超静定梁结构非线性大变形问题的优化算法与应用  

Optimization Algorithm for Solving Nonlinear Large Deformation Problem of Indeterminate Beam

作　　者：侯祥林[1] 王洁乐 李琦[1] 孙红[1] 

机构地区：[1]沈阳建筑大学交通与机械工程学院,辽宁沈阳110168

出　　处：《沈阳建筑大学学报（自然科学版）》2014年第5期909-916,共8页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家科技支撑计划项目(2011BAJ02B05-05);辽宁省自然科学基金项目(201102181)

摘　　要：目的研究建立超静定梁结构非线性大变形问题的优化算法,分析超静定梁大变形条件下的结构约束力,解决实际工程中的具体问题.方法以超静定悬臂梁力学模型为研究对象,建立变形平衡条件下的坐标位置方程.将梁变形后的节点未知坐标和未知的多余约束力作为设计变量,局部变形分析,构建满足坐标关系函数方程的目标函数,建立求解超静定梁大变形问题的优化求解方法.结果运用Fortran-PowerStation软件编写优化求解通用计算程序,分别求得在Py=20和Py=40条件下,超静定梁结构的位移和转角变形量.将计算算例优化结果与ANSYS有限元计算结果进行分析对比,得出最大位移的相对误差在5%以下,最大转角的相对误差在7.5%以下,验证了算法的有效性和精确性.结论针对梁的超静定大变形问题提出的优化求解算法,有效地解决超静定大变形梁等工程结构的约束力求解,为实际工程中具体问题提供了新算法.A optimization algorithm for solving nonlinear large deformation problem of indetermi- nate beam is proposed in this paper. Based on a mechanical model of statically indeterminate canti- lever beam, equilibrium equations of deformations were established. Taking unknown node coordi- nates of deformed beam and unknown extra constraint forces as design variables, based on the a- nalysis of local deformations, the objective functions that satisfy the coordinate relationship func- tion equations are built. Though optimization of the objective functions, the large deformation prob- lem of this beam can be solved. Calculated results are compared with the results of ANSYS and show that under the conditions of P = 20,40, the relative error of the maximum displacement lessthan 5% and the relative error of the maximum rotation less than 7.5% ,which verify the validity and accuracy of the proposed algorithm. The optimization algorithm of indeterminate beam large deformation provides a basis for the actual project specific issues.

关 键 词：超静定梁 非线性大变形 优化算法 程序设计 

分 类 号：TU322[建筑科学—结构工程]