Non-linear strain–displacement equations exactly representing large rigid-body motions. Part II. Enhanced finite element technique

The precise representation of arbitrarily large rigid-body motions in the displacement patterns of curved Timoshenko–Mindlin-type (TM) shell elements has been considered in Part I of the present work. This consideration required the development of strain–displacement equations of the finite deformation TM shell theory, written in local curvilinear coordinates, with regard to their consistency with the large rigid-body motions. For this purpose the displacement vectors of the face surfaces are introduced and resolved in the reference surface frame. In this paper economical schemes of evaluating the stiffness matrix by means of the analytical integration inside the element and an advanced approach for solving incremental equilibrium equations are discussed in detail. The developed approach may allow the use of load increments that are much larger than possible with the approach proposed in Part I. The numerical results are presented to demonstrate the high accuracy and effectiveness of the developed four-node curved shell elements and to compare their performance with non-linear solid-shell elements extracted from the literature.