用变分法解箱形井塔开孔矩形薄板的弯曲

本文根据变分原理，导出了各种不同的束条件下开孔矩形薄板在横向均布荷载作用下的挠度方程，由此方程可进一步求出其内力分量和应力分量。     

矩形悬臂厚板的解析解

首先把胡海昌提出的弹性厚板弯曲问题的简化方程表示成为Hamilton正则方程,然后利用辛几何方法对全状态相变量进行分离变量,求出其本征值后,再按本征函数展开的方法求出矩形悬臂厚板的解析解。由于在求解过程中不需要事先人为地选取挠度函数,而是从厚板弯曲的基本方程出发,直接利用数学的方法求出可以满足其边界条件的这类问题的解析解,使得问题的求解更加合理论化。最后还给出了计算实例来验证所采用的方法以及所推导出的公式的正确性。     

弯曲振动矩形薄板的辐射声场研究

本文对边界简支弯曲振动矩形薄板的辐射声场进行了研究,得出了其辐射声场的解析表达式,并计算了声场的三维及二维指向性图案．     

弹性矩形薄板弯曲问题的一个解法

本文建立一个关于弹性矩形薄板弯曲的解析解法。该方法适用于求解任意荷载及边界条件下矩形薄板的弯曲问题，特别是对具有边梁支承的矩形板，更显示出特有的优越性。     

矩形薄板弹性弯曲的精确解析解法

本文根据矩形薄板弹性弯曲微分方程的一般解求得了满足全部边界条件和角点条件的精确解     

具有边梁的悬臂矩形板的弯曲问题

本文建议一个求解具有边梁悬臂矩形板弯曲问题的解析解法。该法将有边梁和无边梁悬臂矩形板弯曲问题的解融为一体，在有边梁悬臂矩形板的解中令边梁弯曲刚度为零即得到无国梁悬臂矩形板的解。     

矩形薄板自由振动的一般解析解

本文求得了矩形薄板弹性横向自由振动位型函数微分方程的一般解。可以求解任意边界矩形薄板的固有频率。以四边固定矩形板为例求解了板的基频及其位型。     

用有限元线法梯形单元分析薄板弯曲问题

本文采用有限元线法构造了一个梯形薄板弯曲单元，适用于分析形状较为复杂，具有任意边界条件及荷载的Ｃ＾１连续问题。     

矩形薄板弯曲问题的U变换-有限元法

该文扩展了U变换-有限元法分析弹性矩形薄板的范围。通过构造一个与简支、固支或二种边界条件组合的矩形板的等效系统,使刚度矩阵成为循环矩阵,采用U变换,成功解耦了有限元矩阵方程,使得有限元计算只须在一个单元上进行。给出了承受板中集中载荷和对边均布弯矩两种载荷形式下的板中挠度解析表达式。所得到的级数解不仅计算效率高,还能给出误差估计的显式表达式,能够直接掌控计算精度。算例中考察了几种不同边界条件下的计算结果,与已有理论结果的对比说明,该方法提高了计算的精度和效率。     

双模量复合材料正交叠层矩形薄板的弯曲问题

本文选择一组满足若干特殊条件的无穷幂级数作为位移函数的试函数,并首次将加权残数法应用于双模量复合材料。对于四边简支承受正弦分布载荷的正交叠层矩形薄板,应用加权残数法求得的中性面位置、位移、内力矩和内力和精确解相当一致。     

TbDyFe磁致伸缩薄膜悬臂梁弯曲性能的研究

以TbDyFe磁致伸缩薄膜悬臂梁为研究对象,采用有限元分析方法(FEM)对薄膜厚度及薄膜与衬底材料的弹性模量比对悬臂梁最大挠度值的影响规律进行了研究.通过FEM计算发现:当薄膜厚度小于衬底厚度的十分之一时,最大挠度值随薄膜厚度线性增加,计算结果与文献的理论计算结果吻合很好;当薄膜厚度为衬底厚度的一半时,悬臂梁的自由端挠度值达到最大.磁性薄膜与衬底材料有效弹性膜量比值的增加可以显著地提高悬臂梁的挠度值,同时挠度最大值向薄膜/衬底厚度比减少的方向移动.     

