各向异性板弯曲分析的一种级数—边界积分法

本文的级数-边界积分方法能精确地满足一般的各向异性薄板或层合板弯曲问题的基本微分方程.它可用统一的级数形式来分析各种具有不同几何形状和边界支承情况的板。文中用此法计算了多组具有代表性的算例,其中包括了固定、简支、自由以及自由边角点4种边界支承情况,还包括了圆形、方形以及三角形3种板几何状况.这些算例的计算结果表明所得的挠度与内力都有很好的收敛性,并证实了该方法的通用性.     

A SEKIES BOUNDARY INTEGRATION METHOD FOR THE BENDING ANALYSIS OF ANISOTROPIC PLATES

A series boundary integration method is given which exactly satisfies the fundamentalequation of bending analysis of general anisotropic plates or laminated plates in Kirchhoffssense.With a unified deflection series,the method may be applied to the plates havingdifferent planforms and support conditions.Several groups of representative examples arecalculated.The examples include circular,square and triangular plates,and theirboundaries include clamped edges.simply supported edges,free edges and free corner.Numerical results indicate rapid convergency for both deflection and stress resultants anddemonstrate wide applicability of the method.     

二维各向异性问题的齐次解完备系及有关问题

本文讨论了一般的各向异性板弯曲问题和各向异性平面问题的基本微分方程齐次解完备系的一种选取方法以及它们在各种对称与反对称条件下的化简结果。考虑到解系的形式与基本方程的特征方程是否存在重根有关,文中导出了一个简单实用的重特征根存在充要条件以及该重根的简易计算式。所有的推导结果表明,这种齐次解完备系在表达、计算、对称性化简方面都较简便。     

A series boundary integration method for the bending analysis of anisotropic plates

A series boundary integration method is given which exactly satisfies the fundamental equation of bending analysis of general anisotropic plates or laminated plates in Kirchhoffs sense. With a unified deflection series, the method may be applied to the plates having different planforms and support conditions. Several groups of representative examples are calculated. The examples include circular, square and triangular plates, and their boundaries include clamped edges, simply supported edges, free edges and free corner. Numerical results indicate rapid convergency for both deflection and stress resultants and demonstrate wide applicability of the method.This subject was supported by the Natural Science Foundation of Guangdong Province.