Henry L. Pierce Laboratory Seminar Series - Prof. J.N. Reddy

                         On Locking-Free Shell Finite Elements

Abstract:
In this lecture, shell finite elements based on seven-parameter and twelve-parameter shell theories for large deformation analysis of composite shell structures are discussed. The seven-parameter shell element is based on a modified first-order shell theory using a seven-parameter expansion of the displacement field [1, 2]. The twelve-parameter shell element is developed using third-order thickness stretch kinematics [3].  Both theories require the use of fully three-dimensional constitutive equations. The virtual work statement is integrated numerically through the shell thickness at each quadrature point of the  mid-surface; hence no thin-shell approximations are imposed in the numerical implementation. The finite element coefficient matrices and force vectors are evaluated numerically using appropriate high-order Gauss-Legendre quadrature rules at the appropriate quadrature points of the element mid-surface. For laminated composite shells, a user prescribed vector field (defined at the nodes) tangent to the shell mid-surface is introduced.  This discrete tangent vector allows for simple construction of the local bases associated with the principal orthotropic material directions of each lamina.  As a result, one is free to employ skewed and/or arbitrarily curved elements in actual finite element simulations. Through the numerical simulation of carefully chosen benchmark problems, it is shown that the developed shell elements are insensitive to all forms of numerical locking and severe geometric distortions and predict very accurate displacement and stress fields.

References:

1)G.S. Payette and J.N. Reddy, Computer Methods in Applied Mechanics and Engineering. 278, 664 704, 201

2)M.E. Gutierrez Rivera and J.N. Reddy, Mechanics Research Communications, 78, 60 70, Dec 201

3)M.E. Gutierrez Rivera, J.N. Reddy, M. Amabili, Composite Structures, 151, 183 196, Sept. 201

Bio:
Dr. Reddy is a Distinguished Professor, Regents’ 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 from University of Alabama in Huntsville. He worked as a Post-Doctoral Fellow in Texas Institute for Computational Mechanics (TICOM) at the University of Texas at Austin, Research Scientist for Lockheed Missiles and Space Company, Huntsville, during l974-75, and taught at the University of Oklahoma from 1975 to 1980, Virginia Polytechnic Institute & State University from 1980 to 1992, and at Texas A&M University from 1992.
Dr. Reddy, an ISI highly-cited researcher, is known for his significant contributions to the field of applied mechanics through the authorship of a large number of journal papers and 21 textbooks and the development of shear deformation plate and shell theories and their finite elements. In recent years, Reddy's research has focused on the development of  lockig-free shell finite elements and nonlocal and non-classical continuum mechanics problems, involving couple stresses, surface stress effects, micropolar cohesive damage, and continuum plasticity of metals.
Dr. Reddy has received numerous honors and awards (too many to list here). He is an elected member of the US National Academy of Engineering and a Foreign Fellow of the Canadian Academy of Engineering, the Indian National Academy of Engineering, and the Brazilian National Academy of Engineering. Also, he received the Prager Medal of the Society of Engineering Science, the 2016 ASME Medal from the American Society of Mechanical Engineers, the 2017 John von Neumann Medal from the US Association for Computational Mechanics, and the 2018 von Karman Medal from the American Society of Civil Engineers.