INFORMATIVO ABCM Nº 114/09 – Seminários do Prof. J.N. Reddy na Poli/USP

Seminários do Professor J.N. Reddy na Escola Politécnica/USP

Prof. J. N. Reddy
Distinguished Professor
Oscar S. Wyatt Endowed Chair in the
Department of Mechanical Engineering
Texas A&M University

O Departamento de Engenharia Mecatrônica e de Sistemas Mecânicos com apoio da Petrobrás (Projeto da Rede Galileu) está promovendo uma série de 4 seminários a serem ministrados pelo Professor J. N. Reddy da “Texas A&M University”, College Station, TX, EUA, nos dias 04, 05, 06 e 11 de Novembro de 2009 (quarta, quinta, sexta e quarta, às 14hs).

Público alvo: Pesquisadores, e pós-graduandos com interesse na área de materiais compósitos e simulação computacional. Favor confirmar presença pelo email ecnsilva017@gmail.com

Local: Escola Politécnica da Universidade de São Paulo (veja adiante os locais específicos para cada seminário).

Data: 04, 05, 06 e 11 de Novembro de 2009 (quarta, quinta, sexta e quarta, às 14h).

Apoio: PETROBRÀS (Projeto Rede Galileu)

Pessoa para Contato: Prof. Dr. Emílio Carlos Nelli Silva (ecnsilva@usp.br)

Prof. J. N. Reddy
(http://authors.isihighlycited.com/ or http://www.tamu.edu/acml).

Professor J. N. Reddy is Distinguished Professor and the Holder of Oscar S. Wyatt Endowed Chair in the Department of Mechanical Engineering at Texas A&M University, College Station, Texas.

Professor Reddy has made research contributions to such diverse fields as mechanics of materials, variational and computational methods, fluid dynamics, and heat transfer. He is internationally known for his lasting contributions to two broad research areas, namely, mechanics of advanced and composite materials and structures and interdisciplinary computational mechanics. He is the author of 16 engineering textbooks (not counting subsequent editions) at the undergraduate and graduate levels, and over 375 journal publications, and 600 conference presentations. The higher-order plate and shell theories he developed to account for transverse shear deformation in composite plate and shell structures bears his name, Reddy’s third-order theory and Reddy’s layerwise theory. They have been used by other researchers around the world to study a variety of structural problems for bending, buckling, and vibration response. The penalty function and least-squares finite element formulations and associated computational models of problems in solid mechanics as well as fluid mechanics have also been cited extensively. He has over 10,000 citations with H-index of over 40 to his credit. Professor Reddy is one of the very few researchers in engineering around world that is recognized by ISI Highly Cited Researchers. His research has been supported by leading funding agencies including the National Science Foundation (NSF), the Army Research Office (ARO), Office of Naval Research (ONR), the Los Alamos National Laboratory, National Aeronautics and Space Administration (NASA), and the Air Force Office of Scientific Research (AFOSR).

Professor Reddy is the recipient of numerous awards, including the Worcester Reed Warner Medal and the Charles Russ Richards Memorial Award of the American Society of Mechanical Engineers (ASME), the 1997 Archie Higdon Distinguished Educator Award from the American Society of Engineering Education (ASEE), the 1998 Nathan M. Newmark Medal from the American Society of Civil Engineers, the 2003 Computational Solid Mechanics Award from the U.S. Association of Computational Mechanics (USACM), and the 2000 Excellence in the Field of Composites and 2004 Distinguished Research Award from the American Society of Composites. Professor Reddy is a Fellow of AIAA, ASCE, ASME, the American Academy of Mechanics, the American Society of Composites, the U.S. Association of Computational Mechanics, the International Association of Computational Mechanics (IACM), and the Aeronautical Society of India. Professor Reddy is the Editor-in-Chief of Applied Mechanics Reviews, Mechanics of Advanced Materials and Structures, International Journal of Computational Methods in Engineering Science and Mechanics, and International Journal of Structural Stability and Dynamics.

Dia 04 de Novembro às 14 hs
Local: Anfiteatro do Prédio da Engenharia Mecânica

LEAST-SQUARES FINITE ELEMENT MODELS
OF PROBLEMS IN SOLID MECHANICS

J.N. Reddy
Distinguished Professor and Oscar S. Endowed Chair
Department of Mechanical and Engineering
Texas A&M University, College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

ABSTRACT

In this lecture, a computational methodology based on least-squares variational principles and the finite element method is discussed for the numerical solution of 1-D and 2-D problems arising in heat transfer and solid mechanics. A detailed discussion of various finite element models using the least-squares and weak form Galerkin formulations will be presented and their relative merits and demerits will be discussed. In particular, displacement type and mixed formulations of one-dimensional problems of heat transfer, bars, and beams will be discussed in detail. Extension of the same ideas to plate bending and natural vibration will also be presented.

