Handbook of mechanical stability in engineering: (in 3 volumes) 1 General theorems and individual members of mechanical systems
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| Sprache: | English Russian |
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Singapore [u.a.]
World Scientific Publ.
2013
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| Beschreibung: | XXX, 601, 7 S. Ill, graph. Darst. |
| ISBN: | 9789814383776 |
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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 1 |p General theorems and individual members of mechanical systems |c Anatoly V. Perelmuter ; Vladimir Slivker |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 2013 | |
| 300 | |a XXX, 601, 7 S. |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 | |
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| 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=026175136&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804150626222866432 |
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| 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
1.
Stability of Equilibrium of Systems That Have
a Finite Number of Degrees of Freedom
1
1.1.
Definition of the Equilibrium Stability
............ 2
1.1.1.
Lagrange-Dirichlet theorem and Lyapunov theorems
5
1.1.2.
Example
1........................ 10
1.2.
Elastic Systems with a Finite Number of Degrees
of Freedom
............................ 13
1.2.1.
Stability functional
—
Bolotin functional
....... 19
1.2.2.
Linearized models of equilibrium stability
problems
......................... 20
1.2.3.
Example
2........................ 24
1.2.4.
Example
3 —
paradoxes in equilibrium stability
problems?
........................ 32
1.2.4.1.
Non-invariance of critical load with respect
to the choice of the system s generalized
coordinates
.................. 38
1.3.
Some General Theorems of the Equilibrium
Stability Theory
......................... 40
1.3.1.
Rayleigh ratio and variational recursive definition
of critical loads
..................... 42
vi
Handbook of Mechanical Stability in Engineering
1.3.2.
Decomposition of the original n-dimensional space
of generalized displacement vectors into a direct sum
of three subspaces
.................... 45
1.3.3.
Normal coordinates of a system
............ 49
1.3.4.
Influence of constraints on the stability
of equilibrium of a linearized elastic system
..... 51
1.3.5.
Papkovich theorem on convexity of a stability area
. 54
1.3.5.1.
Reservations for the Papkovich theorem
. . 61
1.3.5.2.
Application aspect of the Papkovich
theorem
.................... 64
1.3.6.
Geometric stiffness matrix revisited
.......... 68
1.3.7.
Stability of equilibrium under
a non-
force action
... 69
1.4.
Characteristic Curve of an Elastic System
.......... 73
1.4.1.
One-degree-of-freedom system
............. 74
1.4.2.
Multiple-degrees-of-freedom system
.......... 78
1.5.
Final Notes to Chapter
1.................... 82
2.
Variational Statement of the Problem
of Equilibrium Stability for Elastic Bodies
85
2.1.
Geometrically Nonlinear Problems of Elasticity
....... 85
2.1.1.
Geometric equations
.................. 85
2.1.1.1.
Varying the stress tensor components
.... 88
2.1.2.
Equilibrium equations and static boundary
conditions
........................ 89
2.2.
Stability of Equilibrium of an Elastic Body
......... 93
2.2.1.
Linearized models of the equilibrium stability
for elastic bodies
.................... 97
2.2.2.
Mechanical interpretation of particular terms
in the stability functional
—
The concept
of an equivalent load
.................. 101
2.2.3.
Criteria of a system s critical state
.......... 104
2.3. Ritz
Method
........................... 107
2.4.
Mixed Functional in the Equilibrium Stability
Problems
.............................
Ill
2.4.1.
Example
......................... 112
2.5.
Timoshenko-Type Functionals
................. 117
2.5.1.
Using statically permissible stresses
in the equilibrium stability functional
......... 123
2.6.
Elastic Systems in Presence of Constraints
.......... 127
Contents vjj
2.6.1.
Elastic
systems with a finite number of degrees
of freedom
........................ 127
2.6.1.1.
Example
.................... 128
2.6.1.2.
General case of allowing for constraints
by decreasing the problem s dimensionality
. 132
2.6.1.3.
Allowing for constraints by increasing
the problem s dimensionality
......... 136
2.6.2.
Elastically deformable body with constraints
..... 139
2.6.2.1.
Elastic body reinforced by an incompressible
thread
..................... 139
2.7.
