Peridynamic Differential Operator for Numerical Analysis
Springer International Publishing (Verlag)
978-3-030-02646-2 (ISBN)
This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson's and Navier's equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization.
Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
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.
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.
Erscheinungsdatum | 18.02.2019 |
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Zusatzinfo | XI, 282 p. 163 illus., 137 illus. in color. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 566 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Technik ► Maschinenbau | |
Schlagworte | Coupled multi-field equations • Data • Differential Equations • Differentiation • discrete • Implicit • Integral equations • integro-differential equations • multi-field equations • Nonlinear • Nonlocal • Ordinary • Partial • Peridynamic • Peridynamic least square minimization • Recovery • Transient • Weak form of peridynamics |
ISBN-10 | 3-030-02646-9 / 3030026469 |
ISBN-13 | 978-3-030-02646-2 / 9783030026462 |
Zustand | Neuware |
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