薄板弯曲问题的P型杂交解析有限元方法

本文采用两套变量构造有限元试函数空间，在单元内部要求试函数精确满足平衡微分方程，在单元边界上对位移和转角分别用Ｐｅａｎｏ升阶函数插值，然后利用广义变分原理建立了一种薄板弯曲问题的Ｐ型杂交解析有限方法，与常规有限元法相比，该方法不心进行过细的网格剖分，通过增加单元插值多项式的阶数Ｐ来提高精度，此外，该方法还具有积分计算只需在单元边界上进行、单元钢度矩阵和载荷向量具有嵌入结构、协调程度可以自动控制等优     

Transient free convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect

A Prandtl transformation method is applied to study the transient free convection of non-Newtonian fluids along a wavy vertical plate in the presence of a magnetic field. A simple transformation is proposed to transform the governing equations into the boundary-layer equations and solved numerically by the cubic spline approximation. A simple coordinate transformation is employed to transform the complex wavy surface to a vertical flat plate for a constant wall temperature by the numerical method. The effects of the magnetic field parameter, the wavy geometry and the non-Newtonian nature of the fluids on the flow characteristics and heat transfer are discussed in detail.     

正交正放类网架结构固有频率及屈曲分析的样条Galerkin法

本文根据考虑剪切变形的具有３个广义位移的平板弯曲理论，把正交正放类平板网架假设为由三层不同性质材料组成的各向正交异性夹层板。文中以双５次Ｂ样条函数中的一组基底作为试函数，用加权残值法中的离散型Ｇａｌｅｒｋｉｎ法，导出了这类网架的频率方程和屈曲方程。数值算例表明，这种方法是方便而精确的。     

Nonstationary deformation of an elastic plate with a notch under the action of a shock wave

The behavior of a thin elastic plate with a rectilinear notch under the action a weak shock wave in air is studied experimentally. A technique is developed for this purpose. The effect of the notch on the strain state of the plate is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 99–104, November 2007.     

用改进型广义协调元分析薄板的振动与稳定

本文在文献[1]和[2]的基础上,将改进型三角形广义协调元TGC-9-1应用于薄板振动和稳定分析中。推导出带有一个内部自由度(外部结点有九个自由度)的三角形板单元的协调质量矩阵和几何刚度矩阵。并通过算例表明,改进型广义协调三角形单元(TGC-9-1)具有良好的性态和更好的精度,程序简便。     

中厚度圆浮板自由振动的一个解析解

本文提出了常水深环境下中厚度圆浮板自由振动的一个解析解.分析中考虑了板横向剪切变形的影响和横截面转动惯性效应,利用空气中中厚度圆板的振型叠加和势流理论,导得了浮板系统频率方程的解析式.由此可看出Y.Tanaka得到的圆形薄浮板的解是本文的特例.最后数值计算还给出了水深和钢缆刚度与频率的关系曲线.并指出了h/a在什么范围可以略去剪切变形和转动惯量的影响.     

Reissner板弯曲的复变函数分析方法

本文建立了Reissner板弯曲问题的复变函数分析方法,它可以有效地用于分析含一般孔洞板弯曲的应力集中问题。作为应用,文中还给出了一些计算实例。     

激光辐照下有界圆厚板的热弹性弯曲响应分析

考虑板弯曲运动的旋转惯性效应和剪切变形效应，建立了轴对称热能沉积作用下，边界固支或简支圆厚板的热弹性弯曲运动控制方程。利用数学变换和摄动法，导出了各种温度－力学边界条件下板的热弹性弯曲挠度及截面广义转角的解析公式。给出了在空间Ｇａｕｓｓ型分布激光束辐照下，板整体弯曲响应的代表性数值计算结果，直观显示了板弯曲挠度的时空变化规律。     

沿垂等温平板的自然对流问题的近似解析解

本文用加权残值得到了沿垂等温平板的自然对流问题的近似解析解。和已有准确解的比较表明，在平板表面附近，近似解有很好的精度，而且速度场的精度比温度场更好一些。文末还对配域法的准收敛问题作了说明。     

On the modelling of dynamic problems for plates with a periodic structure

Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This problem for periodic plates has been solved independently in [5] and [10], using asymptotic homogenization. However, homogenization neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the order of the period length. The proposed model is applied to the analysis of some vibration problems.