Elastic Systems in Presence of Perfectly Rigid Bodies
.... 142
2.7.1.
Equilibrium of an elastic system in presence
of rigid bodies
...................... 142
2.7.2.
Kinematic relationships for a perfectly rigid body
—
Rodrigues
formula and its simplifications
....... 146
2.7.3.
Work of forces applied to a perfectly rigid body
... 149
2.7.4.
The equilibrium stability functional for a system
that contains a perfectly rigid body
.......... 151
2.7.5.
Geometric stiffness matrix for a perfectly
rigid body
........................ 155
2.7.5.1.
Systems with a finite number of degrees
of freedom
................... 157
2.7.6.
Example
......................... 157
2.7.6.1.
Modeling of springs by compressible bars
. . 159
2.8.
Continuous RB-Bodies in Application Models
of Elasticity
........................... 162
2.9.
Final Notes to Chapter
2.................... 166
3.
Asymptotic Analysis of Post-Critical Behavior
167
3.1.
Role Played by Initial Imperfections
............. 167
3.1.1.
Stability in large : Upper and lower critical loads
. 176
3.2.
Systems with Multiple Degrees of Freedom
.......... 183
3.2.1.
Preliminary analysis
.................. 185
3.2.2.
Analysis in higher approximations
........... 188
3.2.3.
Classification of singular points
............ 189
3.2.4.
Quality of equilibrium in singular points
....... 191
3.3.
Final Notes to Chapter
3.................... 194
4.
Stability of Equilibrium of Straight Bars
197
4.1.
Stability of Equilibrium of a Compressed Bar
........ 198
viii
Handbook of Mechanical Stability in Engineering
4.1.1.
Boundary conditions in equilibrium stability
analysis of a compressed bar
.............. 204
4.1.2.
Orthogonality of a bar s buckling modes
....... 209
4.1.3.
Initial imperfections
................... 211
4.1.3.1.
Analysis with the deformed shape
(second-order)
................. 214
4.1.4.
Post-critical behavior of a bar in combined
bending and compression
................ 215
4.1.5.
Equilibrium stability of a Timoshenko
bar
—
allowing for shear deformation
......... 221
4.1.6.
Stability of equilibrium of a compressed
bar that rests on an elastic bed
............ 224
4.2.
Variational Derivation of the Equation of Stability
for a Compressed Bar
...................... 227
4.2.1.
Stability of equilibrium of a compressed bar
in the
Euler—
Bernoulli technical theory
of bars
.......................... 227
4.2.2.
Stability of equilibrium of a Timoshenko bar
..... 231
4.3.
Stability of Equilibrium of a Compressed Spring
....... 236
4.3.1.
Model with two degrees of freedom
.......... 236
4.3.2.
Discrete-continuous model
............... 238
4.3.2.1.
Allowing for shear deformation
....... 242
4.3.3.
Model of an equivalent bar
............... 243
4.3.3.1.
Allowing for shear
............... 247
4.4.
Buckling of a Bar in Tension
.................. 249
4.5.
Spatial Buckling Modes of a Compressed Bar
........ 255
4.6.
Does the Critical Force Depend on the Lateral Load?
.... 260
4.7.
Rayleigh Ratio and Timoshenko Formula
........... 266
4.7.1.
A Timoshenko-type formula
for a Timoshenko bar
.................. 271
4.8.
Spatial Bar
........................... 273
4.8.1.
Bernoulli-Euler bar
................... 274
4.8.2.
Stability of equilibrium of a Bernoulli-Euler bar
in bending in a three-dimensional space
........ 280
4.8.2.1.
Simplifications in the functional
(8.28) . . . 282
4.8.2.1.1.
Simplification
1 ......... 283
4.8.2.1.2.
Simplification
2 ......... 283
4.8.2.1.3.
Simplification
3 ......... 283
4.8.2.1.4.
Simplification
4 ......... 284
Contents jx
4.8.2.2. Euler
equations for the functional
(8.32) . . 285
4.8.2.3.
Example
1 —
stability of the planar mode
of bending of a Bernoulli-Euler bar
..... 286
4.8.2.4.
Example
2 —
stability of a bar
bent in two planes
.............. 288
4.8.3.
