构造上正交各向异性半球形凸起凹凸板等效刚度研究

根据半球形凹凸板周期性将其划分得到代表性体元结构.首先研究代表性体元的刚度特性,利用变形等效原理、均质化和刚度组合法得到半球形凹凸板的等效刚度.然后将得到的三个主向刚度代入四边简支板Navier解中求解板中心挠度.通过有限元数值模拟解和Navier解进行对比分析,从而验证该文得到的主向刚度的准确性.然后讨论了代表性体元的材料尺寸对所得等效刚度的影响.随着代表性体元边长与凸起半径的比值逐渐增大,所得结果精度越来越高,且等效刚度公式适用于不同厚度的半球形凹凸板.最后给出了较为简洁的工程应用公式,并给出了凸起半径的近似取值范围和工程应用算例.     

Minimum Stiffness Criteria for Edge Reinforcements of Elastically Clamped Plates

In many structural situations, e.g. in aerospace engineering, composite plates with edge reinforcements are used, for example as stiffeners of a fuselage section of an airplane. Based on an explicit analysis of the buckling behavior of the laminate plate, a minimum stiffness criterion is presented in this contribution. A transformation of the governing equations into a dimensionless system is used, that proved to be very advantageous. Besides a minimum stiffness criterion that can be used for generation of minimum stiffness diagrams, an absolute minimum stiffness is found that enables the reinforcement to act like a simple support for arbitrarily slender plates. The relevance of the criteria for stiffener design is discussed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Methods for Calculating Stiffness Properties of Periodic Structures

We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.     

Non-Asymptotic Modelling of Medium Thickness Plates with Plane Periodic Structure

The main aim of this contribution are presented a certain selected problems (aspects) of non–asymptotic modelling of medium thickness (or Reissner–type) rectangular plates with a plane periodic in–homogeneous structure. In course of non–asymptotic modeling, by using tolerance averaging technique (TAT), apart from the known separation for biperiodic and uniperiodic plates, it is necessary to introduce extra partitions. The four non–asymptotic models of plates with plane periodic structure can be led out independently (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical Solution of the Bending Problem for Rectangular Orthotropic Plates with a Variable in-Plane Stiffness

Mechanics of Composite Materials - The analytical solution of the bending problem for a clamped rectangular plate with a variable in-plane stiffness is found by using the method of superposition....     

Steady Periodic Water Waves with Unbounded Vorticity: Equivalent Formulations and Existence Results

In this paper we consider the steady water wave problem for waves that possess a merely \(L_r\) -integrable vorticity, with \(r\in (1,\infty )\) being arbitrary. We first establish the equivalence of the three formulations – the velocity formulation, the stream function formulation, and the height function formulation – in the setting of strong solutions, regardless of the value of \(r\) . Based upon this result and using a suitable notion of weak solution for the height function formulation, we then establish, by means of local bifurcation theory, the existence of small-amplitude capillary and capillary–gravity water waves with an \(L_r\) -integrable vorticity.     

Asymptotic Method of Homogenization in Problems of Heating Composite Plates of Periodic Structure in a High-Frequency Electromagnetic Field

In this paper, we examine the influence of electromagnetic and thermal fields on an inhomogeneous medium of periodic structure and heating of a laminated composite of periodic structure in a high-frequency electromagnetic field.     

On Periodic Solutions of the Periodic

By treating the periodic Riccati equation ${\rm\dot{z}=a(t)z^2+b(t)z+c(t)}$ as a dynamical system on the sphere S, the number and stability of its periodic solutions are determined. Using properties of Moebius transformations, an exact algebraic relation is obtained between any periodic solution and any complex-valued periodic solution. This leads to a new method for constructing the periodic solutions.     

Stiffness of ODEs

It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.Supported by a Dundee University Research Initiatives Grant.Supported by NSF Grant DMS-9116110.     

矩形中厚板和夹层板的后屈曲

本文研究了矩形Ｒｅｉｓｓｎｅｒ中厚板和夹层板的后屈曲特性。首先将矩形中厚板和夹层板的基本方程和边界条件表述成统一的无量纲形式。对不同的边界条件，特别是不对称边界条件，文中发展了一种应用于非线性分析的混合Ｆｏｕｒｉｅｒ级数求解新方法，获得了级数形式的精确解。非线性偏微分方程化为无穷元非线性代数方程组，数值计算中截取有限项进行迭代求解。