Handbook of mechanical stability in engineering: (in 3 volumes) 2 Stability of elastically deformable mechanical systems
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Singapore [u.a.]
World Scientific Publ.
2013
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| Beschreibung: | XXX, 9 S., S. 603 - 1188 Ill., graph. Darst. |
| ISBN: | 9789814383783 |
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| LEADER | 00000nam a2200000 cc4500 | ||
|---|---|---|---|
| 001 | BV041200249 | ||
| 003 | DE-604 | ||
| 005 | 20131219 | ||
| 007 | t | ||
| 008 | 130802s2013 si ad|| |||| 00||| eng d | ||
| 020 | |a 9789814383783 |9 978-981-4383-78-3 | ||
| 035 | |a (OCoLC)859375443 | ||
| 035 | |a (DE-599)BVBBV041200249 | ||
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| 100 | 1 | |a Perelʹmuter, Anatolij V. |e Verfasser |0 (DE-588)124666396 |4 aut | |
| 245 | 1 | 0 | |a Handbook of mechanical stability in engineering |b (in 3 volumes) |n 2 |p Stability of elastically deformable mechanical systems |c Anatoly V. Perelmuter ; Vladimir Slivker |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 2013 | |
| 300 | |a XXX, 9 S., S. 603 - 1188 |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 700 | 1 | |a Slivker, Vladimir I. |e Verfasser |4 aut | |
| 773 | 0 | 8 | |w (DE-604)BV041200205 |g 2 |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026175139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026175139 | ||
Datensatz im Suchindex
| _version_ | 1804150626214477824 |
|---|---|
| adam_text | CONTENTS
Preface
—
Vol.
1
to Vol.
3 xv
Acknowledgments
—
Vol.
1
to Vol.
3 xxiii
Contents
—
Vol.
1
to Vol.
3 xxv
About the Authors
xxix
9.
Stability of Equilibrium of Plates
—
Kirchhoff—
Love and Reissner Plates
603
9.1.
Stability of Equilibrium of Kirchhoff-Love Plates
.... 604
9.1.1.
Basic relationships in the theory of thin
plates
......................... 604
9.1.2.
Variational derivation of the equilibrium
stability equation for the Kirchhoff-Love
plates
......................... 609
9.1.2.1.
Boundary conditions
.......... 615
9.1.3.
Stability of equilibrium of a cantilever strip
. . 617
9.1.4. Sommerfeld
problem
................ 620
9.1.4.1.
Stability of equilibrium of a
half-strip reinforced by a thread
. . . 622
9.1.4.2.
Stability of equilibrium of a
half-strip without a thread
...... 625
9.1.5.
Southwell-Skan problem
.............. 629
9.1.6.
Stability of equilibrium of round plates
..... 630
9.1.6.1.
Stability of equilibrium of a round
plate under a radial compression
by forces on its contour
........ 633
vi
Handbook of Mechanical Stability in Engineering
9.1.6.2.
Equilibrium stability functional for
a plate in polar coordinates
...... 640
9.1.6.3.
Stability of equilibrium of a round
plate loaded by a torque
—
Dean
problem
................. 640
9.2.
Stability of Equilibrium of Reissner Plates
........ 645
9.3.
Slender Plates
- - von
Karman
Theory
........... 647
9.3.1.
Variational statement of the problem
...... 653
9.4.
Post-critical Behavior of Slender Plates
.......... 657
9.4.1.
Character of post-critical deformation
..... 657
9.4.1.1.
Model problem
............. 658
9.4.2.
Solution based on
von
Karman
theory
..... 661
9.5.
Final Notes to Chapter
9................... 667
10.
Systems with Unilateral Constraints
671
10.1.
Elements of the Theory of Systems with Unilateral
Constraints
........................... 671
10.1.1.
Preliminaries
..................... 671
10.1.2.
Limitations for virtual displacements
...... 675
10.1.3.
Equilibrium conditions
............... 676
10.2.
Critical Value of the Load Intensity
............ 681
10.3.
Determining the Upper Critical Load
........... 690
10.4.
Illustrative Examples
..................... 695
10.5.
High-rise Building on a Unilateral Elastic Bed
...... 703
10.6.
Possible Destabilization of Systems with Unilateral
Constraints
........................... 706
10.7.
Final Notes to Chapter
10.................. 708
11.
