一类超静定变截面压杆临界荷载的优化算法  

An Optimal Algorithm for the Critical Load of a Class of Statically Indeterminate Variable Cross-section Compression Bar

作　　者：侯祥林[1] 王似巍 王家祥[2] 贾连光[2] 

机构地区：[1]沈阳建筑大学机械工程学院,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）》2017年第1期104-110,共7页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(51578346);辽宁省自然科学基金项目(2015020129)

摘　　要：目的研究一端固定,一端链杆约束的一类超静定变截面梁临界载荷的优化算法原理,探讨超静定压杆临界载荷数值方法.方法基于差分原理和优化基本原理,运用差分方法将平衡状态下非线性微分方程离散化.以杆件每个离散点挠度,临界荷载和多余约束力为设计变量,以临界载荷所满足差分方程与边界条件构建目标函数,在Fortran-Power Station环境下,编制优化程序,进行常截面梁与变截面梁具体算例分析对比.结果提出了一类超静定变截面压杆的临界载荷的无约束优化算法,并验证了方法的正确性和有效性.结论算法能够有效解决工程中变截面超静定梁结构临界载荷的计算问题,为工程设计与分析提供支持.The principle of the optimization algorithm for the critical load of a statically indeterminate variable cross-section beam with one end fixed and one end chain rod constraint was studied, and the numerical method for the critical load of the static pressure bar was discussed. Based on finite difference method and optimization method, the nonlinear differential equations in equilibrium state were discretized. The bar deflections at each discrete point, the critical load and the extra binding force were took as the design variables. Critical load difference equation and boundary conditions were used to construct the objective function. An optimization algorithm procedure was built with the computer language Fortran-PowerStation and was verified with concrete examples of uniform bar and variable cross-section bar. optimization algorithm of the statically indeterminate variable cross-section beam was built, whose correctness and effectiveness, was verified The algorithm can solve the critical load calculating issue of statically indeterminate variable cross-section beam effectively and could provide some support to the engineering design and analysis.

关 键 词：超静定变截面压杆 临界载荷 非线性差分方程 优化算法 程序设计 

分 类 号：TU311[建筑科学—结构工程] O302[理学—力学]