2013/01/25 by Yury Grabovsky, Davit Harutyunyan, Grabovsky, Yury +1
Engineering · #Analysis of PDEs (math.AP) #Composite Structure Analysis and Optimization #Elasticity and Material Modeling #FOS: Mathematics #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1301.6079
openalex publication_date 2013/01/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Using rigorous constitutive linearization of second variation introduced in [6] we study weak stability of homogeneous deformation of the axially compressed circular cylindrical shell, regarded as a 3-dimensional hyperelastic body. We show that such deformation becomes weakly unstable at the citical load that coincides with value of the bifurcation load in von-Kármán-Donnel shell theory. We also show that the linear bifurcation modes described by the Koiter circle [11] minimize the second variation asymptotically. The key ingredients of our analysis are the asymptoticaly sharp estimates of the Korn constant for cylindrical shells and Korn-like inequalities on components of the deformation gradient tensor in cylindrical coordinates. The notion of buckling equivalence introduced in [6] is developed further and becomes central in this work. A link between features of this theory and sensitivity of the critical load to imprefections of load and shape is conjectured.