基于力等价结构的复杂超静定结构求解新方法研究  

A NEW METHOD FOR SOLVING COMPLEX STATICALLY INDETERMINATE STRUCTURES BASED ON FORCE EQUIVALENT IDEA

作　　者：汪大洋[1] 孙静 梁颖晶[1] 刘东滢 蔡长青[1] 朱勇[1] WANG Dayang;SUN Jing;LIANG Yingjing;LIU Dongying;CAI Changqing;ZHU Yong(School of Civil Engineering,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学土木工程学院,广州510006

出　　处：《力学与实践》2023年第4期899-908,共10页Mechanics in Engineering

基　　金：广东省线下一流本科课程“结构力学”(粤教高函[2022]10号);广东省研究生示范课程“结构动力学”(2020SFKC057);广东省高等学校教学管理学会重点项目“结构力学”(X-KCSZ2021015)资助。

摘　　要：超静定结构内力计算是结构力学课程学习的重点和难点,当超静定次数较多时,采用传统方法计算时难度极大且不易理解。本文总结提出了力等价结构思想,力等价结构与原结构在内力、变形上完全等价,基于该思想提出了复杂超静定结构内力计算的新方法,并将其应用到位移法、混合法求解多次超静定的复杂结构算例中。通过与传统方法对比,验证了所提力等价结构思想的可行性。所提方法可大大降低复杂超静定结构基本未知量的数目,简化计算过程,提高求解效率。The internal force calculation of statically indeterminate structures is the key and most difficult point in the course of structural mechanics.When degree of statical indeterminacy is large,it is very difficult to calculate with traditional methods and it is not easy to understand.The idea of force equivalent structure is summarized in this paper.The force-equivalent structure is completely equivalent to the original structure in terms of internal forces and deformations.Based on this idea,a new method for internal force calculation of complex statically indeterminate structures is proposed,which is thereafter applied to both the displacement method and the hybrid method to solve multiple statically indeterminate complex structures.Compared with traditional methods,the feasibility of the proposed force equivalent structure idea is verified.The proposed method can greatly reduce the number of basic unknowns of complex statically indeterminate structures,simplify the calculation process and improve the solution efficiency.

关 键 词：结构力学 力等价结构 超静定结构 位移法 混合法 

分 类 号：TU311.1[建筑科学—结构工程]