) to the boundary element method (BEM). As opposed to the analytical formulation which is dedicated to baffled circular cylinders only, the numerical model allows us to treat any axisymmetric shell, such as cylindrical and spherical shells, or more complex shells of revolution. The structure is idealized by two-node ring finite elements and the boundary equation is solved using the method of singularities.     

R-function method in studying the vibrations of orthotropic shells with varying thickness

The paper proposes a method to study the natural vibrations of orthotropic shells with varying thickness. The method employs the R-function and Ritz methods. The use of R-functions allows examining shells with complex planform and different boundary conditions. The method is validated by comparing the results it produces with those obtained by other methods. The effect of geometrical (the shape of the shell, radius of curvature, shape of the hole, thickness) and mechanical (boundary conditions, angle of anisotropy axes) parameters on the spectrum of natural vibrations is analyzed     

Free vibrations of flexible shallow shells of complex shape

A method is proposed for studying the free vibrations of flexible shallow shells with a complex planform. The method is based on variational and R-function methods. The R-function method allows constructing a system of basis functions in an analytic form. This makes it possible to reduce the Donnell-Mushtari-Vlasov equations to Duffing equations. The amplitude-frequency characteristics of shallow shells with a complex planform are given for different curvatures and boundary conditions. The results obtained are compared with published results for simply supported square shells to demonstrate the reliability and efficiency of the method __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 99–109, April 2007.     

Determining the natural frequencies of highly inhomogeneous shells of revolution with transverse strain

A method of studying the natural vibrations of highly inhomogeneous shells of revolution is developed. The method is based on a nonclassical theory of shells that allows for transverse shear and reduction. By separating variables, the two-dimensional problem is reduced to a sequence of one-dimensional eigenvalue problems. The inverse iteration method is used to reduce these problems to a sequence of inhomogeneous boundary-value problems solved by the orthogonal sweep method. The capabilities of the method are illustrated by solving certain representative problems and comparing their solutions with those obtained using the three-dimensional theory of elasticity, the classical theory of shells, and the refined Timoshenko model __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 38–47, September 2007.     

均布载荷作用下具有光滑中心波纹膜片的非线性分析

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用格林函数方法，波纹膜片的非线性边值问题化为了非线性积分方程的求解。为了求解积分方程并防止发散，一个插值参数被引入到迭代格式中。计算表明，当载荷很小时，任何插值参数值均能保证迭代的收敛性，取插值参数值接近或等于1获得较快的收敛速度，而当载荷较大时，插值参数值不能取得过大。绘出了波纹膜片的特征曲线，得到的特征曲线可供设计参考。可以断言，当载荷不大时，特征曲线是近似线性的，随着载荷的增大，特征曲线开始向上弯曲，明显偏离线性。本文中提出的解决方法适应于任意轴向截面的波纹壳体。     

Free vibration of functionally graded truncated conical shells under internal pressure

The influence of internal pressure on the free vibration behavior of functionally graded (FG) truncated conical shells are investigated based on the first-order shear deformation theory (FSDT) of shells. The initial mechanical stresses are obtained by solving the static equilibrium equations. Using Hamilton’s principle and by including the influences of initial stresses, the free vibration equations of motion around this equilibrium state together with the related boundary conditions are derived. The material properties are assumed to be graded in the thickness direction. The differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to discretize the governing equations and the related boundary conditions. The convergence behavior of the method is numerically investigated and its accuracy is demonstrated by comparing the results in the limit cases with existing solutions in literature. Finally, the effects of internal pressure together with the material property graded index, the semi-vertex angle and the other geometrical parameters on the frequency parameters of the FG truncated conical shells subjected to different boundary conditions are studied.     

Solution of elastic-plastic shallow shell problems by the boundary element method

The boundary integral equations for elasto-plastic problems of shallow shells are established by using the fundamental solutions of shallow shells derived previously. The strains and stress-resultants in the plastic region are used as unknown variables. The simultaneous nonlinear equations of these variables and unknown boundary values are established and solved by direct iteration method.     

Nonlinear axisymmetric deformation of anisotropic spherical shells

A method of solving problems of nonlinear deformation of anisotropic spherical shells with consideration of critical points and postcritical behavior is outlined. The method employs the method of incremental loading in which the load increment is specified with an unknown coefficient determined as an unknown function equivalent to the other ones. The algorithm is based on the numerical discrete-orthogonalization method, which allows analyzing the deformation path for a number of shells with different anisotropy parameters     

Unitive analysis schemes on problems of multiple moving boundaries with 3-D liquid-solid multiple nonlinear coupling for uplift of anchored liquid storage tanks

I.Intr0ducti0nAnchored1iquidstoragetanksareextensivelyusedinbusiness,nuclearpowerplants,spaceflightandpetrochemicalindustry.Theystoragepetrochemicalproductions0fover9Opercentintheworld.Theanchoredliquidstoragetanksarecontinuelydamagedduringearthquakestoha…     

