基于Maple的三铰斜拱力学分析及矢跨比优化  

Mechanical Analysis and Optimization of Vector-span Ratio of Three-hinged Inclined Arch Based on Maple

作　　者：毛星波 盛冬发 朱军 MAO Xingbo;SHENG Dongfa;ZHU Jun(School of Civil Engineering,Southwest Forestry University,Kunming 650224,China)

机构地区：[1]西南林业大学土木工程学院,昆明650224

出　　处：《实验室研究与探索》2022年第10期8-12,共5页Research and Exploration In Laboratory

基　　金：国家自然科学基金项目(11862023)。

摘　　要：对三铰斜拱的合理拱轴线问题、影响线计算问题和矢跨比优化问题进行了分析。假定截面弯矩恒等于零,解得三铰斜拱在水平均布荷载作用下的合理拱轴线函数。基于静力平衡方程推导了支座反力影响线函数,并进一步求得截面内力的影响线表达式。建立了以各控制点内力平方和为目标函数的矢跨比优化模型。最后,进行了相应Maple程序的编制,并通过工程算例进行了验证。结果表明,合理拱轴线函数使算例弯矩大体趋近于零;Maple分析所得影响线与SAP2000结果基本吻合;矢跨比优化使截面轴力减小了9.05%。以上工作可为三铰斜拱相关力学分析及优化设计提供一定的便利与参考。The problem of reasonable arch axis,calculation of influence line and optimization of vector-span ratio of three-hinge inclined arch are analyzed.Assuming that the bending moment of the section is equal to zero,the reasonable arch axis function of the three-hinged inclined arch under uniformly distributed horizontal loads is obtained.Based on the static equilibrium equation,the influence line function of the support reaction force is derived,and the expression of the influence line of the section internal force is further obtained.The optimization model of the vector-span ratio with the sum of squares of internal forces at each control point as the objective function is established.Finally,the corresponding Maple program is compiled based on the theory in this paper,and the theory is verified by an engineering example.The results show that the rational arch axis function makes the bending moment approximate to zero.The influence line obtained by Maple analysis is consistent with SAP2000.The axial force of cross section can be reduced by 9.05%when the ratio of vector to span is optimized.The above work can provide some convenience and reference for relevant mechanical analysis and optimization design of three-hinged inclined arch.

关 键 词：三铰拱 斜拱 合理拱轴线 影响线 矢跨比 

分 类 号：U448.22[建筑科学—桥梁与隧道工程]