大转动几何非线性梁变形问题的优化求解  

New Optimization Method of Geometric Non-Linear Beams with Large Rotation

作　　者：侯祥林[1] 尤超[2] 

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]沈阳建筑大学土木工程学院,辽宁沈阳110168

出　　处：《沈阳建筑大学学报（自然科学版）》2006年第5期726-731,共6页Journal of Shenyang Jianzhu University：Natural Science

基　　金：辽宁省教育厅项目(20040297)

摘　　要：目的提出一种有效确定梁大变形量的求解思路,解决对几何非线性梁大变形问题的直接分析.方法直接从梁变形后的平衡状态出发,将梁分为有限子段,对每个子段在其流动坐标上进行小变形计算,并在总体坐标上累积端点坐标.建立了以平衡状态端点坐标为设计变量,以端点的计算积累坐标与端点坐标差平方为目标函数的获得梁大变形量的无约束优化方法.结果通过编制的优化程序进行了悬臂梁受集中载荷时的大变形问题的计算,并与Ansys有限元法计算结果进行对比.结论以建立平衡位置坐标和结构变形的协调条件为目标函数,提出的大变形问题的直接优化算法,实现了平衡位置的结构变形的直接分析计算,为几何非线性大变形问题的直接计算分析提供了新途径.In this paper, a new kind of optimization algorithm about deformation of geometric non - linear beams with large rotation is proposed. Unlike previous method, equilibrium state is directly adopted. The beam is dividied into limited sections; small deformations are analyzed in local coordinate of each section; overall coordinate of nodes are decided through accumation. Making equilibrium points coordinate as design variables, error of equilibrium points coordinate and accumating coordinate as objective function, an optimization problem is formed. Deformation of beam under concentrate force is computed with program. Contrasted with Ansys method, effectiveness is verified by practical example. The new optimization method will be used to define engineering large deformation problem.

关 键 词：几何非线性 悬臂梁 大变形(大转动) 优化算法 目标函数 

分 类 号：O343.5[理学—固体力学]