薄壳问题的一种数值解法

本文直接从三维弹性力学微分方程出发,依据三维的Kelvin解,应用最小二乘法建立了三维虚边界元法解薄壳问题的一般方法。本方法的显著优点是：不论求解何种壳体问题,思想是不变的,均以三维的Kelvin解来建立方程,而勿需对不同几何形状的壳本采用不同的基本解。文中给出了数值算例,以作为本方法的应用。本文方法与边界元直接法相比,优点在于无需处理奇异积分,且系数阵是对称的;再者,本文方法思想简单,程序实现容易。     

Conforming radial point interpolation method for spatial shell structures on the stress-resultant shell theory

The implementation of the conforming radial point interpolation method (CRPIM) for spatial thick shell structures is presented in this paper. The formulation of the discrete system equations is derived from a stress-resultant geometrically exact theory of shear flexible shells based on the Cosserat surface. A discrete singularity-free mapping between the five degrees of freedom of the Cosserat surface and the normal formulation with six degrees of freedom is constructed by exploiting the geometry connection between the orthogonal group and the unit sphere. A radial basis function is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometries. The major advantage of the CRPIM is that the shape functions possess a delta function property and the interpolation function obtained passes through all the scattered points in the influence domain. Thus, essential boundary conditions can be easily imposed, as in finite element method. A range of shape parameters is studied to examine the performance of CRPIM for shells, and optimal values are proposed. The phenomena of shear locking and membrane locking are illustrated by presenting the membrane and shear energies as fractions of the total energy. Several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the present CRPIM. The convergence rate of the results using a Gaussian (EXP) radial basis is relatively high compared to those using a multi-quadric (MQ) radial basis for the shell problems.     

Spline-approximation solution of problems of the statics of orthotropic shallow shells with variable parameters

An approach to the solution of problems of the statics of shallow orthotropic shells is proposed. It is based on reducing a two-dimensional boundary value problem to a one-dimensional one using the spline-collocation method and solution of the problem by the stable numerical method of discrete orthogonalization. Solutions are presented for problems on the stress state of orthotropic shells of double curvature for several values of the elastic constants of the material. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 60–66, July, 2000.     

Stability and limit states of elastoplastic spherical shells under static and dynamic loading

The problem of elastoplastic deformation, buckling, and postcritical behavior of spherical shells is solved using a finite element method and a cross-type explicit scheme of time integration. Stability problems for hemispherical shells under external pressure and compression between rigid plates are considered. The influence of holes and boundary conditions on shell deformation is investigated. It is shown that the calculation results are in good agreement with experimental data.     

Solving problems on the stress state of thin shells of revolution under local loads

An approach to the solution of problems on the deformation of locally loaded orthotropic shells of revolution is proposed. Some analytical transformations are carried out to reduce the initial resolving system of partial differential equations to the form where the constant terms representing the surface loads are continuous functions of the circumferential coordinate. This allows us to accelerate the convergence of the trigonometric series that represent the desired solution. One-dimensional boundary-value problems are solved by a stable numerical method. Examples of solving problems on the stress state of a cylindrical shell are presented. The scientific results of the present work were obtained during implementation of Project No. 14 of the Ukrainian Scientific and Technological Center. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 106–113, April, 2000.     

Stress–Strain Analysis of Smooth and Ribbed Shells under Local Loads

Static problems for smooth and discretely reinforced cylindrical shells under local loads and complex boundary conditions are solved. The stress–strain states of the casing and ribs are determined by the technical theory of shells and the Kirchhoff–Clebsch theory of rods, respectively. The reinforcing elements are arranged eccentrically. They are of equal or different stiffness, which is also variable along the length. The problems are solved using the finite-difference method. Theoretical results obtained from a refined mesh are compared with experimental data     

A model of layered prismatic shells

The present paper is devoted to a model for elastic layered prismatic shells which is constructed by means of a suggested in the paper approach which essentially differs from the known approaches for constructing models of laminated structures. Using Vekua’s dimension reduction method after appropriate modifications, hierarchical models for elastic layered prismatic shells are constructed. We get coupled governing systems for the whole structure in the projection of the structure. The advantage of this model consists in the fact that we solve boundary value problems separately for each ply. In addition, beginning with the second ply, we use a solution of a boundary value problem of the preceding ply. We indicate ways of investigating boundary value problems for the governing systems. For the sake of simplicity, we consider the case of two plies, in the zeroth approximation. However, we also make remarks concerning the cases when either the number of plies is more than two or higher-order approximations (hierarchical models) should be applied. As an example, we consider a special case of deformation and solve the corresponding boundary value problem in the explicit form.