In this lecture (1) a high-order spectral/hp continuum shell finite element for the numerical simulation of the fully finite deformation mechanical response of isotropic, laminated composite, and functionally graded elastic shell structures and (2) non-local continuum mechanics theories and applications will be discussed. The shell element is based on a modified first-order shell theory using a 7-parameter expansion of the displacement field (2016). The non-local theories discussed include higher gradient to truly nonlocal. In this lecture, an overview of the author’s recent research on nonlocal elasticity and couple stress theories in formulating the governing equations of functionally graded material beams and plates will be discussed. In addition to Eringen’s nonlocal elasticity (1972), two different nonlinear gradient elasticity theories that account for (a) geometric nonlinearity and (b) microstructure-dependent size effects are discussed to establish the connection between them. The first theory is based on modified couple stress theory of Mindlin (1963) and the second one is based on Srinivasa-Reddy gradient elasticity theory (2013). These two theories are used to derive the governing equations of beams and plates. In addition, the graph-based finite element framework (GraFEA) suitable for the study of damage in brittle materials will be discussed. GraFEA stems from conventional finite element method (FEM) by transforming it to a network representation based on the study by Reddy and Srinivasa (2015) and advanced by Khodabakhshi, Reddy, and Srinivasa (2016).
- M. E. Gutierrez Rivera and J.N. Reddy (2016), Mech. Res. Comm.
- A. C. Eringen (1972): Int. J. Engng Sci, 10, p. 1.
- R. D. Mindlin (1963): Experi. Mech., 3(1), p. 1.
- A. R. Srinivasa and J. N. Reddy (2013): J. Mech. Phys. Solids, 61(3), p. 873.
- J. N. Reddy and A. R. Srinivasa (2015): Finite Elements in Anal. Design, 104, 35-40.
About the Speaker
Dr. Reddy is the Oscar S Wyatt Endowed Chair Professor, Distinguished Professor, and Regents Professor of Mechanical Engineering at Texas A&M University. He is a highly-cited researcher, author of 20 textbooks and over 550 journal papers, and a leader in the applied mechanics field for more than 40 years.
Dr. Reddy is known worldwide for his significant contributions to the field of applied mechanics through the authorship of widely used textbooks on the linear and nonlinear finite element analysis, variational methods, composite materials and structures, applied functional analysis, and continuum mechanics. His pioneering works on the development of shear deformation theories (that bear his name in the literature as the Reddy third-order plate theory and the Reddy layerwise theory) have had a major impact and have led to new research developments and applications.
Dr. Reddy’s earlier research focused primarily on mathematics of finite elements, variational principles of mechanics, shear deformation and layerwise theories of laminated composite plates and shells, analysis of bimodular materials, modeling of geological and geophysical phenomena, penalty finite elements for flows of viscous incompressible fluids, least-squares finite element models of fluid flows and solid continua. Some of the ideas on shear deformation theories and penalty finite element models of fluid flows have been implemented into commercial finite element computer programs like ABAQUS, NISA, and HyperXtrude.
In recent years, Dr. Reddy's research deals with 7- and 12-parameter shell theories, nonlocal and non-classical continuum mechanics problems, and problems involving couple stresses, surface stress effects, discrete fracture and flow, micropolar cohesive damage, and continuum plasticity of metals from considerations of non-equilibrium thermodynamics - as they appear in blood flow, bones, and materials with hard inclusions and phases.
His recent (since 2015) honors include: Member of US National Academy of Engineering, Foreign Fellow of Indian National Academy of Engineering, Hall of Fame of the College of Engineering, Technology, and Architecture at Oklahoma State University, Prager Medal from Society of Engineering Science, ASME Medal from the American Society of Mechanical Engineers, and Thomson Reuters IP and Science’s Web of Science Highly Cited Researchers - Most Influential Minds.
Host: Professor Narayan Aluru