求解梁大变形问题的一种精细分析方法  

A new precision computational model for large deflection analysis of beams

作　　者：余婧妮 向宇[1] 李晓妮[1] 孙玉海[1] 王小龙[1] 

机构地区：[1]广西汽车零部件与整车技术重点实验室(广西科技大学),广西柳州545006

出　　处：《广西科技大学学报》2014年第4期34-39,共6页Journal of Guangxi University of Science and Technology

基　　金：广西教育厅项目(201204LX268)资助

摘　　要：在梁发生大变形后的平衡位置取一微段进行分析,从变形前后的几何关系与变形后的平衡方程出发建立计算模型,推导出求解梁大变形问题的一阶控制微分方程组,为处理梁大挠度变形问题提供了一种新的半数值半解析算法.为保证求解的精确与稳定,文中采用精细积分法与增量优化迭代的方法求解该一阶控制微分方程组.数值算例结果表明,本文的计算模型与求解方法精度高,稳定性好.A small section of the beam after deformation, which is in a state of static equilibrium position, is taken as the isolated body. According to the load analysis and the geometry relationship before and after deformation, the first order controlling equations of a bending beam with large deflection are obtained by the load analysis. A semi- analytical and semi-numerical method is presented to analyze the large deformation of beams. In order to guarantee the stability and accuracy in solving the controlling equations, the precision integration method and the incremental optimization iteration are utilized. Numerical results show that the present method is accurate and stable.

关 键 词：大变形 几何非线性 优化 精细积分法 增量迭代 

分 类 号：TG115.5[金属学及工艺—物理冶金]