Variational and finite element methods: a symbolic computation approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin u.a.
Springer
1990
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 254 S. graph. Darst. |
| ISBN: | 3540515984 0387515984 |
Internformat
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| 100 | 1 | |a Beltzer, Abraham I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Variational and finite element methods |b a symbolic computation approach |c A. I. Beltzer |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1990 | |
| 300 | |a XI, 254 S. |b graph. Darst. | ||
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| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Calculus of variations |x Data processing | |
| 650 | 4 | |a Finite element method |x Data processing | |
| 650 | 4 | |a LISP (Computer program language) | |
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Datensatz im Suchindex
| _version_ | 1804118274921725952 |
|---|---|
| adam_text | Titel: Variational and finite element methods
Autor: Beltzer, Abraham I
Jahr: 1990
Contents
I
Symbolic
Manipulation
Codes....................
1
1.1
Notions
of
LISP
and
Expert
Systems..............
1
1.2
First
Sessions.........................
2
1.3
Matrices...........................
8
1.4
Solving
Equations.......................
11
1.5
Limits
and
Expansions.....................
15
1.6
Integration..........................
16
1.7
Some
Useful
Commands
and
Options.
Pattern
Matching
....
21
1.8
Conditionals,
Iterations
and
Compound
Statements.......
24
1.9
Few
Hints
..........................
26
1.10
Example:
Steady-State
Linear
Vibrations............
27
1.11
Example:
Transient
Vibrations.................
33
1.12
Example:
Free
Nonlinear
Vibrations..............
36
1.13
Example:
Forced
Nonlinear
Vibrations.............
40
II
Variational
Approach
and
Equations
of
Motion
.............
44
2.1
Mechanics
of
a
Particle....................
44
2.2
System
of
Particles.
Generalized
Coordinates..........
46
2.3
Functional
and
its
Euler-Lagrange
Equation
..........
47
2.4
Hamilton’s
Principle
for
Discrete
Systems
...........
49
2.5
Constrained
Motions.....................
51
2.6
Virtual
Work.........................
53
2.7
D’Alembert’s
Principle.
Nonconservative
Systems.......
53
2.8
Transition
to
Continuous
Systems...............
56
2.9
Hamilton’s
Principle
for
Continuous
Systems,
Part
I.......
57
2.10
Hamilton’s
Principle
for
Continuous
Systems,
Part
II......
59
2.11
Minimum
of
Potential
Energy.
Imposed
and
Natural
Boundary
Conditions...........
61
2.12
Computer-generated
Governing
Equations...........
63
2.13
Single
Degree
of
Freedom...................
64
2.14
Two
Degrees
of
Freedom.
Double
Nonlinear
Pendulum.....
67
2.15
Dynamic
Shock
Absorber...................
69
2.16
Continuous
Systems......................
71
2.17
Automatic
Generation,
Part
I
.................
72
X
Contents
2.18
Automatic
Generation,
Part
II.................
73
2.19
Second
Variation
and
Nature
of
Extremum
...........
75
2.20
Legendre’s
Condition.....................
77
2.21
Transversality
Conditions...................
79
2.22
Generalizations
and
Transformations
of
Variational
Problems
.
.
80
2.23
Minimum
Pressure
Drag
....................
83
2.24
Constrained
Minimum
Pressure
Drag
.............
86
in
Direct
Methods
...........................
89
3.1
The
Philosophy........................
89
3.2
The
Method
of
Least
Squares.
Trial
Functions
.........
91
3.3
Beam
on
Elastic
Foundation,
Part
I...............
93
3.4
Beam
on
Elastic
Foundation,
Part
II............—.
95
3.5
The
Bubnov-Galerkin
Method.................
96
3.6
Beam
on
Elastic
Foundation,
Part
III..............
97
3.7
The
Rayleigh-Ritz
Method...................
99
3.8
Master
Program........................
101
3.9
Applications..........................
103
3.10
Improved
Master
Program...................
104
3.11
Considerations
of
Accuracy..................
106
3.12
Plate
on
Elastic
Foundation..................
108
3.13
Further
Investigations
of
Plates
................
Ill
3.14
Other
Direct
Methods....................
114
3.15
Shock
Absorber,
Preliminary
Considerations..........
117
3.16
Shock
Absorber,
Program
and
Results.............
120
3.17
Flow
Through
a
Duct.....................
123
3.18
Temperature
Field
in
a
Plate,
Part
I
..............
126
3.19
Temperature
Field
in
a
Plate,
Part
II..............
127
3.20
Free
Vibrations
by
the
Rayleigh-Ritz
Method..........
130
3.21
Free
Vibrations
of
a
Non-uniform
Beam............
132
3.22
Master
Programm.......................
133
3.23
Free
Vibrations
by
gthe
Bubnov-Galerkin
Method
.......
136
3.24
Nonlinear
Vibrations
by
the
Bubnov-Galerkin
Method.....
139
3.25
Mathematical
Considerations.
Scalar
Products
of
Functions
.
.
.
142
3.26
Operators
and
Functionals...................
143
3.27
Symmetric
and
Positive
Definite
Operators...........
145
3.28
Minimum
Theorem
and
Minimizing
Sequence.........
146
3.29
Orthogonal
and
Linearly
Independent
Functions........
148
IV
Introduction
to
the
Finite
Element
Method...............
150
4.1
Finite
Elements.
The
Element
Stiffness
Matrix.........
150
4.2
Energy
Analysis
of
a
Finite
Element..............
155
4.3
Truss
Element
........................
159
4.4
Physical
Meaning
of
the
Element
Matrices...........