Stability of Equilibrium of Planar Bar Structures
711
11.1.
Planar Bar Structures
..................... 712
11.1.1.
General solution of homogeneous equat ions of
equilibrium stability for an individual bar
. . . 714
11.1.2.
Stiffness matrix of an individual bar
....... 721
11.1.2.1.
Stiffness matrix of a bar with other
methods of its end fixation
...... 725
11.1.2.2.
Some properties of Kornoukhov
functions and a procedure for
calculation of those
........... 729
Contents
vii
11.1.2.3. Initial
stiffness matrix and
geometric stiffness matrix
for a bar
................. 731
11.1.3.
Criterion for a critical state in a bar
structure
....................... 734
11.1.3.1.
Do we need higher buckling
modes?
.................. 740
11.1.3.2.
A qualitative technique for
determining critical loads
....... 742
11.1.4.
Example: A paradox in stability problems
. . . 745
11.1.5.
Bubnov
problem
.................. 752
11.1.6.
Stiff inserts at the ends of a bar
......... 756
11.1.6.1.
A possible mistake in the stability
analysis in presence of rigid
bodies
.................. 760
11.2.
Deformed-shape-based Analysis of a Planar Bar
Structure
............................ 761
11.2.1.
Deformed-shape-based analysis of an
individual bar
.................... 761
11.2.1.1.
Method of initial parameters
..... 762
11.2.1.2.
Reactions at the ends of a bar
caused by lateral actions
....... 765
11.2.2.
Monocycle, quasi-monocycle
and polycycle
analysis of bar systems
............... 769
11.2.3.
Mohr formula in application to bar structures
in combined bending and compression
..... 771
11.3.
Final Notes to Chapter
11.................. 778
12.
FEM
in Stability Problems
781
12.1.
Basics of
FEM
......................... 783
12.1.1.
Shape functions and a shape function matrix
for a finite element
................. 784
12.1.2.
General requirements to shape functions
.... 786
12.1.3.
Comparative analysis of shape functions
.... 789
12.1.4.
General formulas for matrices Rq and
G
.... 792
12.2.
Stiffness Matrices of a Bar in Plane
............ 793
12.2.1.
A Bernoulli-Euler bar
............... 793
12.2.2.
Timoshenko bar
................... 795
viu
Handbook of Mechanical Stability in Engineering
12.2.2.1.
Model I: Linear approximations of
displacements and rotations
..... 798
12.2.2.2.
Model II: Coupled approximations
of displacements and rotations
—
Linear-quadratic shape functions
. . 800
12.2.2.3.
Model III: Cubic-quadratic
approximations of displacements
. . . 802
12.2.2.4.
General representation of
matrices Rq and
G
for a
Timoshenko bar
—
Comparative
analysis of three finite element
models
.................. 805
12.2.2.5.
Example
................. 807
12.3.
Stiffness Matrix of a Spatial Bar
.............. 812
12.3.1.
A Bernoulli-Euler bar
............... 812
12.3.2.
Timoshenko bar
................... 819
12.3.3.
Stiff inserts at the ends of a bar
......... 825
12.3.4.
Geometric stiffness matrix of a node
...... 833
12.4.
Plate Finite Elements
..................... 835
12.4.1.
Plate finite element in application to the Suv
functional
...................... 836
12.4.1.1.
A rectangular finite element
..... 838
12.4.2.
Finite elements of flexural plate
......... 841
12.4.2.1.
Kirchhoff-Love plate
.......... 843
12.4.2.2.
Reissner plate
.............. 848
12.4.3.
A hybrid
FEM
approach
.............. 852
12.4.3.1.
Timoshenko bar
............ 856
12.4.3.2.
Reissner plate
.............. 859
12.5.
Perfectly Rigid Bodies as Parts of Discrete Design
Models
.............................. 864
12.6.
FEN Relationships for Geometrically
Nonlinear Models
....................... 866
12.6.1.
Four floors of geometrically nonlinear
models
........................ 866
12.6.2.
Decomposition of strains into a sum of linear
and quadratic parts: Second-order theory
. . . 869
12.6.3.
Matrix-operator form of the full potential
energy functional
.................. 875
12.6.4.
Equations in increments
.............. 880
Contents ix
12.6.5.
Equilibrium stability models
........... 886
12.6.5.1.
