Elementary, Static Beam Theory is as Accurate as You Please

Abstract

Starting with a solution of elementary beam theory and integrating polynomials in the thickness coordinate, we generate kinematically-admissible strain fields and statically-admissible strain fields whose average approximates the actual two-dimensional strain field in an orthotropic beam to within a relative mean square error of the order of magnitude of an arbitrary power of the ratio of the thickness of the beam to a characteristic wavelength of the elementary beam solution.