FE Solver Integration Framework

This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

Integrating finite element analysis (FEA) with systems engineering (SE) improve traceability, consistency, interoperability and collaboration between SE and FEA activities in multiple engineering disciplines. The first step in achieving this is a software-independent description of FEA models, which are characterized by numerical approximations of partial differential equations (PDEs) derived from physical laws, and finite elements representing unknown physical quantities. In previous work, we presented a finite element mathematics specification that is formal and understandable by most engineers. It provides all information needed for generation of shape functions for physical quantities. In this work, we propose a specification of physics used in FEA to complement our earlier mathematics specification.



We first compare existing FEA physics descriptions and their corresponding software implementations to highlight the benefits of domain-independent model descriptions used by PDE solvers. A significant drawback of PDE representations is they do not show all physical quantities from which they are derived. To tackle this, we represent the physical laws and derivations needed for FEA PDEs in machine-readable graphs. Instead of classifying physics problems by the kind of PDE used in FEA, as in PDE solver packages, we formalize problems as paths through these graphs. This increases transparency by capturing modelling decisions that are currently done on paper or electronic documents.



We combine the graph-based specification of FEA physics above with the finite element mathematics specification developed earlier to generate linear system of equations (algebraic FEA models) for solving the problem numerically. The combination will enable FEA engineers to design their own libraries (potentially automatically) if they choose, or associate existing solvers. It also generalizes mappings from physics to FEA models, a task currently repeated across specific disciplines. The framework could be standardized and integrated with SE modeling languages, improving interoperability and collaboration between systems and FEA engineers.