Timoshenko bar
..................... 290
4.8.4.
Stability of equilibrium of a flexural Timoshenko bar
in a three-dimensional space
.............. 293
4.8.4.1.
Example
3 —
stability of the planar mode
of bending of a Timoshenko bar
....... 297
4.9.
Stability of Bars in Torsion
.................. 299
4.9.1.
Integration of the equation set
(9.8).......... 305
4.9.2.
Torsion of a bar in absence of a longitudinal force
. . 307
4.9.3.
Boundary conditions
.................. 308
4.9.4.
Examples
........................ 310
4.9.4.1.
The case of a bar clamped on two ends
. . . 311
4.9.4.2.
The case of a cantilever bar
......... 313
4.9.4.2.1.
Semi-tangential external
moment
.............. 313
4.9.4.2.2.
Moment of dead forces
..... 314
4.9.5.
Torsion of a Timoshenko bar
.............. 315
4.9.5.1.
The case of a cantilever Timoshenko bar
. . 321
4.9.5.1.1.
Semi-tangential external
moment
.............. 321
4.10.
Final Notes to Chapter
4.................... 322
5.
Stability of Equilibrium of Curved Bars
325
5.1.
Basic Equations for a Curved Bar in the Linear Model
. . . 326
5.1.1.
Simplifications of equations for a curved bar
with the incompressible axis
.............. 329
5.1.1.1.
Example
1................... 332
5.1.1.2.
Example
2................... 338
5.2.
Variational Derivation of the Equilibrium Stability
Equations for a Curved Bar
.................. 341
5.3.
Stability of Equilibrium of an Incompressible
Curved Bar
...........................344
5.3.1.
Stability of an incompressible circular ring
under dead radial forces
................346
x
Handbook of Mechanical Stability in Engineering
5.3.2.
Stability of an incompressible circular arch
under hydrostatic pressure
............... 347
5.3.2.1.
Circular two-hinged arch
........... 348
5.3.2.2.
Circular hinge-free arch
............ 351
5.3.3.
Stability of a ring under a polar radial load
..... 353
5.3.4.
Stability of arches under a vertical load
........ 353
5.4.
Stability of Equilibrium of Flat Arches
............ 356
5.4.1.
A model problem
— von
Mises
truss
......... 357
5.4.2.
A flat arch under a vertical load
............ 365
6.
Stability of Equilibrium of Thin-Walled Bars
373
6.1.
Open-Profile Thin-Walled Bar
................. 374
6.1.1.
Equilibrium stability functional for a bar
in bending and compression
.............. 374
6.1.1.1.
Boundary conditions
............. 384
6.1.2.
Initial state of stress of a bar in bending
and compression
..................... 388
6.1.2.1.
Characteristic equation for critical forces
in an eccentrically compressed bar
...... 391
6.1.2.2.
Thin-walled bar compressed along the line
of shear centers
................ 395
6.1.2.3.
Centrally compressed thin-walled bar
.... 400
6.1.2.4.
Stability of equilibrium of a thin-walled
bar with the non-warped cross-section
. . . 402
6.2.
Lateral Bending of Thin-Walled Bars
............. 407
6.2.1.
Stability of a planar bending mode for a thin-walled
bar
—
The case of pure bending
............ 410
6.2.2.
Generalized Prandlt-Michell problem
......... 411
6.2.2.1.
Solution based on the Alfutov
functional,
Ѕд
................. 412
6.2.2.2.
Solution based on the correct
functional,
S
.................. 414
6.2.2.3.
Comparing two solutions
........... 415
6.2.2.4.
Modified problem
—
problem B
...... 415
6.2.3.
Generalized Timoshenko problem
........... 416
6.2.4.
How to allow for the level of application
of the external lateral load
............... 419
6.3.
Thin-Walled Bars Considered by the Semi-Shear
Theory
.............................. 423
Contents
χι
6.3.1.
Stability of equilibrium of an eccentrically
compressed bar
..................... 425
6.3.1.1.
The case of
a non-
warped cross-section
. . . 428
6.3.2.
Stability of equilibrium in lateral bending
of bars considered by the semi-shear theory
..... 429
6.3.3.
A multi-story building as a thin-walled bar
...... 431
7.
