Nonlinear deformation and stability of oval cylindrical shells under pure bending and internal pressure

The stability problem of a cylindrical shell of oval cross section loaded by a bending moment and internal pressure is studied. The variational displacement finite-element method is used. For the prebuckling stress-strain state, the bending and nonlinearity are taken into account. The effects of the nonlinear nature of the deformation and the cross-sectional ovality of the shells on the critical loads and buckling modes are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 119–125, May–June, 2006.     

Nonlinear Deformation and Stability of Elliptic Cylindrical Shells under Torsion and Bending

The problem of nonlinear deformation and buckling of noncircular cylindrical shells under combined loading is solved by the variational finite-element method in the displacement formulation. A numerical algorithm for solving the problem is proposed. Stability of cylindrical shells with an elliptic cross-sectional contour under a combined action of torsion and bending is analyzed. The effect of cross-sectional ellipticity and nonlinear prebuckling deformation on the critical loads and buckling mode is studied.     

复合材料层合圆柱壳的有限元分析

本文根据Reissner-Mindlin型的全局位移场(一阶和三阶)，应用有限元预测一修正法，数值计算和分析了机械载荷作用下复合材料层合圆柱壳的挠度和横向剪应力。首先按照一般的有限元分析过程(没有引入剪切修正系数)计算出层合圆柱壳的挠度预测值；然后利用Lagrange插值构造横向剪应力的一般形式，使得满足层间连续和表面上为零的条件，通过最小二乘法拟合三维应力平衡方程获得横向剪应力；最后在单元上计算和引入剪切修正系数，再经过有限元分析计算出层合圆柱壳的挠度修正值。数值计算结果与三维线弹性解的比较表明，挠度修正值和横向剪应力的精度是十分满意的。     

Inelastic deformation of flexible cylindrical shells with an elliptic hole

The elastoplastic state of isotropic homogeneous cylindrical shells with elliptic holes and finite deflections under internal pressure is studied. Problems are formulated and numerically solved taking into account physical and geometrical nonlinearities. The distribution of stresses (displacements, strains) along the boundary of the hole and in the zone of their concentration is analyzed. The data obtained are compared with the numerical solutions of the physically nonlinear, geometrically nonlinear, and linear problems. The stress-strain state of cylindrical shells in the neighborhood of the elliptic hole is analyzed with allowance for nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 46–54, May 2007.     

Nonlinear stability of a defective cylindrical shell

A cylindrical shell with a shape defect is studied. A one DOF modelling is derived. Its nonlinear behaviour is investigated by using both harmonic balance method and normal form theory. Stability domains are computed according to 2 parameters related to the frequency and the amplitude of the external forcing.     

Initial postbuckling behavior of cylindrical composite shells under axisymmetric deformation

A solution is obtained that describes the postbuckling behavior of cylindrical shells in the case of axisymmetric buckling. The basis for this solution is Koiter’s asymptotic method and the nonlinear equations of the third-order Timoshenko theory of shells. It is shown that the bifurcation point in this case is a symmetrically unstable one. The effect of the initial axisymmetric deflections on the buckling loads is weaker when buckling is axisymmetric. The results obtained by Koiter’s special theory evidence this __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 108–118, April 2006.     

侧向不均匀冲击下环向加筋圆柱壳的动力响应

针对空投鱼雷入水冲击问题,研究了环向加筋圆柱壳在侧向不均匀冲击载荷作用下的动力响应。考虑了壳体剪切变形、转动惯性以及加筋肋骨的拉伸、弯曲和剪切变形,运用Hamilton变分原理推导出了运动方程,并且采用一种半解析有限差分法进行了求解。分析了加肋数目、截面宽度比及加筋形式等因素对结构动力响应的影响。     

Inelastic deformation of flexible cylindrical shells with a curvilinear hole

The elastoplastic state of thin cylindrical shells weakened by a curvilinear (circular) hole is analyzed considering finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distributions of stresses (strains, displacements) along the hole boundary and in the zone of their concentration are studied. The results obtained are compared with solutions that account for physical (plastic strains) or geometrical (finite deflections) nonlinearity alone and with a numerical linear elastic solution. The stress-strain state around a circular hole is analyzed for different geometries in the case where both nonlinearities are taken into account __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 115–123, December, 2006.     

Studies of nonlinear deformation and stability of stiffened oval cylindrical shells under combined loading by bending moment and boundary transverse force

The finite-element statement of stability problems for stiffened oval cylindrical shells is presented with the moments and the nonlinearity of their subcritical stress-strain state taken into account. Explicit expressions for the displacements of elements of noncircular cylindrical shells as solids are obtained by integration of the equations derived by equating the linear deformation components with zero. These expressions are used to construct the shape functions of the effective quadrangular finite element of natural curvature, and an efficient algorithm for studying the shell nonlinear deformation and stability is developed. The stability of stiffened oval cylindrical shells is studied in the case of combined loading by a boundary transverse force and a bending moment. The influence of the shell ovality and the deformation nonlinearity on the shell stability is investigated.     

