Nonlinear Dynamic Buckling Of Circular Arches Under An Impact Loading

As the high strength and high performance materials are widely used in structural engineering,the arch become more slender and softer.When a sufficiently large impact load is applied to the arch,the arch will buckle in a instability mode dynamically.Impact load is kind of accidental load carrying a powerful energy which is of emergency and disaster,and have a huge threat to the safety of the structures.The impact load is also a common load appeared in practical engineering and its effect on the structure cannot be ignored.However,the effects of the impact load on structures are given insufficient consideration during the structure design,which leads a huge security problems on the application of the arch.On the other hand,the dynamic buckling of the arch can be used in some engineering structures,such as the elastic buckling deformation of the arch can be used as a kind of switching in micro-electro-mechanical system(MEMS).Hence,the study on the dynamic buckling behavior of the arch under an impact load is great of practical significance and engineering value.In order to perfect the study of the dynamic buckling and determine the mechanical behavior of the arch,this thesis investigates the nonlinear dynamic buckling of the arch subjected to an impact load by employing the analytical method incorporating the finite element method and experimental method.The effects of boundary conditions,temperature and imperfection on the dynamic buckling of the isotropic arch are investigated comprehensively,and the law of the dynamic buckling behaviors of the arch are also summarized.Finally,the dynamic buckling of the functionally graded GPL reinforced composites(FG-GPLRC)arch is furtherly studied,and the difference between FG-GPLRC arches and isotropic arches is also discussed in detail.The main contents of the aforementioned study are stated as follow:(1)Based on the principle of conservation of energy,a criterion is established for predicting the dynamic buckling load of the isotropic arch under an impact load.The analytical solutions of the dynamic buckling load for the arch with fix-ended,pin-ended and elastic-ended subjected to impact load is determined by using the criterion.The critical modified slenderness for governing the dynamic limit point buckling and dynamic bifurcation buckling of the aforementioned arch are also identified.An impact test and a finite element simulation are further carried out to verify the analytical result.It can be concluded that the criterion of dynamic buckling gives a faster way to obtain the critical dynamic buckling load of the isotropic arch.(2)Based on the criterion of dynamic buckling,a mechanical models of the dynamic buckling of the isotropic elastic-ended arch under an arbitrary step radial point load and a step uniform radial load are established,respectively,from which the analytical solutions of critical dynamic buckling loads of the isotropic arch are determined.It is found that the isotropic elastic-ended arch subjected to an arbitrary step radial point load can only buckle in an asymmetry limit point instability mode.A model test and a finite element simulation are also carried out to verify the analytical result.(3)Considering the effect of the temperature,the inter force of the arch is studied theoretically,and the equations of motion for dynamic buckling of the arch are also established,from which the analytical solution for the dynamic buckling load of the isotropic arch under a step load in thermal environment can be derived.The dynamic buckling behavior of the isotropic arch under a step load in thermal environment is explicitly,and it is found that the arch can buckle dynamically in a limit point instability mode or in a bifurcation mode in thermal environment.The critical modified slenderness and the critical temperature,which governs the dynamic buckling mode switching behavior,are also determined through the investigation.(4)A strain functions considering the effect of the geometric imperfection are established,and the buckling modes of the isotropic imperfect arch are determined based on the function.The critical dynamic buckling load of the e isotropic imperfect arch under step loading corresponding to different buckling modes is further derived.The effect of the geometric imperfection on the dynamic buckling load and critical modified slenderness of the isotropic arch is studied in detail.It is found that the isotropic arch with symmetric imperfection under a step uniform radial load can buckle in a multiple limit point instability mode dynamically.(5)The dynamic buckling behavior of the FG-GPLRC arch with elastic-ended under step load is investigated.The dynamic buckling loads and critical geometric parameters of the FG-GPLRC arch under different forms of step load are obtained through the analysis.A parametric study is also carried out comprehensively to investigate the influence of graphene platelets(GPLs)distribution,concentration,dimension of GPLs as well as the arch geometrical parameters on the dynamic buckling load of the arch.It is found that the dynamic stability of the arch can be considerably improved by adding a lower quantity of GPLs as reinforcing nanofillers.Furthermore,the analytical results are verified by FEM developed herein.It is found that the criterion of dynamic buckling used in the isotropic arch can also provide accurate prediction for dynamic buckling load of the FG-GPLRC arch.The conclusions of the study in this thesis enrich the research of nonlinear dynamic buckling of the arch,and the effects of load forms,boundary conditions,temperature and imperfection on the dynamic buckling behavior of the isotropic arch are explicitly.Moreover,it proved that the criterion of dynamic buckling for isotropic arches is also apply to FG-GPLRC arches as well,which gives theoretical support to the study of dynamic buckling of composite arches.