基于尖点突变理论的平行组拼双肋拱侧倾失稳临界荷载计算新方法

基于尖点突变理论,首次以平行组拼双肋拱为研究对象,设定了结构侧倾屈曲位移函数,构建了侧倾失稳变形能量表达式,通过数学转换,建立了尖点突变模型,获得了平行组拼双拱肋系统的平衡曲面M方程和分歧点集B方程,通过分析体系失稳条件,计算了分歧点集解,推导了系统侧倾失稳临界荷载计算公式,提出了平行组拼双肋拱侧倾失稳临界荷载计算新方法;最后与有限元数值解进行了对比分析,结果表明:文中所推导的侧倾失稳临界荷载理论解与有限元数值解吻合良好,验证了基于尖点突变理论的平行组拼双肋拱侧倾失稳临界荷载计算方法的正确性,为拱结构侧倾屈曲的研究开辟了一条新途径。

A New Calculation Method of Lateral Buckling Critical Load of Parallel Dual-Arch-Ribs Based on the Cusp Catastrophe Theory

Based on the cusp catastrophe theory, the lateral buckling of parallel dual-arch-ribs was studied. The displacement function, as well as the energy representation were constructed when there was a lateral buckling in the dual arch-ribs. By mathematical transform，the energy cusp catastrophe model was established, then the system's equilibrium surface M equation and bifurcation point set B equation were obtained. Through the analysis of buckling conditions of dual-arch-ribs system, bifurcation point was calculated, and the formula of lateral buckling critical load was derived，furthermore, a new calculation method of lateral buckling critical load of parallel dual-arch-ribs was proposed. At last, comparing theoretical results based on the cusp catastrophe theory with those obtained from FEM, it is verified that the calculation method presented is sufficiently accurate. The study has opened up a new way for the lateral buckling of the arch structures.