非理想边界拱的面内失稳模式与屈曲荷载

将拱结构中既非固结也非铰支的非理想边界考虑为沿不同方向的具有一定刚度的弹性约束,利用变形几何关系和能量变分原理推导了拱的非线性平衡方程.以圆弧拱为例建立了径向均布荷载下外荷载与结构内力、径向位移之间的关系,通过定义拱的深浅参数和临界约束刚度进行分析并得到了跳跃屈曲、分岔屈曲等的发生条件及存在区间.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,且用数值法分析了不同约束刚度时的屈曲路径和临界荷载.结果表明,临界深浅参数和临界约束刚度对圆弧拱的屈曲模式及屈曲临界荷载影响显著.

Planar Buckling Mode and Critical Load for Arch Structure with Non-ideal Boundary

The non-ideal boundary conditions (neither fixed nor hinged) of arch structure were considered as an elastic constraint with certain stiffness in different directions, and the nonlinear equilibrium equation was determined by using deformation geometric relation and energy variation principle. A circular arch under radial uniform load was taken as an example to establish the relationships between the external load and the internal force, and the radial displacement. By defining the shallowness and critical constraint stiffness, the snap-through buckling and bifurcation buckling were studied and the occurrence condition and distribution range were investigated. The buckling path and critical buckling load in the proposed method were in good agreement with the results from the finite element method. And the numerical method was used to study the buckling path and critical buckling load for different stiffness of elastic constraint. The results show that the critical shallowness and the critical constraint stiffness play a fundamental role in the buckling mode and critical buckling load for circular arch.