摘要
目的研究建立一种精确有效的多余力约束力求解的新算法,解决超静定变截面梁的复杂工程结构问题.方法基于结构力学力法原理和最优化原理,结合变截面超静定梁的非线性微分方程求解的数值算法,以多余未知约束力为设计变量,以约束点满足的协调关系形成目标函数,构建了超静定变截面梁的多余未知约束力的优化求解,运用Visual Basic开发了超静定变截面梁多余未知约束力优化求解程序和梁结构变形曲线计算程序.结果优化直接算法求解的超静定变截面梁的两个具体算例1、2中计算的多余约束力,达到了要求的计算精度.结论此研究方法作为研究超静定问题的新思路,将为复杂工程结构问题的分析提供条件.
In the view of the complex engineering problem of statically indeterminate beam with varying section, a new optimum algorithm computing redundant unknown force are studied. Combined structural mechanics principle and optimization method with numerical algorithms for nonlinear differential equations, making redundant unknown forces as design variables, relation of the compatibility conditions as objective function, the optimum algorithm is proposed to analyze redundant unknown force and deformation about statically indeterminate beam with varying section. Program is made by Visual Basic language, and two computed examples are analyzed. By comparing them with analytical solution, accuracy and correctness of the new computing method are showed. It will be well used to solve complex engineering problems.
出处
《沈阳建筑大学学报（自然科学版）》
CAS
北大核心
2012年第5期842-846,共5页
Journal of Shenyang Jianzhu University：Natural Science
基金
国家自然科学基金项目(51008200)
辽宁省自然科学基金项目(201102181)
辽宁省教育厅项目(L2010445)
关键词
超静定变截面梁
非线性微分方程
多余约束力
变形曲线
优化算法
statically indeterminate beam with varying Section
nonlinear differential equation
redundant constraints
deformation curve
optimum algorithm