Conservative External Forces and Moments:
Paradoxes and Misbeliefs
435
7.1.
Some Cases of Behavior of External Forces
..........437
7.2.
Hydrostatic Load
........................443
7.2.1.
The equilibrium stability functional under
the action of a hydrostatic load
............444
7.3.
Polar Load
............................446
7.4.
Moment Load
..........................447
7.4.1.
Definition of generalized moments
...........447
7.4.1.1.
Feature (a)
...................453
7.4.1.2.
Feature (b)
..................453
7.4.2.
Components of the moment vector and the rotation
vector in the Lagrangian and Eulerian coordinate
systems
..........................454
7.4.2.1.
Semi-Lagrangian coordinates
.........457
7.4.3.
Conditions of conservativeness of the external
moment vector
.....................459
7.4.4.
General case of a dead force moment
.........469
7.4.5.
Some mechanical realizations of the dead
force moments
......................473
7.4.5.1.
Bimoment actions
...............475
7.4.6.
Equilibrium equations that correspond to rotational
degrees of freedom of a mechanical system
......476
7.4.7.
An attempt to introduce a vector of generalized
rotations
.........................478
7.5.
Stability of Bars in Three-Dimensional Space
........480
7.5.1.
Back to the problem of stability of a bar
in torsion
........................480
7.5.1.1.
Example
—
stability of equilibrium
of an isolated node
..............482
7.5.2.
Back to the problem of stability of the planar
mode of bending
....................484
xii
Handbook of Mechanical Stability in Engineering
7.5.2.1.
Bernoulli-Euler bars
............. 484
7.5.2.2.
Timoshenko bars
............... 487
7.5.2.3.
Simply supported bar in pure bending
. . . 488
7.5.3.
Pure bending of a cantilever bar
............ 492
7.5.3.1.
Problem (a)
.................. 493
7.5.3.2.
Problem (b)
.................. 494
7.5.3.3.
Problem (c)
.................. 495
7.5.3.4.
Problem (d)
.................. 496
7.5.3.5.
Problem (e)
.................. 497
7.5.4.
Distributed moment load
................ 501
7.5.4.1.
Bernoulli-Euler bar
.............. 501
7.5.4.2.
Timoshenko bar
................ 503
7.5.5.
Losing stability in a state of equilibrium without
initial stresses
...................... 508
7.6.
Argyris Paradox and Accompanying Myths
......... 510
7.6.1.
Argyris paradox: Myth of a semi-tangential nature
of the bending moment
................. 510
7.6.2.
Myth of a potential nature of the elasticity
force moments
...................... 513
7.6.3.
Rotation/slope components and derivatives
of lateral displacements of a bar s axis
........ 513
7.6.4.
Components of the rotation vector as generalized
coordinates of the system
................ 515
7.7.
Final Notes to Chapter
7.................... 516
8.
Spatial Curved Bar
—
Kirchhoff-Klebsch Theory
519
8.1.
Basic Knowledge About the Geometry
of a Spatial Curve
........................ 519
8.2.
Curved Bar and Its Geometry
................. 523
8.3.
Kinematic Relationships for a Bar
............... 529
8.4.
Equations of Equilibrium for a Bar
.............. 533
8.5.
Physical Equations
....................... 536
8.6.
Planar Curved Bar
....................... 538
8.6.1.
Stability of the planar mode of bending
of a curved bar
..................... 540
8.6.1.1.
A circular arch in pure bending
—
Timoshenko problem
............. 541
8.6.1.2.
A circular ring under a radial load
— Nicolai
problem
.................... 545
Contents xiji
8.6.1.2.1.
The case of a dead
external load
........... 545
8.6.1.2.2.
Tracking load
........... 547
8.6.1.2.3.
Polar load
............. 548
8.7.
Rectilinear Bar with an Initial Twist
............. 549
8.8.
