Language:
English
繁體中文
Help
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
The Generalized Fourier Series Metho...
~
Constanda, Christian.
The Generalized Fourier Series Method = Bending of Elastic Plates /
Record Type:
Language materials, printed : Monograph/item
Title/Author:
The Generalized Fourier Series Method/ by Christian Constanda, Dale Doty.
Reminder of title:
Bending of Elastic Plates /
Author:
Constanda, Christian.
other author:
Doty, Dale.
Description:
XIII, 254 p. 186 illus., 37 illus. in color.online resource. :
Contained By:
Springer Nature eBook
Subject:
Solid Mechanics. -
Online resource:
https://doi.org/10.1007/978-3-030-55849-9
ISBN:
9783030558499
The Generalized Fourier Series Method = Bending of Elastic Plates /
Constanda, Christian.
The Generalized Fourier Series Method
Bending of Elastic Plates /[electronic resource] :by Christian Constanda, Dale Doty. - 1st ed. 2020. - XIII, 254 p. 186 illus., 37 illus. in color.online resource. - Developments in Mathematics,651389-2177 ;. - Developments in Mathematics,41.
1. The Mathematical Model -- 2. Generalized Fourier Series -- 3. Interior Dirichlet Problem -- 4. Interior Neumann Problem -- 5. Interior Robin Problem -- 6. Exterior Dirichlet Problem -- 7. Exterior Neumann Problem -- 8. Exterior Robin Problem -- A. Numerical Issues -- B. Numerical Integration -- C. Interior Boundary Value Problem for D[x,y] -- D. Exterior Boundary Value Problems for D^A[X,y] -- E. Numerical Integration of P[x,y] and P^A[x,y] -- References -- Index.
This book explains in detail the generalized Fourier series technique for the approximate solution of a mathematical model governed by a linear elliptic partial differential equation or system with constant coefficients. The power, sophistication, and adaptability of the method are illustrated in application to the theory of plates with transverse shear deformation, chosen because of its complexity and special features. In a clear and accessible style, the authors show how the building blocks of the method are developed, and comment on the advantages of this procedure over other numerical approaches. An extensive discussion of the computational algorithms is presented, which encompasses their structure, operation, and accuracy in relation to several appropriately selected examples of classical boundary value problems in both finite and infinite domains. The systematic description of the technique, complemented by explanations of the use of the underlying software, will help the readers create their own codes to find approximate solutions to other similar models. The work is aimed at a diverse readership, including advanced undergraduates, graduate students, general scientific researchers, and engineers. The book strikes a good balance between the theoretical results and the use of appropriate numerical applications. The first chapter gives a detailed presentation of the differential equations of the mathematical model, and of the associated boundary value problems with Dirichlet, Neumann, and Robin conditions. The second chapter presents the fundamentals of generalized Fourier series, and some appropriate techniques for orthonormalizing a complete set of functions in a Hilbert space. Each of the remaining six chapters deals with one of the combinations of domain-type (interior or exterior) and nature of the prescribed conditions on the boundary. The appendices are designed to give insight into some of the computational issues that arise from the use of the numerical methods described in the book. Readers may also want to reference the authors’ other books Mathematical Methods for Elastic Plates, ISBN: 978-1-4471-6433-3 and Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation, ISBN: 978-3-319-26307-6.
ISBN: 9783030558499
Standard No.: 10.1007/978-3-030-55849-9doiSubjects--Topical Terms:
1211586
Solid Mechanics.
LC Class. No.: QA404.7-405
Dewey Class. No.: 515.96
The Generalized Fourier Series Method = Bending of Elastic Plates /
LDR
:04215nam a22004095i 4500
001
1027751
003
DE-He213
005
20201121101151.0
007
cr nn 008mamaa
008
210318s2020 gw | s |||| 0|eng d
020
$a
9783030558499
$9
978-3-030-55849-9
024
7
$a
10.1007/978-3-030-55849-9
$2
doi
035
$a
978-3-030-55849-9
050
4
$a
QA404.7-405
072
7
$a
PBWL
$2
bicssc
072
7
$a
MAT033000
$2
bisacsh
072
7
$a
PBWL
$2
thema
082
0 4
$a
515.96
$2
23
100
1
$a
Constanda, Christian.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
672360
245
1 4
$a
The Generalized Fourier Series Method
$h
[electronic resource] :
$b
Bending of Elastic Plates /
$c
by Christian Constanda, Dale Doty.
