I will begin by probing into the past to discover the origins of the Finite Element Method (FEM), and then trace the evolution of those early developments to the present day in which the FEM is ubiquitous in science, engineering, mathematics, and medicine, and the most important discretization technology in Computational Mechanics. However, despite its enormous success, there are still problems with contemporary technology, for example, building meshes from Computer Aided Design (CAD) representations is labor intensive, and a significant bottleneck in the design-through-analysis process; the introduction of geometry errors in computational models that arise due to feature removal, geometry clean-up and CAD “healing,” necessary to facilitate mesh generation; the inability of contemporary technology to “close the loop” with design optimization; and the failure of higher-order finite elements to achieve their full promise in industrial applications. These issues are addressed by Isogeometric Analysis (IGA), the vision of which was first presented in a paper published October 1, 2005 [1].

I will briefly present the motivation leading to IGA, its status, recent progress, areas of current activity, and what it offers for analysis model development and the design-through-analysis process.

Finally, I will speculate on the future of Computational Mechanics, the technologies that will prevail, computer developments, and the role of machine learning.

Dr. Thomas J.R. Hughes holds B.E. and M.E. degrees in Mechanical Engineering from Pratt Institute and an M.S. in Mathematics and Ph.D. in Engineering Science from the University of California at Berkeley. He taught at Berkeley, Caltech and Stanford 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, Chairman of the Division of Mechanics and Computation, and held the Mary and Gordon Crary Family Chair of Engineering. Dr. Hughes is a fellow of the American Academy of Mechanics (AAM), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Civil Engineers (ASCE), the American Society of Mechanical Engineers (ASME), the U.S. Association for Computational Mechanics (USACM), the International Association for Computational Mechanics (IACM), the Society of Industrial and Applied Mathematics (SIAM), and the American Association for the Advancement of Science (AAAS). He is co-editor of the international journal Computer Methods in Applied Mechanics and Engineering, a founder and past President of USACM and IACM, past Chairman of the Applied Mechanics Division of ASME, and past Chairman of the U.S. National Committee on Theoretical and Applied Mechanics (USNC/TAM). Dr. Hughes is an elected member of the U.S. National Academy of Sciences, the U.S. National Academy of Engineering, the American Academy of Arts and Sciences, and the Academy of Medicine, Engineering and Science of Texas, and a Foreign Member of the Royal Society of London, the Austrian Academy of Sciences (Section for Mathematics and the Physical Sciences), and the Istituto Lombardo Accademia di Scienze e Lettere (Mathematics Section). Dr. Hughes is one of the most widely cited authors in Engineering Science. He has been elected to Distinguished Member, ASCE’s highest honor, and has received ASME’s highest honor, the ASME Medal. He has also received the Huber Prize and Von Karman Medal from ASCE, the Timoshenko, Worcester Reed Warner, and Melville Medals from ASME, the Von Neumann Medal from USACM, the Gauss-Newton Medal from IACM, the SIAM/ACM Prize in Computational Engineering Science, the Ralph E. Kleinman Prize from SIAM and many other national and international awards. Dr. Hughes has received honorary doctorates from the Université catholique de Louvain, the University of Pavia, the University of Padua, the Norwegian University of Science and Technology (Trondheim), Northwestern University (Evanston), and the University of A Coruña. The Special Achievement Award for Young Investigators in Applied Mechanics is an award given annually by the Applied Mechanics Division of ASME. In 2008 this award was renamed the Thomas J.R. Hughes Young Investigator Award. In 2012 the Computational Fluid Mechanics Award of the United States Association for Computational Mechanics was renamed the Thomas J.R. Hughes Medal. Dr. Hughes has presented multiple plenary lectures at World Congresses of Computational Mechanics and United States National Congresses of Computational Mechanics. He also delivered a plenary lecture at the International Congress of Mathematicians (Numerical Analysis, Hyderabad, 2010).

References 1. T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135–4195.