含固支端梁的解析解  

Analytical solutions for beams with fixed ends

作　　者：詹春晓[1] 刘一华[1] 

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《应用力学学报》2016年第2期201-207,367,共7页Chinese Journal of Applied Mechanics

摘　　要：采用弹性力学的应力函数法求含固支端梁的应力和位移时,无法严格满足固支端的实际边界条件,需要采用简化的固支边界条件。本文对已有的简化固支边界条件进行了改进,基于新的简化固支边界条件,推导出了四种含固支端梁的应力和位移的解析解,并进行了相应的数值计算,对几种固支边界条件进行了讨论。由本文方法得到的上表面受均布载荷作用悬臂梁的位移u和v的解析解与有限元解的最大误差分别为3.0%和1.0%,两端固支梁的应力σx的解析解与有限元解的最大误差为5.3%。通过理论与数值结果的比较表明,本文改进的固支边界条件是对固支端一种很好的简化。When Airy stress function method of elasticity is used to solve the stress and displacement of the beam with fixed ends, the actual boundary condition of the fixed end cannot be satisfied strictly, so a simplified boundary condition has to be applied. In this paper, the existed, simplified boundary conditions of the fixed end are improved. Based on the new simplified boundary condition, the analytical solutions of stresses and displacements are presented for four kinds of beams with fixed ends, and the corresponding numerical calculations are carried out subsequently. Several simplified boundary conditions of the fixed end are discussed. The comparison between the analytical and numerical solutions shows that the maximum errors of the displacements u and v between the analytical solution and the FEM result for the cantilever beam subjected to uniform load on its upper surface are 3.0% and 1.0%, respectively, and the maximum error of the stress σx for the fixed-fixed beam is 5.4%. Therefore, the new fixed boundary condition proposes a good simplification for the fixed end.

关 键 词：梁 固支端 边界条件 应力函数 解析解 

分 类 号：O343.1[理学—固体力学]