Hierarchical Partition of Unity Field Compositions (HPFC) for Optimal Design in the Presence of Cracks

摘要

In this paper, the theory of Hierarchical Partition of Unity Field Compositions (HPFC) is applied for the analysis of cracks and for the optimal design in the presence of cracks. In the HPFC procedure, the geometrical, material and behavioral fields defined over primitive domains are composed through Boolean operations similar to the Constructive Solid Geometry Procedure of CAD. Here, cracks are modeled as compositions of a continuous field with a discontinuous enrichment field. Convergence of the composed fields is ensured by developing constructions that obey the partition of unity property. Non-Uniform Rational B-Splines (NURBS) which are a common choice for modeling curves and surfaces in CAD systems are used to discretize the geometry, material, and behavioral felds (local approximations) over the primitive regions and to describe crack shapes as well as the discontinuous behavioral feld corresponding to the crack. Following several validation examples, crack propagation simulations without remeshing, and example problems aimed at determining the optimal location and shape of defense holes in the presence of fracture constraints are demonstrated.