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Mechanical Engineering Colloquium

A Robust Continuum Shell Element for Large Deformation Analysis of Composite Structures

Prof. J. N. Reddy
Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering Texas A&M University

April 13, 2015 at  11:00 AM
Macdonald Engineering Room 267


In this lecture a high-order spectral/hp continuum shell finite element for the numerical simulation of fully finite deformation mechanical response of isotropic, laminated composite, and functionally graded elastic shell structures is discussed. The shell element is based on a modified first-order shell theory with a seven-parameter expansion of the displacement field. The seventh parameter is included to allow for the thickness stretch and the use of fully three-dimensional constitutive equations in the numerical implementation. 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 allowes 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 element is insensitive to all forms of numerical locking and severe geometric distortions and predicts very accurate displacement and stress fields.


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 and worked as a Post- Doctoral Fellow in Texas Institute for Computational Mechanics 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 Tech from 1980 to 1992, and Texas A&M University from 1992 till now.

Dr. Reddy is the author of numerous journal papers and several well-received textbooks in the area of composite materials and structures, variational methods, plates and shells, and linear and nonlinear finite elements. He has delivered over 130 plenary, keynote, or general invited lectures at international conferences and institutions; taught over 90 short courses on finite elements, composite materials, and nonlocal structural theories. Professor Reddy advised 32 postdoctoral fellows and research visitors and over 105 graduate theses.

Dr. Reddy’s research is concerned with the development of higher-order theories of plates and shells and extensions and applications of the finite element method to a broad range encompassing composite structures, numerical heat transfer, computational fluid dynamics, and more recently to biology and medicine. His shear deformation plate and shell theories and their finite element models and penalty finite element models of fluid flows have been implemented into commercial finite element computer programs like ABAQUS, NISA, and HyperForm. Dr. Reddy is one of the original top 100 ISI Highly Cited Researchers in Engineering around world with over 16,500 citations with h-index (h-index is the largest number h such that h publications have at least h citations) of over 61 as per Web of Science; as per Google Scholar the number of citations is over 39,500 with h-index of 81 and i10-index of 363 (i.e., 363 papers are cited at least 10 times). The National Academy of Engineering (NAE) has named Dr. Reddy among its 2015 class of new members. He was recognized for his contributions to composite structures and engineering education and practice. A more complete resume with links to journal papers can be found here Advanced Computational Mechanics Laboratory.