Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements

In the paper, the bending stiffness and strength of multilayer structural elements in relation to the mechanical properties of layers and their number layout and sizes are investigated and the corresponding correlations are established. It is found that the most rational structure of a multilayer element in bending is a symmetric three-layer structure formed from two materials with the thickness of the core less than the half-thickness of the element. The values of normal stresses in the layers of a multilayer beam in bending depends on its bending stiffness and the position of layers relative to the neutral axis. The influence of the number of layers on the stiffness of the structural element and on the magnitude of normal stresses is insignificant.     

High-order squeezing of pure superposition states

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细胞自动机方法解小挠度薄板弯曲问题

固体力学中的细胞自动机方法是一种分析固体力学问题的新方法，它将结构的静平衡认为是在力和位移边界条件下，物体元胞间的自组织过程，它不需要象现有有限元那样形成整体刚度矩阵和求解整体平衡方程，对计算机容量要求低，可望成为分析大型结构的有效方法，且特别适宜于并行计算。为拓展其应用范围，本文将其应用于小挠度弹性薄板弯曲的静力计算以检验其可行性。文中给出了详细的计算步骤，以实际算例为基础，探讨了该方法的有效性，并对其优点和目前存在的问题进行了讨论。     

A method for predicting the deflection of reinforced concrete beams strengthened with carbon plates

For strengthening bent beams, plates of reinforced plastics are glued to their tensioned surface. As s result, the beam becomes layered, and it is possible to control its rigidity and deflection. Based on the methods of structural mechanics of layered media, a method is elaborated for determining the deflection of such beams on the entire range of loading up to their ultimate failure. A comparison between the theoretical and experimental results is carried out. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 45–60, January–February, 2006.     

A reference solution for phase change with convection

A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd.     

一种考虑剪切变形的平行四边形厚/薄板通用单元

根据Timoshenko二广义位移梁理论，构造了深梁位移场的插值函数。利用斜坐标系与直角坐标系的变换关系、有限条带思想和深梁位移插值函数，构造了一种考虑剪切变形的平行四边形厚／薄板弯曲通用单元的位移(曲率、剪应变、转角、横向位移)插值函数，导出了刚度矩阵和非结点荷载等效力。并对简支阍支方板、Razzaque斜板、四边简支斜交板弯曲进行了数值计算。算例表明此单元有较好的精度，对于薄板不出现剪切闭锁，可适应于目前桥梁建设中大量采用的斜交板桥结构分析。     

BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT－IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD

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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.     

Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论，考虑材料物性参数随坐标和温度变化的特性，研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题，基于一维DQ法和Galerkin技术，给出了一对边固支，另对边任意约束时板弯曲问题的半解析解，以Si3N4/SUS304板为例考察了材料组份，温度场，面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响。