A General Meta-graph Strategy for Shape Evolution under Mechanical Stress. Issue 1 (2nd January 2019) - Montoya-Zapata, Diego; Acosta, Diego A.; Ruiz-Salguero, Oscar; Posada, Jorge; Sanchez-Londono, David
Abstract: The challenges that a shape or design stands are central in its evolution. In the particular domain of stress/strain challenges, existing approaches eliminate under-demanded neighborhoods from the shape, thus producing the evolution. This strategy alone incorrectly (a) conserves disconnected parts of the shape and (b) eliminates neighborhoods which are essential to maintain the boundary conditions (supports, loads). The existing analyses preventing (a) and (b) are conducted in an ad-hoc manner, by using graph connectivity. This manuscript presents the implementation of a meta-graph methodology, which systematically lumps together finite element subsets of the current shape. By considering this meta-graph connectivity, the method impedes situations (a) and (b), while maintaining the pruning of under-demanded neighborhoods. Research opportunities are open in the application of this methodology with other types of demand on the shape (e.g., friction, temperature, drag, and abrasion).