Reddy discusses applied mechanics at Talbot Lecture

04/06/2017
 
Professor J.N. Reddy
Professor J.N. Reddy
Held on April 4, the Spring 2017 Arthur Newell Talbot Distinguished Lecture featured Professor J.N. Reddy, the Oscar S. Wyatt Endowed Chair and Distinguished Professor in the Department of Mechanical Engineering at Texas A&M University.
 
His lecture was titled: On a Robust Shell Finite Element and Non-local and Non-classical Continuum Mechanics Theories. 
 
“I am honored by the invitation to present the 2017 Talbot Lecture and thank the Talbot family for their support,” Professor Reddy said. “Like Professor Talbot, I regard that most important and satisfying part of my professional life has been to create knowledge and facilitate learning through classroom teaching, advising and mentoring students, and writing of textbooks.”
 
In fact, Reddy has written an incredible 20 textbooks and 550 journal papers, said Kritzer Distinguished Professor Narayana Aluru, who hosted Reddy’s visit. 
 
Reddy has been a leader in applied mechanics for more than 40 years and is known worldwide for his significant contributions to this field. His pioneering works on the development of shear deformation theories have had a major impact and have led to new research developments and applications.
 
Arthur Newell Talbot was named Professor of Municipal and Sanitary Engineering in charge of Theoretical and Applied Mechanics at Illinois until 1926, and regarded teaching as the most important aspect of his work at the university. The Arthur Newell Talbot Distinguished Lecture is made possible through the support of the Talbot family, in honor of their ancestor’s commitment to learning and teaching.
 
Abstract
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).