2-D constitutive equations for orthotropic Cosserat type laminated shells in finite element analysis

Abstract We propose 2-D Cosserat type orthotropic constitutive equations for laminated shells for the purpose of initial failure estimation in a laminate layer. We use nonlinear 6-parameter shell theory with asymmetric membrane strain measures and Cosserat kinematics as the framework. This theory is specially dedicated to the analysis of irregular shells, inter alia, with orthogonal intersections, since it takes into account the drilling rotation degree of freedom. Therefore, the shell is endowed naturally with 6 degrees of freedom: 3 translations and 3 rotations. The proposed equations are formulated from the statement of the generalized Cosserat plane stress with additional transverse shear components and integrated over the shell's thickness using the equivalent single layer approach (ESL). The resulting formulae are implemented into the own Fortran code enabling nonlinear shell analysis. Some numerical results are presented to show the performance of the proposed approach.