Possible simplifications of the
equilibrium stability model
...... 888
12.6.5.2.
Stability coefficient
........... 889
12.7.
Final Notes to Chapter
12.................. 892
13.
Hinged Bar Systems
893
13.1.
Preliminaries
.......................... 893
13.2.
Geometrical Nonlinearity for Truss-type Bars
....... 896
13.2.1.
Geometric equations
................ 897
13.2.2.
Equilibrium equations
............... 901
13.2.3.
Physical equation
.................. 904
13.2.4.
Example
....................... 904
13.2.5.
Geometrically nonlinear equations in
variations
....................... 909
13.3.
Stable Configurations of a Substatic System
....... 913
13.3.1.
Static-kinematic classification
........... 914
13.3.2.
A criterion of selection of instantaneously
rigid systems
..................... 919
13.4.
Buckling of Nodes Out of a Truss Plane
.......... 922
13.4.1.
Unsupported length of diagonals in
compression
..................... 926
13.5.
Estimation of Forces in Null Bars
.............. 926
13.6.
Estimation of the Node Stiffness Effect
.......... 928
13.7.
Compound Bars
........................ 934
13.7.1.
Idealized model
................... 934
13.7.2.
Effect of initial imperfections
........... 936
13.7.3.
Interaction between buckling modes
....... 939
13.7.4.
Spatial compressed lattice bars
.......... 944
13.7.4.1.
Tetrahedral bars
............ 944
13.7.4.2.
Trihedral bars
.............. 948
14.
Dynamic Criterion of Stability and
Non-Conservât
ive
Systems
949
14.1.
Dynamic Analysis of Equilibrium Stability
........ 949
14.1.1.
Basics
......................... 949
14.1.2.
A system with one degree of freedom
...... 953
14.1.2.1.
Dead force
................ 954
14.1.2.2.
Follower load
.............. 955
14.1.2.3.
Polar load
................ 957
Handbook of Mechanical Stability in Engineering
14.1.2.4.
Combined loading by dead and
follower forces
.............. 958
14.1.2.5.
Reuth force
............... 962
14.2.
Systems with Multiple Degrees of Freedom
........ 963
14.2.1.
General
........................ 963
14.2.1.1.
Conservative system
.......... 969
14.2.1.2.
Nonlinear system, general case
.... 972
14.2.2.
System with two degrees of freedom
—
detailed analysis
................... 973
14.2.2.1.
General analysis of equilibrium
stability for a system with two
degrees of freedom
........... 977
14.2.3.
Influence of constraints on equilibrium
stability of non-conservative systems
...... 978
14.2.4.
Damping and its role in the equilibrium
stability
........................ 981
14.2.4.1.
Non-conservative external forces
and dissipation: Ziegler paradox
. . . 985
14.3.
Nikolai Problem
........................ 992
14.3.1.
Tangential external moment
—
static
analysis
........................ 995
14.3.2.
Axial external moment
—
static analysis
.... 996
14.3.3.
Tangential external moment
—
dynamic
analysis
........................ 996
14.4.
Continuous Non-conservative Systems
........... 1000
14.4.1.
Variations of external forces under
conservative and non-conservative loads
.... 1002
14.4.2.
Discretization of conservative and
non-conservative systems
............. 1006
14.4.2.1.
Bubnov-Galyorkin method
—
general
.................. 1007
14.4.2.2.
Bubnov-Galyorkin method using
fundamental basis functions
..... 1010
14.4.2.3.
Finite element method for
non-conservative problems
...... 1011
14.4.2.4.
Discretization by mass
......... 1011
14.5.
Beck Problem
.......................... 1013
14.5.1.
A constant-direction force
............. 1014
14.5.2.
A follower force
................... 1016
14.5.3.
A generalized problem
............... 1018
Contents xi
14.6.
Flutter When Fluid Comes Out of Tube
.......... 1021
14.7.
Models with a Truncated Number of
Inerţial
Characteristics
......................... 1025
14.7.1.
Conservative system
................ 1026
14.7.2.
Non-conservative system
.............. 1029
14.7.3.
The effect of truncation by mass on the area
of equilibrium stability
............... 1031
14.7.3.1.
Beck s bar with two concentrated
masses
.................. 1033
14.7.4.
