General Multilayer Geometrically‐Exact Beams and 1‐D Plates with Piecewise Linear Section Deformation

Abstract

Abstract A general theory of geometrically‐exact multilayer beams and 1‐D plates, which can be viewed as a special version of a Cosserat continuum, is presented. The formulation allows for shear deformation in each layer; the deformed cross section is piecewise linear such that interlayer continuity is exactly satisfied. Large deformation and large overall motion can be analyzed, as a salient feature of the geometrically‐exact formulation. The number of layers is unlimited, with the reference centroidal line arbitrarily chosen among the layers. The unique features of the present formulation provide a versatile model to investigate the behavior of an important class of composite/multilayer structure that have ply drop‐off, or that are connected together at any arbitrary layers. Also derived are two important particular cases of the general formulation: (i) The case in which only the reference layer undergoes finite rotations, whereas rotations in the outer layers are small relative to that of the reference layer, (ii) the fully linearized case.