跨中集中荷载作用下弹性约束圆弧拱的稳定性分析  

Analysis of buckling for a circular arch with rotational elastic constraints under a central concentrated load

作　　者：曾有艺[1] 易壮鹏[1] 颜东煌[1] 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410114

出　　处：《应用力学学报》2016年第5期904-909,942,共6页Chinese Journal of Applied Mechanics

基　　金：国家重点基础研究发展(973)计划(2015CB057706);国家自然科学基金(51178058;11002030);长沙理工大学土木工程重点学科基金(15ZDXK01;13ZDXK06)

摘　　要：研究了跨中集中荷载作用下两端由不同转动刚度弹性约束的铰支圆弧拱的面内稳定性。由变形几何关系、变分原理得到了拱的非线性平衡方程,建立了外荷载、结构内力、径向位移的对应关系,通过定义拱的深浅参数和约束刚度参数进行分析,并得到了跳跃屈曲和分岔屈曲的发生条件及存在区间。通过数值分析可知本文方法所得屈曲路径和屈曲荷载与有限元法所得结论吻合良好,极值点、临界荷载相对差值在1%左右。对不同结构参数区间圆弧拱在集中荷载作用下的屈曲路径和临界荷载进行了分析,结果表明约束刚度对屈曲路径和临界荷载起决定性的作用,深浅参数决定屈曲发生条件、屈曲形式、极值点对数。The in-planar stability of hinged-hinged circular arch adopting rotational elastic constraints with different stiffness at two ends under a central concentrated load is investigated. The nonlinear equilibrium equation of the arch is deduced by using the geometrical relationship of deformation and energy variational principle. The relationships between external load and internal force, radial displacement are established. Then by defining the shallowness and constraint stiffness parameter of the circular arch the snap-through buckling and bifurcation buckling are analyzed and the occurrence condition and the distribution range for them are investigated. The buckling path and critical buckling load by the proposed method in this paper match well with results from the finite element method. The buckling path and critical buckling load for different structural parameters of the circular arch under a central concentrated load are studied. The results show that the constraint stiffness plays the fundamental roles on the buckling paths and critical loads, and the shallowness determines the occurring conditions, forms of buckling and the paris of critical loads for the circular arch.

关 键 词：转动弹性约束 圆弧拱 集中荷载 屈曲 变分原理 

分 类 号：O343.9[理学—固体力学]