Dynamic buckling and post-buckling of imperfect orthotropic cylindrical shells under mechanical and thermal loads, based on the three dimensional theory of elasticity

摘要

The three-dimensional theory of elasticity in curvilinear coordinates is employed to investigate the dynamic buckling of an imperfect orthotropic circular cylindrical shell under mechanical and thermal loads. Accurate form of the strainexpressions of imperfect cylindrical shells is established through employing the general Green's strain tensor for large deformations and the equations of motion are derived in terms of the second Piola-Kirchhoff stress tensor. Then, the governingequations are properly formulated and solved by means of an efficient and relatively accurate solution procedure proposed to solve the highly nonlinear equations resulting from the above analysis. The proposed formulation is very general as it can include the influence of the initial imperfections, temperature distribution, and temperature dependency of the mechanical properties of materials, effect of various end conditions, possibility of large-deformation occurrence and application of any combination of mechanical and thermal loadings. No simplifications are done when solving the resulting equations. Furthermore, in contrast to the displacement-based layer-wise theories and the three-diniensional approaches proposed so far, the stress, force and momentboundary conditions as well as the displacement type ones, can be incorporated accurately in these formulations. Finally, a few examples of mechanical and thermal buckling of some orthotropic cylindrical shells are considered and results of the presentthree-dimensional elasticity approach are compared with the buckling loads predicated by the Donnell's equations, some single-layer theories, same available results of the layer-wise theory and the recently published three-dimensional approaches and theaccuracy of the later methods are discussed based on the exact method presented in this paper.