Face-based Selection of Corners in 3D Substructuring

In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of proposing a new heuristic algorithm for this purpose. Considering faces as the basic building blocks of the interface, inherent parallelism, and better robustness with respect to disconnected subdomains are among features of the new technique. The advantages of the presented algorithm in comparison to some earlier approaches are demonstrated on three engineering problems of structural analysis solved by the BDDC method.

The development of a scanning strategy for the manufacture of porous biomaterials by selective laser melting.

Porous structures are used in orthopaedics to promote biological fixation between metal implant and host bone. In order to achieve rapid and high volumes of bone ingrowth the structures must be manufactured from a biocompatible material and possess high interconnected porosities, pore sizes between 100 and 700 microm and mechanical strengths that withstand the anticipated biomechanical loads. The challenge is to develop a manufacturing process that can cost effectively produce structures that meet these requirements. The research presented in this paper describes the development of a 'beam overlap' technique for manufacturing porous structures in commercially pure titanium using the Selective Laser Melting (SLM) rapid manufacturing technique. A candidate bone ingrowth structure (71% porosity, 440 microm mean pore diameter and 70 MPa compression strength) was produced and used to manufacture a final shape orthopaedic component. These results suggest that SLM beam overlap is a promising technique for manufacturing final shape functional bone ingrowth materials.