Stress and strain fields in non-prismatic inhomogeneous beams

Abstract

Abstract. Beamlike structures are commonly studied via 1D beam models, which are more efficient than 3D finite element methods, but do not permit accurate predictions of 3D stresses in non-prismatic cases. Despite the progress made in their modeling, either via direct 1D approaches or dimensional reductions from 3D formulations, the accurate analytical prediction of stresses and strains in beamlike yet 3D elements, with non-uniform properties both in terms of materials and cross-section shape, subject to large displacements, is an open problem. This work presents a model for such elements that is particularly suitable for efficient numerical implementations and that allows accurate analytical predictions of stresses and strains. A paradigmatic example shows the importance of non-trivial stress terms that are absent in prismatic homogeneous elements and the inadequacy of usual beam models and stepped-beam approaches when dealing with predictions of stresses and strains in non-prismatic inhomogeneous cases.