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     

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     

变厚度圆柱壳的轴对称弯曲问题

本文详细地研究了厚度h=h_0ξ~的圆柱壳的轴对称弯曲问题.文中通过引入一个位移函数H(ξ),将该问题的方程组化成一个关于H(ξ)的6阶常微分方程,用广义超几何函数给出问题的精确解.     

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...     

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)     

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.     

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。     

Jump Conditions in the Non-linear Theory of Thin Irregular Shells

The non-linear theory of thin shell structures with irregularities of geometry, material properties, loading and deformation is developed. The irregular shell is modelled by a reference network being a union of piecewise smooth surfaces and curves, with various fields satisfying relaxed regularity requirements. By transforming the virtual work principle postulated for the entire reference network, we derive the corresponding local field equations and side conditions. Particular attention is paid to formulate the general form of static and kinematic jump conditions at singular geometric and physical curves. Several special kinds of irregularities are considered and some particular forms of the jump conditions are discussed.     

Solution of Some Structural Analysis Problems by Orthogonal Collocation

Abstract

Application of the method of orthogonal collocation to boundary value problems in structural and applied mechanics is investigated. Typical boundary value problems, such as the torsion of rectangular bars and the bending of plates, are employed as illustrative examples. Simplicity in application and good accuracy of orthogonal collocation are demonstrated by the solution of such complex problems as the large deflection analysis of rectangular isotropic, orthotropic, and sandwich plates. Results are compared wherever possible with existing solutions based on much more laborious and lengthy methods of computation. Excellent agreements are obtained.     

Influence of Variable Thickness on Displacements and Stresses in Nonthin Cylindrical Orthotropic Shells with Elliptic Cross-Section

The influence of varying thickness at constant mass on the stress–strain state of orthotropic cylindrical shells with elliptic cross-section is analyzed by solving two-dimensional boundary-value problems     

Forced Geometrically Nonlinear Vibrations of Thin Shells of Revolution with Piezoelectric Layers*

International Applied Mechanics - A combined numerical-and-analytical technique for studying the geometrically nonlinear vibrations of thin shells of revolution with piezoelectric layers is...     

变刚度层叠梁的力学性能研究

为满足不同场景下的功能需求,变刚度结构得到越来越广泛的应用．以机器人手臂为例,在执行操作时,需要其手臂的结构刚度足够大,避免出现过大的扭曲和变形,而在与人交互时,又需要其结构足够柔软,以保证在此过程中与人交互的安全性．该类变刚度结构可根据需求通过外部激励在柔性和刚性状态之间自由切换．在该文章中,研究分析了层叠梁结构,通过理论推导和数值模拟,对其力学性能做出了很好的预测,同时为此类结构的研究提供了有效可靠的思路和方法．     

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

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The Matching Property of Infinitesimal Isometries on Elliptic Surfaces and Elasticity of Thin Shells

Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h ^β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W ^2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.