Higher order shear deformable geometrically exact shells based on a new kinematic assumption

In this paper, we propose a new geometrically exact shell model integrating higher order shear deformation theory (HSDT). Departing from the classical geometrically exact shell model, the proposed shell model fundamentally reconstructs the basic kinematic assumption through synergistic use of the unit normal vector field and director field, enabling higher order deformation pattern of transverse fibers. This reconstruction naturally leads to newly defined generalized strain components and a novel constitutive relation. Compared to the five-DOF classical geometrically exact shell model, seven DOFs are allocated to each node at the element level due to employing the unit normal vector field in constructing kinematic relations. The additional DOFs are eliminated in the global equations by enforcing the constraint conditions for the unit normal vector field according to kinematic relations. Since the unit normal vector is employed as an intermediate quantity in this model, distinct from the updates of director field, a specialized update procedure is developed to maintain orthonormality of the unit normal vector field during large rotations. The MITC scheme is borrowed in this model to address membrane and shear locking phenomena. A comprehensive set of numerical examples is presented to illustrate the effectiveness of the present formulation in predicting static behaviors of shells undergoing large deformations and rotations.