力学中的最优值与黄金数的关系研究  

Study on the Relationship Between Optimal Value in Mechanics and the Golden Number

作　　者：韦璐茜 覃英宏 潘卓均 汪天宇 黄婵 黄美玲 WEI Lu-xi;QIN Ying-hong;PAN Zhuo-jun;WANG Tian-yu;HUANG Chan;HUANG Mei-ling(School of Civil Engineering and Architecture,Guangxi Minzu University,Nanning 530004,China;School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China)

机构地区：[1]广西民族大学建筑工程学院,南宁530004 [2]广西大学土木建筑工程学院,南宁530004

出　　处：《工程建设与设计》2023年第15期40-44,共5页Construction & Design for Engineering

摘　　要：力学中存在着许多最优值问题,过往研究更多地从数学和力学角度分析,鲜有分析最优值与美学中的黄金数0.618的关系。通过理论研究发现:(1)黄金方程可以反映悬臂梁在常见荷载作用下的弯矩分布规律,梁的反弯点位置与黄金数相关;(2)在材料力学中,摩尔圆确定应力状态,却忽略了中间主应力的效应,当岩石的拉压强度比是黄金数的倒数时,中间主应力与其他主应力的关系满足黄金比例,此时岩石强度达到最大值;(3)当岩石的拉压强度比为黄金数的3次方时,土体的内摩擦角为36°,是所有常见土体中的最大平均值。黄金数不仅可以作为提高力学效率的关键判定因素,还可以应用于各类工程中,为工程设计的合理性与经济性的统一打下基础。There are a lot of optimal value problems in mechanics.The previous researches are mostly from the mathematical and mechanical perspective,but rarely analyze the relationship between optimal value and golden number in aesthetics 0.618.Through theoretical research,it is found that:(1)The gold equation can reflect the bending moment distribution law of the cantilever beam under common loads,and the position of the beam's reverse bending point is related to the golden number.(2)In the mechanics of materials,the mohr circle determines the state of stress,but ignores the effect of intermediate principal stress.When the tensile-compression strength ratio of rock is the inverse of the golden number,the relationship between intermediate principal stress and other principal stresses meets the golden ratio,and the rock strength reaches the maximum value.(3)When the tensile-compression strength ratio of rock is a cube of the golden number,the internal friction angle of soil is 36°,which is the maximum average of all common soils.The golden number can not only be used as a key factor to improve mechanical efficiency,but also can be applied to all kinds of engineering,which lays a foundation for the unification of rationality and economy of engineering design.

关 键 词：力学 黄金数 中间主应力 摩尔圆 最优值 

分 类 号：TU31[建筑科学—结构工程] O3[理学—力学]