Bending of cross-ply laminated plates resting on elastic foundations under thermo-mechanical loading

This article investigates the bending response of an orthotropic rectangular plate resting on two-parameter elastic foundations under thermo-mechanical loadings. Analytical solutions for deflection and stresses are investigated by using an unified shear deformation plate theory. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. The governing equations that include the interaction between the plate and the foundations are obtained. Numerical results are presented to demonstrate the behavior of the system. The influences of aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response are studied.     

悬臂弯曲加载表面裂纹长度与施力点位移的相关性研究

在悬臂弯曲加载方式下,采用五件带缺口光滑板状试样,通过循环载荷控制模式,研究了表面裂纹长度2c与试样施力点位移的相关性,结果表明:表面裂纹长度与施力点位移的谷值无相关性,但与施力点位移的峰值DP具有明显的相关性,即在表面裂纹扩展初期,DP几乎不发生变化,但随着表面裂纹的进一步扩展,DP开始增加,在表面裂纹扩展的后期,DP显著增加;在表面裂纹扩展的中后期,2c与DP满足递增多项式关系。根据2c与DP的函数关系,可为实现复杂环境条件下表面裂纹长度的自动化测量提供依据。     

基于改进傅里叶级数的矩形板薄板振动特性分析

基于改进傅里叶级数对任意边界条件下的矩形薄板振动特性进行分析,通过傅立叶正弦级数的引入,修正了边界条件上的不连续性;此外,通过改变横向位移约束弹簧刚度值k和旋转约束弹簧刚度值K来模拟任意边界下矩形薄板的振动情形,克服了以往只能求解某些特定简化边界条件下振动问题的缺陷。通过与文献及有限元软件计算结果的对比,验证了此方法的有效性;研究表明,矩形薄板不同边界条件下固有频率值差异较大,但均随长宽比增大而减小。     

Large deflection behavior of functionally graded plates under pressure loads

Large deflection analysis of rectangular functionally graded plates is studied in this paper. It is assumed that the mechanical properties of the plate, graded through the thickness, are described by a simple power law distribution in terms of the volume fractions of constituents. The plate is assumed to be under pressure load. The fundamental equations for rectangular plates of FGM are obtained using the Von-Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for rectangular functionally graded plates are given in dimensionless graphical forms. The effects of material properties on the stress field through the thickness are determined and discussed.     

受静压力作用加筋板隔声性能研究

基于随机平面波声源建立混响声源激励的加筋板隔声计算模型,通过对试验模型数值计算,二者结果基本吻合;计算存在静压力时加筋板隔声特性表明,存在静压力时加筋板基频移动会致低频隔声量显著增加,压力增加到一定程度时隔声量基本不再增加;此刻为存在预应力的实际结构物隔声量计算提供参考。     

Hydrostatic method for the calibration of hydrophones at excess static pressure

Translated from Izmeritel'naya Tekhnika, No. 10, pp. 51–53, October, 1989.     

Bending analysis of functionally graded annular sector plates by extended Kantorovich method

The small deflection equation for isotropic and non-homogenous thin annular sector subject to transverse loading is derived in polar coordinate. The Poisson’s ratio of the plate is assumed to be constant, but the Young’s modulus varies continuously through the radial direction according to the power-law function. A closed-form solution with fast convergence rate is obtained using the extended Kantorovich method and the classical theory of thin plates (Kirchhoff theory). The validity and accuracy of results are examined by resolving the problem using commercial finite element code ABAQUS and a good agreement between them is obtained for either deflection or stress resultants.     

Exact Solution for Bending of Shape Memory Alloy Beams

Bending is an attractive mode of operation and application of shape memory alloys (SMA). To date numerical methods, such as the finite element method, have been used to model the coupled thermo-mechanical behavior of these alloys. In this article, an analytical approach is developed to calculate the exact solution of SMA beams deflection due to an external force. The approach is based on the assumption of linear distribution of strain along the height of a beam cross section. The approach is validated by comparing the results with the existing plastic solution and experimental data.