Calculations methodology of the instabilities for thin shell structures

This paper presents a calculation methodology of the instabilities applicable for the design of axisymmetric thin structures against buckling risk. The application case discussed here is a tank loaded by external pressure and seismic effects. The calculations have been made by the Finite Element Method with the CASTEM System Codes. In a first step, the structure is supposed perfect and the calculations are made with an axisymmetric thin shell model. The analysis is made in the following way: - research of the Euler critical load in the aim of determining the most sensitive parts against buckling risk, - then, taking into account the plasticity by the research of the bifurcation loads for every parts previously determined. The axisymmetric model gives good results for high circumferential modes. In the case of earthquake, simulated by lateral loads, complementary results about shear buckling modes are obtained using a three dimensional model. However, the real structure is not perfect but includes necessarily initial imperfections. Consequently, in a second step, the study consists in determining the critical load reduction due to the introduction of an initial imperfection. For this, we use: - even, analytical formulae, in analogy with the beam theory, supposing that the defect is parallel to the buckling mode of the perfect structure, - or, directly, three dimensional calculations on a sector of structure including an initial defect. However, calculations show that the defect parallel to the buckling mode of the perfect structure, is not always conservative in a stand point of design. This puts the stress on the problem of the determination of the most penalizing initial defect and limits, consequently, the use of the first method only for a coarse evaluation of the reduction