163
4.5
Global
Reference
Systems...................
167
4.6
Generalizations.
Governing
Equations
of
a
Structure......
171
4.7
Assembling..........................
175
4.8
Formalization
of
Assembling..................
181
4.9
Truss.............................
182
4.10
Further
Analysis
of
a
Truss..................
187
Contents
XI
4.11
Composite
Beam.......................
191
4.12
Particular
Cases........................
193
4.13
Automatic
Generation
of
the
Assembly
Stiffness
Matrix.....
195
4.14
Optimization.........................
199
4.15
Reduced
Stiffness
Matrix...................
201
4.16
Free
Vibrations
of
Beams...................
204
4.17
Plate
Element,
Part
I
.....................
208
4.18
Plate
Element,
Part
II.....................
211
4.19
Particular
Cases.
Batch
Mode.................
214
4.20
Compatibility
and
Convergence................
218
4.21
Natural
Coordinate
Systems..................
219
4.22
The
Concept
of
Isoparametric
Elements............
225
4.23
Some
Plane
Elements.....................
228
4.24
Concluding
Remarks
......................
235
Appendix..............
236
Problems................................238
Answers.........
243
References...............................250
Index
..................................253
|
| any_adam_object | 1 |
| author | Beltzer, Abraham I. |
| author_facet | Beltzer, Abraham I. |
| author_role | aut |
| author_sort | Beltzer, Abraham I. |
| author_variant | a i b ai aib |
| building | Verbundindex |
| bvnumber | BV004046354 |
| callnumber-first | T - Technology |
| callnumber-label | TA347 |
| callnumber-raw | TA347.F5 |
| callnumber-search | TA347.F5 |
| callnumber-sort | TA 3347 F5 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 910 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)20262058 (DE-599)BVBBV004046354 |
| dewey-full | 620/.001/515353 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620/.001/515353 |
| dewey-search | 620/.001/515353 |
| dewey-sort | 3620 11 6515353 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004046354 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:07:42Z |
| institution | BVB |
| isbn | 3540515984 0387515984 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002531657 |
| oclc_num | 20262058 |
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| owner | DE-91 DE-BY-TUM DE-703 DE-706 DE-634 DE-83 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-703 DE-706 DE-634 DE-83 DE-188 |
| physical | XI, 254 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| spelling | Beltzer, Abraham I. Verfasser aut Variational and finite element methods a symbolic computation approach A. I. Beltzer Berlin u.a. Springer 1990 XI, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calcul des variations ram LISP (langage de programmation) ram LISP inriac calcul variation inriac code manipulation symbolique inriac méthode variationnelle inriac méthode élément fini inriac Éléments finis, Méthode des ram équation mouvement inriac Datenverarbeitung Calculus of variations Data processing Finite element method Data processing LISP (Computer program language) Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf MACSYMA (DE-588)4168439-4 gnd rswk-swf Technische Mechanik (DE-588)4059231-5 s Finite-Elemente-Methode (DE-588)4017233-8 s MACSYMA (DE-588)4168439-4 s DE-604 Variationsrechnung (DE-588)4062355-5 s Mechanik (DE-588)4038168-7 s DE-188 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002531657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beltzer, Abraham I. Variational and finite element methods a symbolic computation approach Calcul des variations ram LISP (langage de programmation) ram LISP inriac calcul variation inriac code manipulation symbolique inriac méthode variationnelle inriac méthode élément fini inriac Éléments finis, Méthode des ram équation mouvement inriac Datenverarbeitung Calculus of variations Data processing Finite element method Data processing LISP (Computer program language) Technische Mechanik (DE-588)4059231-5 gnd Mechanik (DE-588)4038168-7 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Variationsrechnung (DE-588)4062355-5 gnd MACSYMA (DE-588)4168439-4 gnd |
| subject_GND | (DE-588)4059231-5 (DE-588)4038168-7 (DE-588)4017233-8 (DE-588)4062355-5 (DE-588)4168439-4 |
| title | Variational and finite element methods a symbolic computation approach |
| title_auth | Variational and finite element methods a symbolic computation approach |
| title_exact_search | Variational and finite element methods a symbolic computation approach |
| title_full | Variational and finite element methods a symbolic computation approach A. I. Beltzer |
| title_fullStr | Variational and finite element methods a symbolic computation approach A. I. Beltzer |
| title_full_unstemmed | Variational and finite element methods a symbolic computation approach A. I. Beltzer |
| title_short | Variational and finite element methods |
| title_sort | variational and finite element methods a symbolic computation approach |
| title_sub | a symbolic computation approach |
| topic | Calcul des variations ram LISP (langage de programmation) ram LISP inriac calcul variation inriac code manipulation symbolique inriac méthode variationnelle inriac méthode élément fini inriac Éléments finis, Méthode des ram équation mouvement inriac Datenverarbeitung Calculus of variations Data processing Finite element method Data processing LISP (Computer program language) Technische Mechanik (DE-588)4059231-5 gnd Mechanik (DE-588)4038168-7 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Variationsrechnung (DE-588)4062355-5 gnd MACSYMA (DE-588)4168439-4 gnd |
| topic_facet | Calcul des variations LISP (langage de programmation) LISP calcul variation code manipulation symbolique méthode variationnelle méthode élément fini Éléments finis, Méthode des équation mouvement Datenverarbeitung Calculus of variations Data processing Finite element method Data processing LISP (Computer program language) Technische Mechanik Mechanik Finite-Elemente-Methode Variationsrechnung MACSYMA |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002531657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT beltzerabrahami variationalandfiniteelementmethodsasymboliccomputationapproach |