摘要
在提出的板形判别条元法的基础上,引入节线二阶导数连续和自由边的力边界条件,导出挠度函数的改进模型,使挠度函数及其一阶和二阶导数都可以仅用节线挠度表示,而不必再用节线挠度及其一阶导数表示,从而使未知数减少一半。根据静力学最小势能原理,导出板形判别的计算模型,使特征矩阵从原来的2(n+1)阶降低到目前的(n+1)阶,提高了计算速度。又从动力学原理出发,推导得到相同的计算模型,进一步证明了计算模型的正确性,最后用实际算例验证了模型。
The improved model of deflection function is established by inducting the conditions of second derivative continuity on the nodal lines and the force boundary conditions of free sides on the basis of the strip element method for shape discrimination proposed by authors. The deflection function and its first and second derivatives can be expressed only by the deflections of the nodal lines, not by the deflections of the nodal lines and their first derivatives. So the unknowns are reduced by half. According to the minimum potential energy principle, the calculation model for shape discrimination is established, the orders of characteristic matrix are reduced from 2（n＋1） to （n＋1）, and hence the computation efficiency is increased. The same calculation model is also established based on the dynamics principle, which further proves that the calculation model is correct. Finally, the model is validated by practical examples.
出处
《工程力学》
EI
CSCD
北大核心
2009年第12期204-210,共7页
Engineering Mechanics
基金
国家自然科学基金项目(50675186)
河北省重大自然科学基金项目(E2006001038)
关键词
板带轧制
板形判别
降阶模型
静力学
动力学
特征矩阵
strip rolling
shape discrimination
reduced order model
statics
dynamics
characteristic matrix
