A weak form quadrature element formulation of geometrically exact shells incorporating drilling degrees of freedom

Geometrically nonlinear analysis of shell structures is conducted using weak form quadrature elements. A new geometrically exact shell formulation incorporating drilling degrees of freedom is established wherein rotation quaternions in combination with a total Lagrange updating scheme are employed for rotation description. An extended kinematic condition to serve as the drilling rotation constraint, derived from polar decomposition of modified mid-surface deformation gradient, is exactly satisfied in the formulation. Several benchmark examples are presented to illustrate the versatility and robustness of the present formulation.