Seminar: Sheet Metal Forming Using an Isogeometric Shell Formulation
February 13, 2012
Dr. David J. Benson
Professor of Computational Mechanics
Department of Structural Mechanics
University of California, San Diego
Friday, March 2, 2012, at 3:00 PM
Warnock Engineering Bldg. Rm. L104
Reception to follow at 4:00 PM
Isogeometric analysis is a new computational method that is based on geometry representation techniques (i.e. basis functions) developed in computer-aided design (CAD), computer graphics (CG), and animation with a far-reaching goal to bridge the existing gap between CAD and analysis. For the first instantiation of the isogeometric methodology, non-uniform rational B-splines (NURBS) were chosen as a basis, due to their relative simplicity and ubiquity in the worlds of CAD, CG, and animation. It was found that not only are NURBS applicable to engineering analysis, in several cases they were better suited for the application at hand, and were able to deliver accuracy superior to standard finite elements.
CAD, CG and animation make use of boundary or surface representation to model geometrical objects, while a lot of analyses require a full volumetric description of the geometry. This makes integration of design and analysis a complicated task because no well-established techniques exits that allows one to go from a boundary to a volumetric representation in a fully automated way.
Shell analysis is a well-developed branch of computational engineering, with a wide range of industrial applications that does not require a volumetric description of the underlying geometry. As a result, bridging design and shell analysis does not constitute such a daunting task. Provided that the geometry surface description makes use of the basis functions with good approximation properties, and that are conforming to a given function space, one may, in principle, perform shell analyses directly off of CAD data.
Sheet metal forming can therefore immediately benefit from the isogeometric approach. We present here our current isogeometric shell formulations for large deformation problems and present results for some of the NUMISHEET benchmark problems.
About Dr. Benson
David J. Benson is a Professor of Computational Mechanics in the Dept. of Structural Engineering, UCSD. He obtained his PhD at the University of Michigan in mechanical engineering. Prof. Benson’s research in computational dynamics has spanned systems of rigid bodies, structural dynamics, and shock physics. After joining the Methods Develoment Group at LLNL to work with John Hallquist on Dyna3d, he focused on structural dynamics and contact algorithms that lead to the first full automobile crashworthiness simulation of a Suzuki Sprint in 1985. Moving to UCSD in 1987, he simulated the shock processing of superconductors and developed a high-resolution shock viscosity used by LLNL’s K Division, concerned with geophysics and nuclear nonproliferation. His research expanded to include multi-material ALE finite element methods, developing critical algorithms for interface reconstruction, multi-material closure theories, maximum stable time step size, and the first successful Eulerian contact formulation that is currently implemented in the Geodyn Godunov code at LLNL. His current research focuses on isogeometric methods, including the first successful higher-order accurate finite element methods without severe stable time step size penalties. He research has also focused on the modeling of heterogeneous materials, including pioneering the direct importing of digital micrographs into finite element models to generate microstructures with his research hydrocode Raven, working with NASA on the development of a high strain rate model for ice for the Space Shuttle return-to-flight effort, molecular dynamics investigations of void growth, modeling the fragmentation of NIF targets for LLNL, the micromechanical modeling of PBXs and multi-phase material models with LANL, and advanced composites material models for Boeing.