The exact solution for thick laminated cantilever cylindrical shell

Discarding any assumption regarding displacement or stress models, the state equation for orthotropy is established in a cylindrical system. The exact solution is presented for the statics of thick closed laminated cantilever cylindrical shells. Every equation of elasticity can be satisfied and all the elastic constants are taken into account. Arbitrary precision of a desired order can be obtained. Project supported by the National Natural Science Foundation of China     

Exact solution for laminated continuous open cylindrical shells

I.Introducti0nNowadays,thecurrenttheoriesofplatesandshe1ls,suchasthetheoriesofReissner's,KirchhoffLove'sandAmbartsumyan'setc,areestablishedons0mehypotheses.Forexample-assumethatthemechanicalquantitiesarethepolynomialsofacertaincoordinatevariable.Itisshown…     

Exact solution of the thick laminated open cylindrical shells with four clamped edges

ＥＸＡＣＴＳＯＬＵＴＩＯＮＯＦＴＨＥＴＨＩＣＫＬＡＭＩＮＡＴＥＤＯＰＥＮＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳＦａｎＪｉａ－ｒａｎｇ（范家让）（ＨｅｆｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ）ＨｅｆｅｉＤｉ...     

The solution of weak formulation for axisymmetric problem of orthotropic cantilever cylindrical shell

Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell is presented, and thermal stresses mixed state equation for axisymmetric problem of closed cantilever cylindrical shell is established. A unified approach and weak solutions are obtained for closed laminated cantilever cylindrical shell of arbitrary thickness under thermal and mechanical loadings. The equation and boundary conditions proposed in this paper are weakened, the method of this paper would be easy to popularize in dynamics analysis of elasticity. Foundation item: the National Natural Science Foundation of China (19392305)     

Analytical solution of radiation sound pressure of double cylindrical shells in fluid medium

ＩｎｔｒｏｄｕｃｔｉｏｎＳｏｕｎｄｒａｄｉａｔｉｏｎｆｒｏｍｔｈｅｄｏｕｂｌｅｓｈｅｌｌｓｗｈｉｃｈａｒｅｔｈｅｍａｉｎｓｔｒｕｃｔｕｒｅｏｆｓｕｂｍａｒｉｎｅｈｕｌｌｓｕｎｄｅｒｅｘｃｉｔａｔｉｏｎｉｎｆｌｕｉｄｍｅｄｉｕｍｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｆｏｒｓｔｕｄｙｉｎｇｔｈｅｓｕｂｍａｒｉｎｅｈｉｄｉｎｇｔｅｃｈｎｏｌｏｇｙ .Ｆｏｒｔｈｅｖｉｂｒａｔｉｏｎｃｈａｒａｃｔｅｒｉｓｔｉｃｏｆｄｏｕｂｌｅｃｏｎｃｅｎｔｒｉｃｓｈｅｌｌｓ,ｉｔｈａｓｂｅｅｎｓｔｕｄｉｅｄｏｎｔｈｅｏｒｙａｎｄｅ…     

矩形悬臂薄板的解析解

首先把弹性薄板弯曲问题的控制方程表示成为Hamilton正则方程,然后利用辛几何方法对全状态相变量进行分离变量,求出其本征值后,再按本征函数展开的方法求出矩形悬臂薄板的解析解。由于在求解过程中不需要事先人为地选取挠度函数,而是从薄板弯曲的基本方程出发,直接利用数学的方法求出可以满足其边界条件的这类问题的解析解,使得问题的求解更加理论化和合理化。文中的最后还给出了计算实例来验证本文所采用的方法以及所推导出的公式的正确性。     

An exact symplectic solution for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates

From the mixed variational principle, by the selection of the state variables and its dual variables, the Hamiltonian canonical equation for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates is derived, leading to the mathematical frame of symplectic geometry and algorithms, and the exact solution for the arbitrary boundary conditions is also derived by the adjoint orthonormalized symplectic expansion method. Numerical results are presented with the emphasis on the effects of length/thickness ratio, arbitrary boundary conditions, degrees of anisotropy, number of layers, ply-angles and the corrected coefficients of transverse shear.     

Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load

Summary An exact axisymmetric piezothermoelastic solution is presented for a simply-supported hybrid cylindrical shell made of cross-ply composite laminate and piezoelectric layers. Numerical results for hybrid shells are presented for sinusoidal and central band thermal and electrical loads. The effect of the loading, the radius-to-thickness ratio, the span-to-radius ratio and the number of layers of the substrate on the response is investigated. The interface between the substrate and the actuated piezoelectric layer has been found to be subjected to high shear stress. It has been shown that the maximum values of the deflection and the stresses, due to thermal load, can be appreciably reduced by appropriate application of actuation potential. Accepted for publication 13 October 1996     

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…     

ANALYTICAL SOLUTION OF RADIATED SOUND PRESSURE OF RING－STIFFENED CYLINDRICAL SHELLS IN FLUID MEDIUM

ＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＯＦＲＡＤＩＡＴＥＤＳＯＵＮＤＰＲＥＳＳＵＲＥＯＦＲＩＮＧ－ＳＴＩＦＦＥＮＥＤＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＩＮＦＬＵＩＤＭＥＤＩＵＭＸｉｅＧｕａｎｍｏ（谢官员模）ＬｕｏＤｏｎｇｐｉｎｇ（骆东平）（Ｒｅｃｅｉｖ...     

叠层连续柱壳热应力问题的弱形式研究

建立了弹性力学基本方程的弱形式,从而得到叠层连续柱壳混合状态方程的边界条件放在一起的算子方程,扩大了求解空间,给出叠层连续闭口柱壳在热荷载和机械荷载作用下的解析解。     

任意厚度层合闭口柱壳的轴对称温度应力

基于层合柱壳混合状态方程和边界条件的弱形式，在轴对称情况下，建立了两端固支层合闭口柱壳的温度应力混合方程，给出了任意厚层合柱壳在温度荷载和机械荷载共同作用下的解析解。     

Buckling analysis of laminated cylindrical shells by 3-D multilayer hybrid element

A 3-D multilayer hybrid element is developed for the analysis of thick laminated plates and shells. The stresses are assumed independently in each sublayer element and the stress continuity between adjacent sublayers is applied to form the stress pattern of the multilayer element. Both interlaminar stress concentration and global structure response can be adequately predicted by the element model. The buckling analysis of orthotropic cylindrical shells under the external pressure is performed and the results show that the plane strain assumption is not applicable to the buckling of long orthotropic cylindrical shells.     

Stress analysis of flexible noncircular cylindrical shells with hinged edges for different critical loads

An analytic nonlinear boundary-value solution is found and used in analysis of the precritical and postcritical stress states of a flexible long cylindrical shell with variable curvature and hinged longitudinal edges under nonuniform loading __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 43–50, February 2006.     

A general solution of axisymmetric problem of arbitrary thick spherical shell and solid sphere

In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions in forms of Legendre series for thick spherical shell and solid sphere are given by using the method of weighted residuals.     

Solution of the deformation problem for flexible noncircular cylindrical shells subject to bending moments at the edges

An exact analytical solution is found to a nonlinear boundary-value deformation problem for a long noncircular cylindrical shell of variable curvature. The shell is subject to bending moments at the edges. The dependence of the stress-strain state of the shell on the curvature is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 93–100, November 2006.     

The general solution for the stress problem of circular cylindrical shells with an arbitrary cutout

I.IntroductionIncircularcylindricaIsheIls.likeaircraftfuselages,deep-diving\-ehicles.pressurevesselsandoiIlines,openingsareinvariabl}'necessaryforavarietyoffunctionalrequirements.Stressconcentrationsonthecontourofcircularornon-circu1arcutoutsreducebearing…     

On two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic bimodulus materials

The paper compares two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different elastic moduli in tension and compression. The approaches use different nonlinear constitutive equations describing the elastic deformation of the transversally isotropic bimodulus materials. Both approaches employ the theory of deformation along paths of small curvature and the Kirchhoff-Love hypothesis for the whole laminate to describe the deformation of the isotropic materials. The problem is solved by the method of successive approximations. The solutions of specific problems obtained by the two approaches are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 59–69, June 2008.     

Analytical solutions for plane problem of functionally graded magnetoelectric cantilever beam

In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magneto-electro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.     

在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。