Abstract:The shell with functionally graded material (FGM) coating is a novel high temperature resistant structure, which has been increasingly applied in the aerospace, nuclear, turbo machinery and other engineering fields. However, there are some defects for practical structure due to the limitation of manufacturing technique. But relevant theoretical research on the thermal buckling behavior of the imperfect cylindrical shell is rather limited in most open literature. Therefore, this work proposed to establish the theoretical solution of the critical buckling temperature rise of the cylindrical shell with an axisymmetric imperfect and FGM coating based on the Donnell shell theory, Koiter model and Galerkin method. The result shows that the theoretical solution is in exact agreement with the literature. In addition, the influences of the profile of the axisymmetric imperfection, the volume fraction of the ceramic phase and the types of the thermal loading on the thermal buckling behavior of the imperfect cylindrical shell with FGM coating are analyzed comprehensively. The study provides a scientific solution and better understanding for the thermal buckling problem of the imperfect cylindrical shell with FGM coating.