纯弯曲理想弹塑性模型梁大变形的优化算法

Optimization Algorithm for Large Deformation of a Cantilever Beam with Elastic-Perfectly Plastic Model under Pure Bending

目的研究纯弯曲理想弹塑性模型悬臂梁大变形问题.方法以受弯曲力偶作用的纯弯曲理想弹塑性模型悬臂梁变形后的平衡状态为研究对象,应力-应变关系采用理想弹塑性模型;再将其分为若干微段,通过整体坐标的递推关系式求得微段端点坐标,构建微段端点未知坐标的目标函数;最后确定纯弯曲理想弹塑性模型悬臂梁大变形的最优化问题,并编制相应优化程序进行求解.结果将本文优化算法用于分析典型算例,并同有限元方法的计算结果相比较,说明提出的优化算法的正确性和有效性.结论本文优化算法为纯弯曲理想弹塑性模型悬臂梁的非线性分析增加了一种新的处理方法,由于其是在变形后的位置上建立平衡方程,因此,适合于非线性分析,具有广阔的应用前景.

Based on the optimization theory, an optimum algorithm is proposed to analyze the large deformation of a cantilever beam with elastic-perfectly plastic model under pure bending. The equilibrium state with elastic-plastic deformation of the cantilever beam is chosen as the object. The constitutive law adopts elastic-perfectly plastic model. Then, the cantilever beam is divided into some slight segments and the endpoint coordinates of slight segments are given through coordinate recursion formulae. Thus, the objective function of the unknown endpoint coordinates of slight segments is formed to induce the original problem as an optimization one and an optimization algorithm is programmed. The corresponding numerical results indicate the validity and reliability of the optimization algorithm compared with finite element method in solving the large deformation problem of a cantilever beam with elastic-perfectly plastic model under pure bending.