Investigation On Thermal Buckling Of Thin-walled Shells With Functionally Graded Material Coating And Geometric Imperfection

Plates and shells with functionally graded material(FGM)coating not only show better mechanical performance and corrosion resistance than the pure metallic structures under high temperature environment,but also are more cost-efficient than the pure FGM structures.Thus,it shows great application potential in many industrial fields,such as aerospace,transportation,petrochemical industry,nuclear and navigation.Since plates and shells with FGM coating are usually subjected to the high temperature load or sharp temperature gradient load in practical work conditions,the thermal stress are harsh and unavoidable for these structures.It is vital to ensure the safety and reliability in the respect of not only the strength and toughness,but also the stability for these plates and shells subjected to thermal load.In this work,a first attempt is made to derive the theoretical critical buckling temperature rise for the metallic rectangular thin plate,and the influence of boundary condition on the thermal stress and thermal buckling behavior are investigated.Then,the inconsistency problem of the critical buckling temperature rise of the cylindrical shell in existing literatures is clarified based on the aforementioned research for rectangular plate.The results show that the reason causing the inconsistency problem is to ignore the effect of boundary condition on the thermal stress in some literature.The clarification of the inconsistency problem of the critical buckling temperature rise provides a more scientific reference for the engineers.Then,based on the classical plate and shell theory and the kinematic relations of strain and displacement proposed by Donnell,the critical buckling temperature rise are deduced for the cylindrical shell with FGM coating.Using the method of multilayer discrete modeling,the correctness of theoretical solution derived in this work is verified by the numerical solutions of ANSYS and ABAQUS,respectively.Since the mathematical express of theoretical solution is too complex,an empirical formula,which is relevant to the material and structural parameters,is proposed to calculate the critical buckling temperature rise of the cylindrical shell with FGM coating.The proposed approximate solution shows great precision in a given range,it provides a convenient approach for the engineers to calculate the critical buckling temperature rise of cylindrical shell with FGM coating.Lastly,it is inevitable that the cylindrical shells used in practical engineering have some initial imperfects due to the limitation of manufacturing technique.In response to this problem,the thermal buckling behavior of imperfect cylindrical shell with a FGM coating and an axisymmetric initial geometric imperfection is investigated base on the Koiter model and Galerkin method.The influences of the amplitude of imperfection,volume fraction of ceramic phase in FGM and form of thermal load on the critical buckling temperature rise are studied comprehensively.The results provide a theoretical criterion for the design of thermal buckling of the imperfect cylindrical shell with FGM coating.