Description:

Abstract:

In this lecture, mass lumped, rate-type C continuous finite element models of arbitrarily higher order using shear deformable beam, plate, and shell elements are discussed. Higher-order elements provide true curvature, improved performance in bending and buckling, and avoid hourglass modes and numerical locking without ad hoc treatments. Historically, first-order shear deformation finite elements have been predominant in explicit finite element codes because of difficulties achieving robust and reliable mass-lumping. We spatially discretize using a standard weak-form 0 Galerkin finite element approximation and optimal C Lagrange shape functions of arbitrarily higher order and integrate throughout time using a central-difference method and a lumped mass matrix. Several numerical examples of nonlinear finite deformation demonstrating the accuracy and utility of the lumped-mass elements developed are presented. 

Bio:

Dr. Reddy is a Distinguished Professor, Regents’ Professor, and the holder of the O’Donnell Foundation Chair IV in Mechanical Engineering at Texas A&M University. He is known for his significant contributions to the field of applied mechanics through the authorship of many textbooks (25) and journal papers (>800). His pioneering works on the development of shear deformation theories have had a major impact and have led to new research developments and applications. In recent years, Reddy's research has focused on the development of locking-free shell finite elements and nonlocal and non-classical continuum mechanics problems dealing with architected materials and structures and damage and fracture in solids. Dr. Reddy has received some of the highest awards, including the Leonardo da Vinci Award from the European Academy of Sciences, the IACM Congress (Gauss-Newton) Medal from the International Association of Computational Mechanics, and the SP Timoshenko Medal from American Society of Mechanical Engineers, He is a member eight national academies. 

ABOUT JAN D. ACHENBACH:

Jan D. Achenbach was the Walter P. Murphy Professor and Distinguished McCormick School 
Professor Emeritus-in-Service at the McCormick School of Engineering and Applied Science at  Northwestern University until his death in August, 2020. He made distinguished contributions to many areas of applied mechanics including fracture mechanics, wave propagation, and quantitative nondestructive evaluation. During his tenure spanning nearly six decades at the McCormick School of Engineering, Prof. Achenbach mentored over 40 Ph.D. students and countless postdocs, many of whom became leaders in industry and academia. His innovations in non-destructive evaluation, such as ultrasonic approaches for inspecting DC-9 aircraft wings without disassembly improved aircraft reliability, saving lives and millions of dollars. Prof. Achenbach received top honors from many professional organizations such as ASME, ASCE, and SES. He was a member of both the National Academy of Engineering and National Academy of Sciences, an elected fellow of the American Academy of Arts and Sciences, and a recipient of both the U.S. National Medal of Technology and the National Medal of Science.