Dynamic stability of viscoelastic circular cylindrical shells taking into account shear deformation and rotatory inertia

The present work discusses the problem of dynamic stability of a viscoelas- tic circular cylindrical shell,according to revised Timoshenko theory,with an account of shear deformation and rotatory inertia in the geometrically nonlinear statement.Pro- ceeding by Bubnov-Galerkin method in combination with a numerical method based on the quadrature formula the problem is reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.For a wide range of vari- ation of physical mechanical and geometrical parameters,the dynamic behavior of the shell is studied.The influence of viscoelastic properties of the material on the dynamical stability of the circular cylindrical shell is shown.Results obtained using different theories are compared.     

Nonlinear stability of truncated shallow conical sandwich shell with variable thickness

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Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response of the cylindrical shell is discussed. The results obtained by various theories are compared.     

Postbuckling of imperfect stiffened cylindrical shells under combined external pressure and heating

1.IntroductionStiffenedcylindricalshellsarewidelyusedinmanytypesofstructures.Inpracticetheyoftensubjecttovarioustypesofcombinedthermalandmechanicalloadingandmayhavesignificantandunavoidableinitialgeometricalimperfections.Therefore,thepostbucklingbehaviorofimperfectstiITenedcylindricalshellsundercombinedexternalpress.ureandthermalloadingmustbewellunderstood.Manypostbucklingstudieshavebeenmadetbrstiffenedcylindricalshellsunderpureaxialcompression,uniformexternalpressureortheircombinations,where…     

爆炸波作用下地下防护结构与围岩的非线性动力相互作用分析

针对实际地下工程中普遍存在的材料非线性以及半无限介质域的处理问题,给出了基于时间有关基本解的时域边界元法与非线性动力有限元法的耦合方法,应用该耦合方法计算了一马蹄形截面地下防护结构与围岩受爆炸冲击波作用下非线性相互作用的时间历程,并与线弹性情况进行了比较分析。结果表明:本文的方法具有较高精度,真实地再现了波在弹性层中传播以及反射的全过程。     

Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure

The nonlinear large deflection theory of cylindrical shells is extended to discuss nonlinear buckling and postbuckling behaviors of functionally graded (FG) cylindrical shells which are synchronously subjected to axial compression and lateral loads. In this analysis, the non-linear strain-displacement relations of large deformation and the Ritz energy method are used. The material properties of the shells vary smoothly through the shell thickness according to a power law distribution of the volume fraction of the constituent materials. Meanwhile, by taking the temperature-dependent material properties into account, various effects of external thermal environment are also investigated. The non-linear critical condition is found by defining the possible lowest point of external force. Numerical results show various effects of the inhomogeneous parameter, dimensional parameters and external thermal environments on non-linear buckling behaviors of combine-loaded FG cylindrical shells. In addition, the postbuckling equilibrium paths are also plotted for axially loaded pre-pressured FG cylindrical shells and there is an interesting mode jump exhibited.     

Nonlinear aeroelastic coupled trim and stability analysis of rotor-fuselage

Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.     

空间杆系与叠层板组合结构的非线性稳定分析

本文用非线性有限元法研究一种空间杆系与复合材料叠层板组合结构的非线性稳定问题。将杆系离散成空间梁柱单元，将复合材料叠层板离散成复合材料叠层板单元，并考虑了几何非线性和板的成层正交各向异性性质。为了获得较高的计算效率并顺利通过稳定临界点，求解非线性平衡方程采用了变增量步长和柱面弧长法迭代策略。在考证了程序的正确性之后，具体分析了几个工程模型，得出了于工程设计有益的结论。     

板壳畸变单元的无网格和有限元自动耦合方法

板壳大变形时单元的严重畸变会使计算精度降低。无网格局部Petrov-Galerkin法是一种真正的无网格方法,能够消除网格畸变,但比有限元法计算效率低。根据板壳网格畸变的局部性特点,利用过渡单元法,基于板壳网格质量,建立了板壳的网格严重畸变区域由有限元分析切换为无网格分析的自动耦合算法,实现了有限元法和无网格局部彼得罗夫．迦辽金法的耦合。应用实例表明：通过自适应耦合,既能发挥有限元法计算效率高的特点,又能发挥无网格法适合大变形分析、没有网格畸变造成计算困难的特点。     

Stability of cylindrical shells with one plane of elastic symmetry under axial compression and torsion

A numerical technique is developed for stability analysis of laminated cylindrical shells with one plane of symmetry subject to axial compression and torsion. Shells filament-wound in directions other than the coordinate axes are considered as a special case. These shells are analyzed for stability under axial compression, external pressure, and torsion. It is shown that shells with a great number of plies and different ply angles may be considered orthotropic __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 115–121, August 2006.     

Nonlinear stability of truncated shallow spherical shell with variable thickness under uniformly distributed load

I.Intr0ducti0nTheclampedtruncatedshailowsphericalshellwithanondeformablerigidbodyatthecenterisoftenusedinstructureandelasticcomponentofprecisioninstrument.Inthebuildingengineering,wemustpreventtheshelllosingstability.Butintheelasticcomponent0fprecisionins…