A framework for creating low-order shell elements free of membrane locking

This paper proposes a first step towards a framework to develop shell elements applicable to any deformation regime. Here, we apply it to the large and moderate deformations of, respectively, plates and shells, showing with standard benchmarks that the resulting low-order discretization is competitive against the best elements for either membrane-dominated or bending-dominated scenarios. Additionally, we propose a new test for measuring membrane locking, which highlights the mesh-independence properties of our element. Our strategy is based on building a discrete model that mimics the smooth behavior by construction, rather than discretizing a smooth energy. The proposed framework consists of two steps: (i) defining a discrete kinematics by means of constraints and (ii) formulating an energy that vanishes on such a constraint manifold. We achieve (i) by considering each triangle as a tensegrity structure, constructed to be unstretchable but bendable isometrically (in a discrete sense). We then present a choice for (ii) based on assuming a linear strain field on each triangle, using tools from differential geometry for coupling the discrete membrane energy with our locking-free kinematic description. We argue that such a locking-free element is only a member of a new family that can be created using our framework (i) and (ii). Copyright (C) 2016 John Wiley & Sons, Ltd.