Critics of the dynamic criterion of equilibrium
stability
........................ 1038
14.8.
On the Application of the Static Approach to
Non-conservative Problems
.................. 1040
14.9.
Final Notes to Chapter
14.................. 1044
14.9.1.
Smith-Herrmann paradox
............. 1045
14.9.2.
Follower force as an ugly duckling of
mechanics
...................... 1046
15.
Post-Critical Deformation
1049
15.1.
Post-critical Behavior of Bars
................ 1050
15.1.1.
Critical state of frame structures
......... 1050
15.1.2.
A bar with its ends resisting axial
displacements
.................... 1051
15.2.
Frame Systems
......................... 1057
15.2.1.
Possibility of a snap-through
........... 1057
15.2.2.
Mixed-method analysis
.............. 1059
15.2.2.1.
Beniaminov formula
.......... 1062
15.2.2.2.
Example
................. 1065
15.3.
Using the Post-critical Behavior of Plates
......... 1066
15.3.1.
Reduction coefficient
................ 1066
15.3.2.
Post-critical behavior of plates in shear
..... 1071
15.4.
Post-critical Interaction Between Buckling Modes
.... 1073
15.4.1.
Global and local buckling modes of a
thin-walled bar
................... 1073
15.5.
Final Notes to Chapter
15.................. 1080
16.
Design Models in Stability Problems:
Practical Examples
1081
16.1.
Stability of a Multi-story Building: The Effect of
Rigidity of Floor Panels
................... 1081
16.2.
Finite Element Modeling of Thin-walled Bars
...... 1085
xii
Handbook of Mechanical Stability in Engineering
16.3.
Stability of Masts with Guy Ropes
............. 1089
16.3.1.
Cable elements in design models
......... 1089
16.3.2.
Potential approaches to the solution
....... 1094
16.4.
Energy-based Estimation of Roles of Particular
Subsystems
........................... 1095
16.4.1.
Restrained and forced buckling
.......... 1095
16.4.2.
Energy characteristics
............... 1097
16.4.3.
Modification of a structure
............ 1102
16.4.4.
Calculation of unsupported length
........ 1103
16.5.
Sensitivity of the Critical Load to Changes in the
System s Stiffness Values
................... 1106
16.5.1.
Uniform stability and optimization of a
structure
....................... 1106
16.5.1.1.
Example of an optimization for
stability
................. 1109
16.6.
Approximate Estimation of Ferroconcrete Behavior
... 1112
16.6.1.
Choosing an elasticity modulus value for
stability check
.................... 1113
16.6.2.
Approximate estimation of creep effects
.... 1116
16.6.3.
An example of design analysis of a real
ferroconcrete structure
............... 1118
Appendices
F
to
J
1123
Appendix F. Jordan Exclusions and Their Use in
Structural Mechanics
..................... 1123
F.I. General description
................. 1123
F.2. Jordan exclusions with a system s stiffness
matrix
........................ 1126
F.3. A finite element s stiffness matrix in case the
element is attached to nodes non-rigidly
.... 1129
F.4. Double Jordan exclusion
.............. 1134
F.5. Jordan transformations in stability problems:
A geometric condensation procedure
...... 1136
Appendix G. Asymptotic Analysis of Finite Element Models
for a Timoshenko Bar
..................... 1137
Appendix H. Generalized Timoshenko problem
......... 1143
H.I. Exact solution of the problem
.......... 1145
H.2. Solution by the
Ritz
method
........... 1149
Appendix I. Strong Bending of Bars
................
Ц50
Contents xiii
1.1. Geometrie
equations
................ 1151
1.2.
Physical equations
................. 1154
1.3.
Equilibrium equations
............... 1155
1.4.
Simplifications on lower floors of geometrical
nonlinearity
..................... 1156
1.5.
Example: Stability of a bar under a
kinematic action
.................. 1158
1.6.
Example: Pure bending of a bar
......... 1162
Appendix J. On a Mathematical Model of a Shear Bar in
Equilibrium Stability
..................... 1163
References in Vol.
2 1171
Author Index in Vol.
2 1-1
Subject Index in Vol.
