弹塑性弯曲直梁的回弹变分原理及应用

由于在建筑结构中,荷载作用下弹塑性梁的变形影响着建筑物的安全性与舒适性。在模具生产中,材料的受力回弹决定着冲压成型构件的精度问题。且弹塑性材料的弯曲变形及回弹变形问题,以往都是通过计算机模拟进行分析计算,因此,为解决上述问题本文推导出弹塑性材料的变形方程和回弹方程。本文以有限变形回弹反耦联系统和反耦方程为基础,应用有限变形回弹反耦联方程和加权余量法建立有限变形回弹变分原理。并应用回弹变分原理中的最小势能原理和最小余能原理求解了弹塑性悬臂梁和简支梁的回弹挠曲线方程。在对计算结果与ANSYS有限元模拟进行对比的过程中,取得了一定的成果,该成果对工程实际具有一定的工程参考价值。

SPRINGBACK VARIATIONAL PRINCIPLE OF ELASTIC-PLASTIC BENDING STRAIGHT BEAM AND ITS APPLICATION

In the building structure, the deformation of elastic-plastic beam under load affects the safety and comfort of the building. In the die production, the springback of materials determines the accuracy of stamping components. In order to solve the above problems, the paper deduces the deformation equation and springback equation of elastic-plastic materials. In this paper, based on the finite deformation rebound anti coupling system and anticoupling equation, the finite deformation rebound anti coupling equation and weighted residual method are used to establish the finite deformation rebound variational principle Based on the principle of minimum potential energy and the principle of minimum complementary energy, the equations of elastic-plastic cantilever and simply supported beam are solved .In the process of comparing the calculation results with ANSYS finite element simulation, some results have been achieved, which have certain engineering reference value for engineering practice