A partial discretization formulation with two-noded finite elements (FEs) under plane stress conditions has been developed for flexural analysis of composite and sandwich beams subjected to transverse loading. The methodology consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) with four degrees of freedom (u, w, τxz and σz) per node. Continuity of interlaminar transverse stresses and displacements at laminae interfaces is implicitly enforced in the formulation. All the fundamental elasticity relationships between the components of stress, strain and displacement fields are explicitly maintained throughout the elastic continuum. Results have been obtained for cross-ply composite and sandwich beams. Excellent agreement with available analytical, mixed semianalytical and FE solutions is observed. Some new results with clamped support conditions have also been obtained and are presented to serve as benchmark solutions for future reference and to show the generality of the formulation.
Steiner symmetrization for anisotropic quasilinear equations via partial discretization
