Implicit Boundary Method for Finite Element Analysis using Structured Grids

Associate Professor Ashok V. Kumar
Department of Mechanical and Aerospace Engineering
University of Florida, Gainesville, FL 32611

In the finite element method, a mesh is used for both representing the geometry of the analysis and for representing the test and trial functions by piece-wise interpolation. A method for analysis using structured grid has been developed to avoid the generation of a conforming mesh. Implicit equations of curves/surfaces are used to not only represent the geometry but also for construction of trail and test functions such that essential boundary conditions are guaranteed to be satisfied. The approach has been applied to solve linear elastostatic problems, where the trial function for the displacement field is constructed using implicit equations of the boundaries and a grid variable that is represented using B-Spline basis functions. Current research is exploring ways to extend the method to applications including micro-mechanics modeling, dynamics and non-linear analysis.

See paper for details:

Ashok V. Kumar, Sanjeev Padmanabhan and Ravi Burla, “Implicit boundary method for finite element analysis using non-conforming mesh or grid”, Int. J. Numer. Meth. Engng (2007), DOI: 10.1002/nme.2216.

Figure: Finite element analysis using structured grid