2 1-7
|
| any_adam_object | 1 |
| author | Perelʹmuter, Anatolij V. Slivker, Vladimir I. |
| author_GND | (DE-588)124666396 |
| author_facet | Perelʹmuter, Anatolij V. Slivker, Vladimir I. |
| author_role | aut aut |
| author_sort | Perelʹmuter, Anatolij V. |
| author_variant | a v p av avp v i s vi vis |
| building | Verbundindex |
| bvnumber | BV041200249 |
| classification_rvk | UF 1610 |
| ctrlnum | (OCoLC)859375443 (DE-599)BVBBV041200249 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV041200249 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:41:55Z |
| institution | BVB |
| isbn | 9789814383783 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026175139 |
| oclc_num | 859375443 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM |
| physical | XXX, 9 S., S. 603 - 1188 Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific Publ. |
| record_format | marc |
| spelling | Perelʹmuter, Anatolij V. Verfasser (DE-588)124666396 aut Handbook of mechanical stability in engineering (in 3 volumes) 2 Stability of elastically deformable mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker Singapore [u.a.] World Scientific Publ. 2013 XXX, 9 S., S. 603 - 1188 Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Strukturelle Stabilität (DE-588)4295517-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Strukturdynamik (DE-588)4226174-0 gnd rswk-swf Festigkeit (DE-588)4016916-9 gnd rswk-swf Elastischer Werkstoff (DE-588)4151686-2 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Festigkeitslehre (DE-588)4016917-0 gnd rswk-swf Elastischer Werkstoff (DE-588)4151686-2 s Strukturdynamik (DE-588)4226174-0 s DE-604 Stabilität (DE-588)4056693-6 s Technische Mechanik (DE-588)4059231-5 s Strukturmechanik (DE-588)4126904-4 s Festigkeitslehre (DE-588)4016917-0 s Festigkeit (DE-588)4016916-9 s Strukturelle Stabilität (DE-588)4295517-8 s Slivker, Vladimir I. Verfasser aut (DE-604)BV041200205 2 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026175139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Perelʹmuter, Anatolij V. Slivker, Vladimir I. Handbook of mechanical stability in engineering (in 3 volumes) Strukturelle Stabilität (DE-588)4295517-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Technische Mechanik (DE-588)4059231-5 gnd Strukturdynamik (DE-588)4226174-0 gnd Festigkeit (DE-588)4016916-9 gnd Elastischer Werkstoff (DE-588)4151686-2 gnd Stabilität (DE-588)4056693-6 gnd Festigkeitslehre (DE-588)4016917-0 gnd |
| subject_GND | (DE-588)4295517-8 (DE-588)4126904-4 (DE-588)4059231-5 (DE-588)4226174-0 (DE-588)4016916-9 (DE-588)4151686-2 (DE-588)4056693-6 (DE-588)4016917-0 |
| title | Handbook of mechanical stability in engineering (in 3 volumes) |
| title_auth | Handbook of mechanical stability in engineering (in 3 volumes) |
| title_exact_search | Handbook of mechanical stability in engineering (in 3 volumes) |
| title_full | Handbook of mechanical stability in engineering (in 3 volumes) 2 Stability of elastically deformable mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker |
| title_fullStr | Handbook of mechanical stability in engineering (in 3 volumes) 2 Stability of elastically deformable mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker |
| title_full_unstemmed | Handbook of mechanical stability in engineering (in 3 volumes) 2 Stability of elastically deformable mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker |
| title_short | Handbook of mechanical stability in engineering |
| title_sort | handbook of mechanical stability in engineering in 3 volumes stability of elastically deformable mechanical systems |
| title_sub | (in 3 volumes) |
| topic | Strukturelle Stabilität (DE-588)4295517-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Technische Mechanik (DE-588)4059231-5 gnd Strukturdynamik (DE-588)4226174-0 gnd Festigkeit (DE-588)4016916-9 gnd Elastischer Werkstoff (DE-588)4151686-2 gnd Stabilität (DE-588)4056693-6 gnd Festigkeitslehre (DE-588)4016917-0 gnd |
| topic_facet | Strukturelle Stabilität Strukturmechanik Technische Mechanik Strukturdynamik Festigkeit Elastischer Werkstoff Stabilität Festigkeitslehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026175139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041200205 |
| work_keys_str_mv | AT perelʹmuteranatolijv handbookofmechanicalstabilityinengineeringin3volumes2 AT slivkervladimiri handbookofmechanicalstabilityinengineeringin3volumes2 |