Peridynamic Differential Operator for Numerical Analysis / by Erdogan Madenci, Atila Barut, Mehmet Dorduncu.

Format:

Book

Author/Creator:

Madenci, Erdogan, author.

Barut, Atila, author.

Dorduncu, Mehmet, author.

Contributor:

SpringerLink (Online service)

Series:

Engineering (Springer-11647)

Language:

English

Subjects (All):

Mechanics.

Mechanics, Applied.

Materials science.

Computer science--Mathematics.

Computer science.

Solid Mechanics.

Characterization and Evaluation of Materials.

Computational Science and Engineering.

Local Subjects:

Solid Mechanics.

Characterization and Evaluation of Materials.

Computational Science and Engineering.

Physical Description:

1 online resource (XI, 282 pages) : 163 illustrations, 137 illustrations in color

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data. 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.

Contents:

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. .

Other Format:

Printed edition:

ISBN:

978-3-030-02647-9

9783030026479

OCLC:

1083523407

Access Restriction:

Restricted for use by site license.