引用本文: 陈英杰, 冯永强, 董静波. 线性强化型弹塑性弯曲直梁挠曲线方程1)[J]. 力学与实践, 2022, 44(2): 351-357.
CHEN Yingjie, FENG Yongqiang, DONG Jingbo. DEFLECTION CURVE EQUATION OF LINEAR STRENGTHENED ELASTIC-PLASTIC BENDING STRAIGHT BEAM1)[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 351-357.
 Citation: CHEN Yingjie, FENG Yongqiang, DONG Jingbo. DEFLECTION CURVE EQUATION OF LINEAR STRENGTHENED ELASTIC-PLASTIC BENDING STRAIGHT BEAM1)[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 351-357.

## DEFLECTION CURVE EQUATION OF LINEAR STRENGTHENED ELASTIC-PLASTIC BENDING STRAIGHT BEAM1)

• 摘要: 针对材料在弹塑性阶段的应用不完全问题,本文用弹塑性分区最小势能原理,推导出线性强化模型下弯曲直梁的势能分区准则和欧拉方程。求解出集中载荷作用下悬臂梁和简支梁的挠曲线方程,将挠曲线方程代入MATLAB软件进行数值计算并将其结果与ANSYS对比分析。结果表明：数值解与有限元值均满足实际工程中允许的误差范围,给出的方法可为解决工程实际问题提供一个新的思路。

Abstract: Aiming at the incomplete application of materials in elastic-plastic stage. In this paper, by using the principle of elastic-plastic partition minimum potential energy, thecriterion of potential energy and Euler equation of bending straight beam under linear strengthening model are derived. The deflection curve equation of cantilever beam and simply supported beam under concentrated load issolved. The deflection curve equation is put into Matlab software for numerical calculation, and the results are compared with ANSYS. The results show that both the numerical solution and the finite element value meet the allowable error range in practical engineering. The proposed method provides a new idea for solving practical engineering problems.

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