靠模成形直梁回弹变形的变分原理及其应用  

The variational principle of straight beam rebound deformation in the model plastic deformation and its application

作　　者：陈英杰[1] 宋锦威 吴静瑶 雷周[1] 

机构地区：[1]燕山大学建筑工程与力学学院,秦皇岛066004

出　　处：《应用力学学报》2017年第2期304-310,共7页Chinese Journal of Applied Mechanics

摘　　要：引入有限变形回弹反耦联系统和反耦联方程的概念,应用有限变形回弹反耦联方程、加权余量法、有限变形回弹变分原理,推导出靠模成形直梁卸载后的回弹挠曲线方程。本文计算了矩形截面的理想弹塑性悬臂梁和简支梁在集中荷载作用下的弯曲。结果表明,应用回弹势能原理能够推导出靠模成形直梁的回弹变形,并且可应用于工程实际。The conceptions of springback anti coupled systems and equations with finite displacements are introduced to derive the deflection equations of straight beam in the model plastic deformation by applying springback anti coupled equations,springback variational principle with finite displacements and weighted residual method after unloading.For applications,the bending of an ideal elastic-plastic cantilever beam and simply supported beam with rectangular cross section under concentrated load is calculated.The calculation results show that the rebound deformation for straight beam in the model plastic deformation can be derived by applying springback potential energy principle,and can be used in practical engineering.

关 键 词：变分原理 最小势能原理 最小余能原理 靠模成形 回弹 反耦联系统 

分 类 号：O343[理学—固体力学]