250
$a
1st ed. 2020.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2020.
300
$a
XIII, 254 p. 186 illus., 37 illus. in color.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
490
1
$a
Developments in Mathematics,
$x
1389-2177 ;
$v
65
505
0
$a
1. The Mathematical Model -- 2. Generalized Fourier Series -- 3. Interior Dirichlet Problem -- 4. Interior Neumann Problem -- 5. Interior Robin Problem -- 6. Exterior Dirichlet Problem -- 7. Exterior Neumann Problem -- 8. Exterior Robin Problem -- A. Numerical Issues -- B. Numerical Integration -- C. Interior Boundary Value Problem for D[x,y] -- D. Exterior Boundary Value Problems for D^A[X,y] -- E. Numerical Integration of P[x,y] and P^A[x,y] -- References -- Index.
520
$a
This book explains in detail the generalized Fourier series technique for the approximate solution of a mathematical model governed by a linear elliptic partial differential equation or system with constant coefficients. The power, sophistication, and adaptability of the method are illustrated in application to the theory of plates with transverse shear deformation, chosen because of its complexity and special features. In a clear and accessible style, the authors show how the building blocks of the method are developed, and comment on the advantages of this procedure over other numerical approaches. An extensive discussion of the computational algorithms is presented, which encompasses their structure, operation, and accuracy in relation to several appropriately selected examples of classical boundary value problems in both finite and infinite domains. The systematic description of the technique, complemented by explanations of the use of the underlying software, will help the readers create their own codes to find approximate solutions to other similar models. The work is aimed at a diverse readership, including advanced undergraduates, graduate students, general scientific researchers, and engineers. The book strikes a good balance between the theoretical results and the use of appropriate numerical applications. The first chapter gives a detailed presentation of the differential equations of the mathematical model, and of the associated boundary value problems with Dirichlet, Neumann, and Robin conditions. The second chapter presents the fundamentals of generalized Fourier series, and some appropriate techniques for orthonormalizing a complete set of functions in a Hilbert space. Each of the remaining six chapters deals with one of the combinations of domain-type (interior or exterior) and nature of the prescribed conditions on the boundary. The appendices are designed to give insight into some of the computational issues that arise from the use of the numerical methods described in the book. Readers may also want to reference the authors’ other books Mathematical Methods for Elastic Plates, ISBN: 978-1-4471-6433-3 and Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation, ISBN: 978-3-319-26307-6.
650
2 4
$a
Solid Mechanics.
$3
1211586
650
2 4
$a
Analysis.
$3
669490
650
1 4
$a
Potential Theory.
$3
672266
650
0
$a
Mechanics, Applied.
$3
596630
650
0
$a
Mechanics.
$3
527684
650
0
$a
Analysis (Mathematics).
$3
1253570
650
0
$a
Mathematical analysis.
$3
527926
650
0
$a
Potential theory (Mathematics).
$3
1255004
700
1
$a
Doty, Dale.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1107056
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783030558482
776
0 8
$i
Printed edition:
$z
9783030558505
776
0 8
$i
Printed edition:
$z
9783030558512
830
0
$a
Developments in Mathematics,
$x
1389-2177 ;
$v
41
$3
1256322
856
4 0
$u
https://doi.org/10.1007/978-3-030-55849-9
912
$a
ZDB-2-SMA
912
$a
ZDB-2-SXMS
950
$a
Mathematics and Statistics (SpringerNature-11649)
950
$a
Mathematics and Statistics (R0) (SpringerNature-43713)
based on 0 review(s)
Multimedia
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login