Finite element analysis in situ

We describe a significant extension of the finite element method (FEM) that allows finite element analysis (FEA) to be performed in situ, on a native geometric representation of a solid domain. The proposed method, called Scan&Solve, is a particular implementation of the solution structure method (SSM) that builds on the classical ideas of Kantorovich and Rvachev. It can be applied to any geometric model and used within any geometric modeling system that supports two fundamental queries: point membership testing and distance to boundary computation. The advantages of this approach include unmatched flexibility in handling geometric errors, small features, complex boundary conditions, and interfaces, while maintaining most of the benefits of classical FEA. This paper describes the technical background behind the proposed method, compares it to classical FEA formulation, details its implementation, and demonstrates its advantages.