An unconditionally stable time integration for the dynamics of elastic beams and shells in finite motions

Abstract. This work presents a numerical framework for long dynamic simulations of structures made of multiple thin shells undergoing large deformations. The C1-continuity requirement of the Kirchhoff-Love theory is met in the interior of patches by cubic NURBS approximation functions with membrane locking avoided by patch-wise reduced integration. A simple penalty approach for coupling adjacent patches, applicable also to non-smooth interfaces and non-matching discretization is adopted to impose translational and rotational continuity. A time-stepping scheme is proposed to achieve energy conservation and unconditional stability for general nonlinear strain measures and penalty coupling terms, like the nonlinear rotational one for thin shells. The method is a modified mid-point rule with the internal forces evaluated using the average value of the stress at the step end-points and an integral mean of the strain-displacement tangent operator over the step computed by time integration points.