Stability and Natural Vibrations of Shells with Variable Geometric and Mechanical Parameters

The bifurcation stability and natural vibrations of shells of revolution with variable geometric and mechanical parameters are studied by using refined models and the variational–difference method. The qualitative and quantitative effects of the external geometry, material properties, and design features on the critical load and natural frequency are evaluated     

A Note on the Iterative Solution of Stress Problems for Plates and Shallow Shells

A technique based on a refined iterative theory and the numerical method of local variations is developed and used to determine the stress–strain state of transversely isotropic shallow shells and plates. All the components of the stress–strain state and boundary-layer effects are taken into account. The solutions are analyzed for accuracy and convergence.     

Numerical and Analytical Approaches to the Stability Analysis of Imperfect Shells

Two new approaches are proposed for the numerical and analytical stability analyses of imperfect shells. One approach is based on the generalized mesh method, whereas the other employs a modified reduced-stiffness method. Both approaches apply to shells with initial geometrical imperfections. Numerical results are compared with experimental data for shells with a single dent. Analytical results are also presented and compared     

Linear and Nonlinear Problems on the Elastic Deformation of Complex Shells and Methods of Their Numerical Solution

Some approaches to the solution of problems on the elastic deformation of thin-walled solids with a complex shape are analyzed on the basis of linear and geometrically nonlinear models. The general characteristic of the classical approaches to the solution of the problems is discussed. Approaches employing new classes of surfaces are considered. Solutions to some problems on the stress state of complex shell elements are presented     

A Method for Solving Two-Dimensional Nonlinear Boundary-Value Problems of Magnetoelasticity for Thin Shells

A method is proposed to solve two-dimensional nonlinear problems of magnetoelasticity for thin shells. A problem is formulated and two-dimensional nonlinear equations of magnetoelasticity for current-carrying shells are derived__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 32–39, May 2005.     

Influence of Geometrical Parameters on the Critical Load in Three-Dimensional Stability Problems for Rectangular Plates and Beams

Two- and three-dimensional stability problems for a rectangular plate under uniaxial compression are solved by the mesh method. It is shown that the difference between the critical loads obtained in the three- and two-dimensional problems is not greater than 5% for arbitrary fixation conditions and arbitrary length and thickness ratio of the plate     

Solution of Physically Nonlinear Problems of the Theory of Orthotropic Shells Using Mixed Functionals

Variants of the theory of nonlinearly elastic orthotropic shells are outlined depending on the relations between the parameters of their composite materials. The corresponding mixed linearized functionals are constructed. A system of resolvent equations that is adjusted to a specific variant of the theory with the help of special matrices is derived. The results of a strain analysis of a cylindrical shell with an opening for four variants of the theory are compared with experimental data     

Influence of the Mechanical and Geometric Parameters of Composite Cylindrical Shells with Local Deflection on the Behavior of the Equilibrium Curves Under Axial Compression

International Applied Mechanics - A procedure for analytical solution of the problem of the stability and post-buckling behavior of composite cylindrical shells with local deflection under axial...     

Numerical Solution of Dynamic Problems for Reinforced Ellipsoidal Shells under Nonstationary Loads

A dynamic problem for reinforced ellipsoidal shells under nonstationary loads is formulated and solved numerically. The results obtained are analyzed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 53–59, April 2005.     

Asymptotic Analysis of the Stresses in Thin Elastic Shells

. In this paper, we identify the limiting stress tensor of a thin elastic shell whose thickness approaches zero. In the linear case, we use a convergence result established for the displacement field in order to get the convergence of the contravariant components of the linearised stress tensor. In the nonlinear case, the identification of the first Piola‐Kirchhoff stress tensor is made through a formal asymptotic analysis. In both cases, we show that these limiting stress fields depend on the geometry of the shell and on the boundary conditions. (Accepted June 1, 1998)     

On the Buckling of Axially Compressed Thin Cylindrical Shells

ABSTRACT

A simple general method for the evaluation of the effect of shape imperfections on the buckling of thin shells is briefly presented. This method is applied to the axially compressed thin cylindrical shell resulting in an efficient numerical procedure for the computation of its buckling strength. The procedure is applicable to any sufficiently smooth imperfection pattern and has given results in good agreement with the available experimental data.     

正交各向异性板壳的弹塑性分析

用最小二乘配点法对正交各项异性薄板和双曲扁壳的弹性问题进行了分析.文中采用Huber—Mises屈服函数在各向异性问题中的推广形式,把材料的塑性变形作为等效塑性荷载处理,并取双五次样条函数为位移试函数,推出了迭代公式.算例证明,该法精度高、收敛快,所需计算机内存少,是简单、精确、高效的.     

Stress State of Thin Spherical Shells with an Off-Center Elliptic Hole

This paper is a numerical study into the joint effect of two factors of asymmetry—ellipticity and eccentricity—on the stress distribution near a hole. As a rule, this effect increases the maximum stresses. The deformation mode is determined in this case by the dominating factor. It is found out that the graphs of stress distribution around a small hole have a fixed point at which they intersect when the axial ratio varies within a wide range, which is typical of a central hole     

用广义样条子域法分析具有环形初始几何缺陷的圆柱壳

基于壳体初挠曲理论,对具有环形初始几何缺陷的圆柱壳进行了静力分析。整个缺陷区段视为由若干斜锥段组成。利用广义样条子域法建立了位移模式,该模式具有自由度少,结点设置灵活之特点。计算结果与有限元计算所得结果基本吻合。