A new computational framework is developed for the numerical simulations of boundary-value problems (BVP) and initial-value problems (IVP) using the finite element method. Two essential elements of the proposed mathematical and computational framework are: (1) the variational consistency (VC) and (2) global differentiability or smoothness of the approximate solutions. The least-squares based variational formulations are found to be variationally consistent, and the use of Ck-approximations provides the global smoothness of the approximate solutions. The use of least-squares principles also leads to a variationally unconstrained minimization problem, where compatibility conditions between approximation spaces � such as inf-sup conditions � never arise. Furthermore, the resulting linear algebraic problem will always have a symmetric positive definite (SPD) coefficient matrix, allowing the use of robust and fast preconditioned conjugate gradient methods for its solution. In this lecture, author�s research in least-squares computational methodology for the study of plate and shell problems as well as the flows of viscous incompressible flows will be discussed. The basic theory of least-squares finite element formulations of the equations governing viscous incompressible flows and those of the shear deformable plate and shell structures will be presented and their application through some benchmark problems will be discussed.

Biography:

Dr. Reddy is a Distinguished Professor and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas. Dr. Reddy earned a Ph.D. in Engineering Mechanics in 1974. He worked as a Post-Doctoral Fellow at the University of Texas at Austin, Research Scientist for Lockheed Missiles and Space Company during l974-75, and taught at the University of Oklahoma from 1975 to 1980 and Virginia Polytechnic Institute & State University from 1980 to 1992. Currently Prof Reddy heads the Engineering Science Programme at National University of Singapore. Dr. Reddy is the author of multiple hundreds of journal papers and more than 12 text books on theoretical formulations and finite-element analysis of problems in solid and structural mechanics (plates and shells), composite materials, computational fluid dynamics, numerical heat transfer, and applied mathematics. He is the first recipient of numerous awards including the 1984 Walter L. Huber Civil Engineering Research Prize of the ASCE, 1992 Worcester Reed Warner Medal and 1995 Charles Russ Richards Memorial Award of the ASME, the 1997 Archie Higdon Distinguished Educator Award from the Mechanics Division of the ASEngEdu, the 1998 Nathan M. Newmark Medal from the ASCE, and the 2000 Technomic Award for Composites from the American Society of Composite Materials. He is a fellow of AAM, ASCE, ASME, IACM, USACM, and ASI. He also received Certificates of Teaching Excellence at Virginia Polytechnic Institute and Outstanding Graduate Teaching award from Texas A&M University.

Dr. Reddy serves on the editorial boards of about two dozen journals, including: Journal of Applied Mechanics (ASME), International Journal for Numerical Methods in Engineering, and International Journal for Numerical Methods in Fluids. He is the Editor-in-Chief of Mechanics of Composite Materials and Structures, and International Journal for Computational Methods in Engineering Science & Mechanics serves as of the editor of International Journal of Structural Stability and Dynamics.