各向异性板弯曲分析的一种级数—边界积分法

基金项目: 广东省自然科学基金资助项目

A Series Boundary Integration Method for the Bending Analysis of Anisotropic Plates

Department of Engineering Mechanics, South China University of Technology, Guangzhou

摘要: 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.

Abstract: 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.

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