Peridynamic Differential Operator for Numerical Analysis

ERDOGAN MADENCI Erdogan Madenci is a professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona.  He received his B.S. degrees on both mechanical and industrial engineering, and his M.S. degree in applied mechanics from Lehigh University, Bethlehem, Pa in 1980, 1981, and 1982, respectively.  He received his Ph.D. degree in engineering mechanics from the UCLA in 1987.  Prior to joining the University of Arizona, he worked at Northrop Corporation, Aerospace Corporation, and Fraunhofer Institute.  Also, he worked at the KTH Royal Institute of Technology, NASA Langley Research Center, Sandia National Labs and MIT as part of his sabbatical leaves.  He is the lead author of three books on Peridynamic Theory and Its Applications, The Finite Element Method Using ANSYS, and Fatigue Life Prediction of Solder Joints.  Recently, he started the Journal of Peridynamics and Nonlocal Modeling as the Co-Editor-in-Chief.  He is a Fellow of ASME and an Associate Fellow of AIAA. ATILA BARUT Atila Barut is a Research Associate Professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona.  He received his B.S. and M.S. degrees in Engineering Sciences in 1988 and 1990, respectively, from the Middle East Technical University, Turkey.  He received his Ph.D. degree in Mechanical Engineering from the University of Arizona in 1998.  Dr. Barut is an expert on the broad area of analytical and computational modeling of solid mechanics.  Particularly, his research focused on the development of new finite elements for the analysis of composite plates and shells, and the peridynamic differential operator and its applications.  He serves on the editorial board of the Journal of Peridynamics and Nonlocal Modeling.   MEHMET DORDUNCU Mehmet Dorduncu is a PostdoctoralResearcher in the Department of Aerospace and Mechanical Engineering at the University of Arizona.  He received his B.S. and M.S. degrees in Mechanical Engineering in 2011 and 2013, respectively, from Erciyas University, Turkey.  He received his Ph.D. degree in Mechanical Engineering from the University of Arizona in 2018.  His research has focused on the advancement of the peridynamic differential operator and its applications. ​

• 1 Introduction.- 2 Peridynamic Differential Operator.- 3 Numerical Implementation.- 4 Interpolation, Regression and Smoothing.- 5 Ordinary Differential Equations.- 6 Partial Differential Equations.- 7 Coupled Field Equations.- 8 Integro-Differential Equations.- 9 Weak Form of Peridynamics.- 10 Peridynamic Least Squares Minimization.