Forty Eighth Congress Of The Indian Society Of Theoretical And Applied Mechanics December 18 21 2003 Birla Institute Of Technology Mesra Ranchi

Author : Junuthula Narasimha Reddy
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.3/5 (91 download)

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Download or read book Development of K-version of the Finite Element Method written by Junuthula Narasimha Reddy and published by . This book was released on 2006 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report summarizes the research carried out under Grant F49620-03-1-0201 on the development of least-squares based finite element models of viscous compressible and incompressible flows as well as shear deformable plates and shells. The main objective of this research was to develop a robust and accurate computational methodology based on least-squares variational principles for the numerical solution of the equations governing plates and shells and viscous incompressible and compressible fluid flows. The use of least-squares principles 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 research, the basic theory of least-squares finite element formulations of the equations governing viscous incompressible flows and shear deformable theories of plate and shell structures was carried out and their application through a variety of benchmark problems was illustrated. In the case of fluid flows, penalty least-squares finite element models using high p-levels and low penalty parameters were developed as a good alternative to mixed least-squares finite element models, also developed in the research.