Extending the Reach of the Finite Element Method: Polyhedral Elements, Solution Remapping, and Nonconforming Embedment

Lecturer: Mark M. Rashid, University of California, Davis, USA
Date: August 17, 2011, 10:00
Location: Institute of Thermomechanics AS CR, v. v. i., Dolejškova 5, Prague, lecture room B
Mark M. Rashid is a professor at the Department of Civil and Environmental Engineering of University of California, Davis, California, USA. His research interest include fracture mechanics, computational mechanics, fluid-structure interaction, blast loading, material modeling, plasticity, MEMS.

The presentation is a part of the Presentation Series on Computational Solid Mechanics held on August 3-17, 2011 in the Institute of Thermomechanics ASCR v. v. i.


The finite element method (FEM) has reached a highly evolved state as a practical tool for addressing technological problems in applied mechanics. Recent decades have seen great advances in solution visualization, in interoperability with CAD software, in parallelization, and in other areas. Yet, for all this software sophistication, there remain classes of problems that continue to present difficulties to conventional FE methodology. Extreme geometric complexity, for example, incurs a large burden in human-effort terms, and therefore in the expense of an analysis. Even greater challenges are manifest when the connectivity of the material domain evolves throughout the course of the solution. Fracture, material removal (cutting, machining), and welding are primary examples. With these applications in mind, a few recent developments in FE methodology will be presented that are intended to make some of these challenging problems more accessible to routine simulation. The “partitioned element method” (PEM) is a new FE-like Galerkin approximation method in which the elements can take essentially any polyhedral shape. This flexibility facilitates a high degree of automation in the meshing phase, even for intricate geometries. A second development seeks to exploit the PEM’s flexibility via degeneracy-tolerant Boolean geometric operations (intersection, union, difference) on polyhedral/polygonal meshes. A new approach to transferring the solution state from one FE mesh to another represents a third development. Finally, a method to insert an independently-generated mesh into a nonconforming “host” mesh will be described. The presentation will synopsize these developments, and will attempt to explain how they fit together to extend the technological reach of FE-based simulation in applied mechanics.

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