摘要
局部纵向屈曲是普遍存在于薄宽带材生产过程的板形缺陷,是屈曲研究的难点,精确的解析求解方法对局部纵向屈曲形成机理的研究和带材板形质量的提高具有重要意义.论文首先将任意位置的局部纵向屈曲分为带材边部和内部两类,然后采用辛弹性力学方法直接推导得到了局部纵向屈曲区域承受不同边界约束条件时的临界屈曲应力和屈曲挠度函数,最后将辛弹性力学求解结果与有限元方法和相关文献求解结果进行了对比.结果表明:辛弹性力学方法与有限元方法相比具有相同计算精度和更高的计算效率,辛弹性力学方法带材屈曲计算精度高于传统能量法;带材边界的约束条件对临界屈曲应力、屈曲区域几何形状和屈曲挠度函数均存在显著影响,验证了传统能量法求解的不足,有利于提高局部屈曲计算精度,具有在线计算带材屈曲的潜力.
Local longitudinal buckling is a strip flatness defect, which is commonly found in the production process of thin and wide strips. The local longitudinal buckling of strips is a difficult problem in buckling research, and an accurate analytical method is very important for the research of formation mechanism of local longitudinal buckling and the improvement of strip flatness quality. To solve the local longitudinal buckling problem of strips, the arbitrary local longitudinal buckling of strips is firstly divided into two types: the edge local longitudinal buckling and the interior local longitudinal buckling. The symplectic elasticity method based on the symplectic geometry is then used to directly derive the critical buckling stress and buckling deflection function when the local longitudinal buckling area is subjected to different boundary constraints. The analytical solution results obtained by the symplectic elasticity method are compared with those by the finite element method and from literature, respectively. The results show that the symplectic elasticity method has the same calculation accuracy but higher calculation efficiency than the finite element method, and the calculation accuracy of the symplectic elasticity method is higher than that of the energy method in the reference. The critical buckling stress, the geometric shape of buckling area, and the buckling deflection function are all affected by the strip boundary conditions, which verifies the superiority of the symplectic elasticity method over the energy method. As an accurate analytical method, the symplectic elasticity method can improve the accuracy of local buckling calculation and has the potential for the online calculation of local buckling of strips.
作者
于海军
何安瑞
孙文权
Haijun Yu;Anrui He;Wenquan Sun(National Engineering Technology Research Center of Flat Rolling Equipment,University of Science and Technology Beijing,Beijing,100083)
出处
《固体力学学报》
CAS
CSCD
北大核心
2021年第5期576-585,共10页
Chinese Journal of Solid Mechanics
基金
广西创新驱动发展专项资金项目(桂科AA17202008)
中央高效基本科研业务费(FRF-NP-19-006)资助。
关键词
薄宽带材
局部纵向屈曲
辛弹性力学
解析求解
thin and wide strip
local longitudinal buckling
symplectic elasticity
analytical solution
作者简介
通讯作者:孙文权,Tel:18610374433,E-mail:wqsun18@163.com.
