Sub-modelling and boundary conditions with pp-type hybrid-equilibrium plate-membrane elements

The main topics of this paper, sub-modelling and associated boundary conditions, are presented in two parts. The first part details a general method for evaluating consistent displacement or traction modes for hybrid equilibrium plate models to represent arbitrarily specified boundary conditions. The inheritance of boundary conditions in a process of uniform h-type refinement is considered as a particular case. The second part investigates the methodology and performance of a sub-modelling technique involving equilibrium elements, which has the aim of recovering a local quantity of interest with greater accuracy than that directly obtained from the original global or parent equilibrium model. A crucial step in this technique is the transfer of appropriate boundary tractions from the parent model to the sub-model (child). The sub-modelling technique is presented initially based on the extraction of a single element for h- and/or p-type refinement into sub-models. A more general form of sub-modelling is then presented in which the boundary of the sub-model does not coincide with that of an element, or patch of elements, in the parent model. This requires the evaluation of modes of traction around an arbitrary region, and a scheme to achieve this is presented and demonstrated using, as an example, a geometric perturbation of a single element extraction. The performances of sub-models are compared using both complete sets of traction modes and reduced, or basic, sets.