Plenary and Semi-Plenary Lectures
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| Title: |
| Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement |
| Lecturer: |
| Thomas J.R. Hughes |
| Abstract: |
| The concept of Isogeometric Analysis is proposed. Basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite element h- and p- refinement schemes are presented and a new, more efficient, higher-order concept, k-refinement, is introduced. Refinements are easily implemented and exact geometry is maintained at all levels without the necessity of subsequent communication with a CAD (Computer Aided Design) description. In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented. Standard patch tests are likewise satisfied. Numerical examples exhibit optimal rates of convergence for linear elasticity problems and convergence to thin elastic shell solutions. A k-refinement strategy is shown to converge toward monotone solutions for advection-diffusion processes with sharp internal and boundary layers, a very surprising result. It is argued that Isogeometric Analysis is a viable alternative to standard, polynomial-based, finite element analysis and possesses several advantages. |
 Dr. Hughes is Professor of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin and holds the Computational and Applied Mathematics Chair III in the Institute for Computational Engineering and Sciences (ICES). Dr. Hughes began his career as a mechanical design engineer at Grumman Aerospace, subsequently joining General Dynamics as a research and development engineer. After receiving his Ph.D. in Engineering Science from the University of California at Berkeley, he joined the Berkeley faculty, eventually moving to California Institute of Technology and then Stanford University before joining the University of Texas at Austin. At Stanford, he served as Chairman of the Division of Applied Mechanics, Chairman of the Department of Mechanical Engineering, and Chairman of the Division of Mechanics and Computation, and occupied the Mary and Gordon Crary Chair of Engineering. Dr. Hughes is a fellow of the American Academy of Mechanics, the American Society of Mechanical Engineers (ASME), the American Society of Civil Engineering (ASCE), the U.S. Association for Computational Mechanics (USACM), the International Association for Computational Mechanics (IACM), and the American Association for the Advancement of Science. He is co-editor of the international journal Computer Methods in Applied Mechanics and Engineering, a founder and past President of USACM and IACM, and past Chairman of the Applied Mechanics Division of ASME. He has received the Walter L. Huber Civil Engineering Research Prize from ASCE, the Melville Medal from ASME, the Computational Mechanics Award from the Japan Society of Mechanical Engineers, the von Neumann Medal from USACM, the Gauss-Newton Medal from IACM, and the Worcester Reed Warner Medal from ASME. Dr. Hughes is a member of the National Academy of Engineering. |
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