Finite Element for Buckling of Curved Beams and Shells with Shear

Abstract

Inclusion of shear deformations allows the bending theory to be extended to relatively thick beams and shells and, at the same time, simplifies the finite element formulation for both thick and thin beams because monotonic convergence may be achieved without ensuring continuity of displacement derivatives between adjacent elements. Consequently, on may use low order interpolation polynomials, including linear ones. This is particularly useful in the case of curved beams because with higher order interpolation polynomials it is very difficult to satisfy exactly the conditions of no self-staining at rigid body rotations and of availability of all constant strain states, while with linear displacement interpolation polynomials and a straight shape of the element these requirements are easily met.