Unconditionally Stable Time Stepping Scheme for Large Deformation Dynamics of Elastic Beams and Shells

An implicit time stepping scheme is proposed to achieve energy conservation and unconditional stability for elastic beams and shells undergoing large deformations. More generally, the method can be applied to all structural models, regardless of the nonlinearity in the relationship linking the strain to the kinematic degrees of freedom (displacements and rotations). In this respect, also nonlinear multi-body coupling laws can be included in penalty form by interpreting them as generalized strains. The time stepping scheme is a simple modification of the mid-point rule with the mean 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.