References for Additional Reading

• J. N. Reddy, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, UK, 2004.
• J. P. Pontaza and J. N. Reddy, “Least-Squares Finite Element Formulation for Shear- Deformable Shells,” Computer Methods in Applied Mechanics and Engineering, Vol. 194 (21-24), pp. 2464-2493, 2005.
• K. S. Surana, A. Rajwani, and J. N. Reddy, “The k-Version Finite Element Method for Singular Boundary-Value Problems with Application to Linear Fracture Mechanics,” International Journal of Computational Methods in Engineering Science and Mechanics, Vol. 7, no. 3, pp. 217-239, 2006.

Dia 05 de Novembro às 14 hs
Local: Anfiteatro do Prédio da Engenharia Mecânica
LEAST-SQUARES FINITE ELEMENT MODELS OF FLOWS
OF VISCOUS INCOMPRESSIBLE FLUIDS

J.N. Reddy
Distinguished Professor and Oscar S. Endowed Chair
Department of Mechanical and Engineering
Texas A&M University, College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

ABSTRACT

A computational methodology based on least-squares variational principles and the finite element method is discussed for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible 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 the context of viscous incompressible flows, least-squares based formulations offer substantial improvements over the weak form Galerkin finite element models, where the finite element spaces for velocities and pressure must satisfy an inf-sup compatibility condition. In contrast, least-squares formulations circumvent the inf-sup condition, thus allowing equal-order interpolation of velocities and pressure, and result (after suitable linearization) in linear algebraic systems with a SPD coefficient matrix. In this lecture, the least-squares finite element formulations of the Navier-Stokes equations governing viscous incompressible flows will be presented, and their application through some benchmark problems will be discussed.

References for Additional Reading

• J. P. Pontaza and J. N. Reddy, “Space-Time Coupled Spectral/hp Least-Squares Finite Element Formulation for the Incompressible Navier-Stokes Equations,” Journal of Computational Physics, 197(2), pp. 418-459, 2004.
• JJ. P. Pontaza and J. N. Reddy, “Least-squares finite element formulations for viscous compressible and incompressible fluid flows,” Computer Methods in Applied Mechanics and Engineering, 195, 2454-2494, 2006.
• JV. Prabhakar and J. N. Reddy, “Spectral/hp Penalty Least-squares Finite Element Formulation for Unsteady Incompressible Flows,” International Journal of Numerical Methods for Fluids, 58 (3), 287-306, 2008.
• JV. Prabhakar, J. Pontaza, and J. N. Reddy, “A Collocation Penalty Least-squares Finite Element Formulation for Incompressible Flows,” Computer Methods in Applied Mechanics and Engineering, 197, 449-463, 2008.

Dia 06 de Novembro às 14 hs
Local: Anfiteatro do Prédio da Engenharia Mecânica
STRUCTURAL THEORIES FOR THE ANALYSIS OF LAMINATED COMPOSITE PLATES: AN OVERVIEW

J.N. Reddy
Distinguished Professor and Oscar S. Endowed Chair
Department of Mechanical and Engineering
Texas A&M University, College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

ABSTRACT

This is lecture reviews various theories used to model the structural behavior of laminated plates. The theories reviewed include the classical, first-order, third-order and layerwise theories. Beginning with the assumed displacement fields, the complete sets of governing equations are derived and representative examples of bending, vibration, and buckling of composite laminates are presented to bring out the differences between theories.

REFERENCE

• Reddy J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, Boca Raton, Florida, 2004.

Dia 11 de Novembro às 14 hs
Local: Anfiteatro do Prédio da Engenharia Metalúrgica
NONLINEAR ANALYSIS OF LAMINATED COMPOSITE STRUCTURES USING A REFINED SHELL FINITE ELEMENT

J.N. Reddy
Distinguished Professor and Oscar S. Endowed Chair
Department of Mechanical and Engineering
Texas A&M University, College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

ABSTRACT

A shell finite element for the nonlinear analysis of laminated shell structures and through-thickness functionally graded shells will be presented [1-3]. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account shell thickness changes and, therefore, 3D constitutive equations are utilized. A tensor-based finite element formulation is used to describe the deformation and constitutive laws of a shell in a natural and simple way by using curvilinear coordinates. In addition, a family of high-order elements with Lagrangian interpolations is used to avoid membrane and shear locking; no mixed interpolations are employed. Numerical comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composite plates and shells as well as functionally graded plates and shells are found to be excellent. These results show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for applications in contact mechanics and damage propagation in shells.

REFERENCES

• Reddy J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, Boca Raton, Florida, 2004.
• Arciniega, R. A. and Reddy, J. N., “Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures,” Computer Methods in Applied Mechanics and Engineering, 196(4-6), 1048-1073, 2007.
• Arciniega, R. A. and Reddy, J. N., “Large Deformation Analysis of Functionally Graded Shells,” International Journal of Solids and Structures, 44(6), 2036-2052, 2007.