An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference

This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms, five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of material inhomogeneity on the elastic and electric fields is discussed. Supported by the National Natural Science Foundation of China (Grant Nos. 10472102 and 10432030) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335107)     

Dynamic Behavior of Rigid–Plastic Sector Plates

The paper studies the dynamic behavior of perfect rigid-plastic plates in the form of a sector with hinged or clamped sides under short-term intensive loads. Two dynamic deformation mechanisms are demonstrated. The dynamic equation is derived for each of the mechanisms. The realization conditions for the mechanisms are analyzed. Analytical expressions are derived for the ultimate (high) loads and the maximum residual deflection. Numerical examples are given     

复合材料迭层板弯曲分步分析法

本文提出了一种用于分析复合材料迭层板弯曲的新方法。首先利用经典理论进行初步分析,之后,据所得横向剪力,设定横向剪切应变,再进一步分析。本文方法基本未知函数少,基本方程易解,计算精度较高。     

Post-bucking of angle-ply laminated plates under thermal loading

Notionsa. b, h Plate dimensionsL', [-. [1- mid-plane displacement componentsu- v- Ic dboensionless mid-plane displacement componentsVy., ac'~ slOPeS in xo and gi plane, ropectivelyJll, N number of terms in Cheby-shev series in x and y directions, respectivelyCCCC all edges clampedSSSS all edges simply supportedCCCS three edges (x = fi and y = 1) clamped and one (y = --1) simply supportedCCSS two edges (x = 11) clamped and two (y = fi) simply supportedCSSS one edge (x = --1) clamped …     

Exact Equilibrium Solutions for Linearly Elastic Plate-Like Bodies

A three-dimensional, explicit and exact, equilibrium solution is derived for transversely isotropic, linearly elastic bodies in the form of a right cylinder simply supported over its lateral boundary and loaded over its end faces. This solution, which generalizes an earlier proposal of Levinson in various respects, is to serve as a benchmark for the corresponding plate theories. This revised version was published online in August 2006 with corrections to the Cover Date.     

Applications of the Poincaré sphere in polarization metrology

The Poincaré sphere representation of polarization states is used to derive two auxiliary equations for phase retardance measurements. These equations, in addition to another two previously derived equations, allow for extending the range of validity of a model for calibrating phase plates in pairs. In another application, the sphere is used to explain a new method for identifying the principal axes of two birefringent phase plates during their calibration.     

The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions

In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions. Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced. Numerical results of solving the problems for polygonal and ferroconcrete plates are presented. Communicated by A. Zhou.     

用功的互等定理求解矩形薄板的自然频率

从虚功原理出发，证明了薄板小挠度弯曲问题的功的互等定理，并由此推出了求解矩形薄板自然频率的公式．算例表明，该公式计算简便，精度较高．