A solid-shell Cosserat point element for the analysis of geometrically linear and nonlinear laminated composite structures

This study deals with the development of a new solid-shell element using the Cosserat point theory for the linear and nonlinear analysis of laminated elastic structures. Generally speaking, the Cosserat point approach considers the element as a structure with a strain energy function that characterizes its response. This strain energy function is additively decomposed into two parts, where the first part depends on an average measure of the deformation and the second part, which is referred to as the inhomogeneous strain energy, controls the element's response to any inhomogeneous deformation. Due to the coupling nature between homogeneous and inhomogeneous deformation in laminated structures, the inhomogeneous strain energy is further additively decomposed into two parts. The first part quadratically depends on the inhomogeneous strain measures, while the second part accounts for the coupling between the homogeneous and inhomogeneous deformations. In the present study, a methodology for the determination of the constitutive coefficients for the two parts of the inhomogeneous strain energy function is presented. The resulting constitutive coefficients ensure an accurate modeling of the inhomogeneous deformations and also ensure that the element has a control on all the inhomogeneous modes of the deformation. Both linear and nonlinear example problems are considered, which demonstrate that the developed laminated Cosserat point element (LSSCPE) is accurate, efficient, robust, and applicable in modeling laminated structures with one element through the structure's thickness.