Wariacyjna Metoda W.Z. Własowa w zastosowaniu do Cienkich Powłok w Kształcie Ostrosłupa Ściętego

Abstract

After a discussion of the general variational method of V.Z. Vlasov enabling us to reduce various complicated partial differential equations of thin-walled prismatic shells to ordinary differential equations, partial differential equations are derived for a conical shell with small taper. By introducing the displacement functions u (z,s) and v (z, s) in the form of a sum of products of two functions, each of a different variable, the normal and shear stresses are determined. Two sets of partial differential equations of conical shells are obtained, of which one, composed of three equations, concerns the bending of the shell, the second, composed of two equations, the torsion of the shell. They are reduced to ordinary differential equations and solved for a prescribed load, the boundary conditions being given for the determination of the integration constants.