集中载荷下四边固支正交各向异性矩形板的线性弯曲问题  

ANALYTICAL SOLUTIONS FOR BENDING OF CLAMPED ORTHOTROPIC RECTANGULAR PLATES UNDER A CONCENTRATED FORCE

作　　者：肖闪闪[1] 陈普会[1] 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016

出　　处：《工程力学》2015年第6期28-32,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(A020305)

摘　　要：采用载荷叠加法将集中载荷下四边固支正交各向异性矩形板线性弯曲的挠度分为3个部分:集中载荷下四边简支板的挠度、上下边简支左右边受弯矩的板的挠度、左右边简支上下边受弯矩的板的挠度,3个挠度之和在满足固支边界条件的情况下即为所要求的挠度的解。采用MATLAB软件编写程序进行计算,并将相同长宽的板在4种不同的厚度和载荷情况下的挠度计算结果与有限元分析结果进行比较,验证了解析解的正确性。最后讨论了经典的Kirchhoff薄板假设对于集中载荷的适用性问题。For a clamped orthotropic rectangular plate, the bending deflection due to a concentrated force can be treated as the superposition of deflections of simply supported plate under three load cases, a concentrated force, moments along two opposite edges and moments along the other two opposite edges. The solution satisfies the boundary conditions of the clamped plate. Matlab program is developed for calculating the deflections of four plates with different thickness and concentrated force positions. The analytical solutions are compared with Finite Element Method results, demonstrating the accuracy of the proposed solution. Finally, the reasonability of Kirchhoff plate assumptions is discussed through the case of clamped plate under a concentrated force.

关 键 词：载荷叠加法 集中载荷 四边固支矩形板 正交各向异性 挠度 

分 类 号：TB33[一般工业技术—材料科学与工程] TB301