Final Notes to the
Kirchhoff
Klebsch Theory
........ 552
Appendices A to
E
555
Appendix A. Grounds for Simplification in the Equilibrium
Stability Functional for a Thin-Walled Bar
.......... 555
Appendix B. Orthogonal Curvilinear Coordinates
-
Formulas
for Strain Components
..................... 559
B.I. Orthogonal curvilinear coordinates
—
General case
. 560
B.2. Orthogonal curvilinear coordinates produced
by a planar curve
.................... 562
Appendix C. Additions to the Papkovich Theorem
........ 563
C.I. Another justification for the Papkovich theorem
. . . 563
C.2. Additional note to the Papkovich theorem
...... 565
Appendix D. Qualitative Estimates of Critical Forces
....... 567
D.I.
Transformations of the load
.............. 568
D.2. Transformations of the stiffness
............ 573
Appendix E. Elements of the Catastrophe Theory
......... 575
E.I. Philosophy of the catastrophe theory
......... 576
E.2. Some elementary catastrophes
............. 579
E.3. Effect of initial imperfections
............. 583
E.4. Interaction between buckling modes
.......... 584
E.5. Procedure for use of the catastrophe theory
..... 591
References in Vol.
1
Author Index in Vol.
1
Subject Index in Vol.
1
|
| 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 | BV041200246 |
| classification_rvk | UF 1610 |
| ctrlnum | (OCoLC)859375351 (DE-599)BVBBV041200246 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV041200246 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:41:55Z |
| institution | BVB |
| isbn | 9789814383776 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026175136 |
| oclc_num | 859375351 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM |
| physical | XXX, 601, 7 S. 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) 1 General theorems and individual members of mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker Singapore [u.a.] World Scientific Publ. 2013 XXX, 601, 7 S. Ill, graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elastischer Werkstoff (DE-588)4151686-2 gnd rswk-swf Festigkeit (DE-588)4016916-9 gnd rswk-swf Strukturdynamik (DE-588)4226174-0 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Strukturelle Stabilität (DE-588)4295517-8 gnd rswk-swf Festigkeitslehre (DE-588)4016917-0 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Stabilität (DE-588)4056693-6 s DE-604 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 Elastischer Werkstoff (DE-588)4151686-2 s Strukturdynamik (DE-588)4226174-0 s Slivker, Vladimir I. Verfasser aut (DE-604)BV041200205 1 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=026175136&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) Elastischer Werkstoff (DE-588)4151686-2 gnd Festigkeit (DE-588)4016916-9 gnd Strukturdynamik (DE-588)4226174-0 gnd Stabilität (DE-588)4056693-6 gnd Strukturelle Stabilität (DE-588)4295517-8 gnd Festigkeitslehre (DE-588)4016917-0 gnd Strukturmechanik (DE-588)4126904-4 gnd Technische Mechanik (DE-588)4059231-5 gnd |
| subject_GND | (DE-588)4151686-2 (DE-588)4016916-9 (DE-588)4226174-0 (DE-588)4056693-6 (DE-588)4295517-8 (DE-588)4016917-0 (DE-588)4126904-4 (DE-588)4059231-5 |
| 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) 1 General theorems and individual members of mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker |
| title_fullStr | Handbook of mechanical stability in engineering (in 3 volumes) 1 General theorems and individual members of mechanical systems Anatoly V. Perelmuter ; Vladimir Slivker |
| title_full_unstemmed | Handbook of mechanical stability in engineering (in 3 volumes) 1 General theorems and individual members of 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 general theorems and individual members of mechanical systems |
| title_sub | (in 3 volumes) |
| topic | Elastischer Werkstoff (DE-588)4151686-2 gnd Festigkeit (DE-588)4016916-9 gnd Strukturdynamik (DE-588)4226174-0 gnd Stabilität (DE-588)4056693-6 gnd Strukturelle Stabilität (DE-588)4295517-8 gnd Festigkeitslehre (DE-588)4016917-0 gnd Strukturmechanik (DE-588)4126904-4 gnd Technische Mechanik (DE-588)4059231-5 gnd |
| topic_facet | Elastischer Werkstoff Festigkeit Strukturdynamik Stabilität Strukturelle Stabilität Festigkeitslehre Strukturmechanik Technische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026175136&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041200205 |
| work_keys_str_mv | AT perelʹmuteranatolijv handbookofmechanicalstabilityinengineeringin3volumes1 AT slivkervladimiri handbookofmechanicalstabilityinengineeringin3volumes1 |