Theoretical And Experimental Study On Nonlinear In-plane Stability Of Circular Arches Under A Central Concentrated Load

Arch structures are widely used in the fields of civil engineering, mechanical engineering and aerospace engineering for its unique structural advantages. The stability of arch is one of the most important controlling factors in structure designing. This paper is concerned with the in-plane stability of both fixed-fixed and pined-pined circular arches with different rise-span ratio subjected to a central concentrated load. Adopting theoretical analysis, numerical simulation and model test t a series of innovative research are carried out.(1) Nonlinear differential equilibrium equations of circular arches are derived and solved. Considering the effects of pre-buckling large deformation, starting from geometrical relationship of deformation, the energy variation principle and the perturbation method is used to deduce the nonlinear differential equilibrium equations of both pined-pined and fixed-fixed circular arches under a central concentrated load when snap-through buckling and bifurcation buckling occur. The distribution of the upper and lower buckling loads are then obtained by solving differential equations. The deformation modes of circular arches are tracked in the whole loading procedure. Based on the numerical analysis and model test, the applicability of the theoretical results is verified.(2) Parametric analysis of the nonlinear in-plane stability of circular arches. The effects of geometric nonlinearity on the initial limited buckling load of circular arches whose rise-span ratio are varied from 1/10 to 1/2.5 are studied. The variation trends of initial limited buckling loads and bucking modes with the rise-span ratios and slenderness ratios are investigated. The internal force variation of circular arches in the instability process is illustrated. The complicated equilibrium path of the pined-pined circular arch with multiple stability critical loads is revealed, while the fixed-fixed circular arch only has the upper and lower limited load. The buckling modes of pined-pined arches comparing to fixed-fixed arches are much more complicated.(3) The experimental research of in-plane nonlinear buckling of circular arch is performed. A detailed experiment scheme is made for the research on the in-plane nonlinear elastic stability of fixed-fixed arch under a central concentrated load. A loading system which can change from load-controlled manner to displacement-controlled manner is designed. For the first time, nonlinear elastic stability experiments of deep arches with great rise-span ratio arc performed. By using the NDI Optotrak Certus, the deformation and mode changes of circular arches in the whole loading process is measured. By comparing finite element results with theoretical solutions, it is found that circular arch with small rise-span ratio will buckle in an in-plane anti-symmetric bifurcation mode even under a symmetric load, which is consistent with the bifurcation buckling phenomenon predicted by theoretical analysis. Further, it is pointed out that the shallow circular arches with small rise-span ratio are much sensitive to the initial defections.