Levon G Petrosian, Vladimir A Ambartsumian

Static and Dynamic Analysis of Engineering Structures

Incorporating the Boundary Element Method

• Gebundenes Buch

Produktdetails

• Verlag: Wiley
• Seitenzahl: 528
• Erscheinungstermin: 11. Mai 2020
• Englisch
• Abmessung: 244mm x 175mm x 36mm
• Gewicht: 1021g
• ISBN-13: 9781119592839
• ISBN-10: 1119592836
• Artikelnr.: 57382246

Autorenporträt

Levon Gregory Petrosian is Plan Review Division Chief at the Washington District Department of Transportation in the US. He was formerly Professor of Structural Engineering and Structural Mechanics at Moscow State University of Engineering and Building Structure (MÈCÈ), Russia, Director of the Armenian Earthquake Engineering Research Institute, Chairman of the Structural Mechanic Department of the Armenian National University of Architecture & Construction, and a renowned expert on the analysis of engineering structures. Vladimar Alexandry Ambartsumian was Professor of Structural Engineering and Structural Mechanics at the Armenian National University of Architecture & Construction and a renowned expert on the analysis of engineering structures.

Inhaltsangabe

About the Authors xi
Preface xiii
Introduction xv
Chapter 1: Methods of Dynamic Design of Structural Elements 1
1.1 The Method of Separation Variables 1
1.2 The Variational Methods 7
1.3 Integral Equations and Integral Transforms Methods 11
1.4 The Finite Element Method 17
1.5 The Finite Difference Method 25
1.6 The Generalized Method of Integral Transformation 27
1.7 The Method of Delta-Transform 44
1.8 The Generalized Functions in Structural Mechanics 63
1.9 General Approaches to Constructing Boundary Equations, and Standardized
Form of Boundary Value Problems 67
1.10 The Relationship of Green's Function with Homogeneous Solutions of the
Method of Initial Parameters 80
1.11 The Spectral Method of Boundary Elements 83
1.12 The Compensate Loads Method 89
Chapter 2: Boundary Elements Methods (BEM) in the Multidimensional Problems
93
2.1 The Integral Equations of Boundary Elements Methods 93
2.2 The Construction of Boundary Equations by the Delta-Transformation
Technique 103
2.3 The Equivalence of Direct and Indirect BEM 114
2.4 The Spectral Method of Boundary Elements (SMBE) in Multidimensional
Problems 118
2.5 The Problems Described by the Integro-Differential System of Equations
124
Chapter 3: Oscillation of Bars and Arches 131
3.1 The Nonlinear Oscillations of Systems with One Degree of Freedom 131
3.2 The Nonlinear Oscillations of Systems with Multiple-Degrees-of-Freedom
141
3.3 The Nonlinear Oscillations of Systems with Distributed Mass 154
3.3.1 Simply Supported Beams 156
3.3.2 Beams With Built-in Ends 157
3.3.3 Beams With One End Hinged Support and Another End Built-in Support
157
3.3.4 The Cantilever Beam 158
3.4 The Oscillations of the Beam of the Variable Cross-sections 161
3.5 The Optimum Design of the Bar 167
3.6 The Oscillations of Flexural-Shifted (Bending-Shifted) Bars Under the
Seismic Impacts 170
3.7 Oscillations of Circular Rings and Arches 176
3.8 The Free Oscillations of System "Flexible Arch-Rigid Beam" 182
3.9 The Results of Dynamic Testing Model of Combined System Rigid-beam and
Flexible Arch 195
3.10 The Oscillations of the Combined System Taking into Account its Extent
at a Given Harmonic Motion Base 207
3.11 The Determination of the Reactions of Multiple Spans Frame Bridges,
Extended Buildings, and Structures Taking into Account the Initial Phase of
Passing (Propagation) of the Seismic Wave 224
Chapter 4: Oscillation of Plates and Shells 243
4.1 The Design of the Cantilever Plate of Minimal Mass Working on the Shift
with the Assigned Fundamental Frequency 243
4.2 The Experimental and Theoretical Research of Oscillation of a
Cantilever Plate with Rectangular Openings 254
4.3 The Oscillations (Vibrations) of Spherical Shells 262
4.4 The Application of the Spectral Method of Boundary Element (SMBE) to
the Oscillation of the Plates on Elastic Foundation 265
Chapter 5: The Propagation of Elastic Waves and Their Interaction with the
Engineering Structures 271
5.1 The Propagation of Seismic Waves in the Laminar Inhomogeneous Medium
271
5.2 Diffraction of Horizontal Waves on the Semi-cylindrical Base of
Structure 277
5.3 Method of Calculation of the Lining of Tunnels to Seismic Resistance
285
5.4 A Study of the Action of Seismic Wave on the Rigid Ring Located in the
Half-plane 298
5.5 Calculations of Underground Structures with Arbitrary Cross-section
under Seismic Action Impact 306
Chapter 6: The Special Features of the Solution of Dynamic Problems by the
Boundary Element Methods (BEM) 315
6.1 One Method of Calculation: The Hilbert Transform and its Applications
to the Analysis of Dynamic System 315
6.2 Construction of Green's Function for Bases Having Frequency-Dependent
Internal Friction 324
6.3 The Green's Functions of Systems with the Frequency-Independent
Internal Friction 332
6.4 The Numerical Realization of Boundary Element Method (BEM) 342
6.5 The Construction of the Green's Function of the Dynamic Stationary
Problem for the Elasto-Viscous Half-Plane 351
Chapter 7: The Questions of the Static and Dynamic Analysis of Structures
on an Elastic Foundation 365
7.1 The Kernel of the Generalized Model of Elastic Foundation (Base) 378
7.2 The Determination of the Characteristics of the Generalized (Unified,
Integrated) Model of the Elastic Foundation (Base) 393
7.3 Contact Problem for the Rigid Die, Lying on the Generalized Elastic
Base 397
7.4 On One Method of Calculation of Structures on an Elastic Foundation 404
7.5 The Calculation of the (Non-isolated) Beams and Plates, Lying on an
Elastic Foundation, Described by the Generalized Model 408
7.6 The Forced Oscillations of a Rectangular Plate on an Elastic Foundation
415
7.7 The Calculation of the Membrane of Arbitrary Shape on an Elastic
Foundation 428
Appendix A: Certificate of Essential Building Data 443
Appendix B: Contact Stresses on the Sole of the Circular Die and the Sole
of the Plane Die 455
B.1 Contact Stresses on the Sole of the Circular Die. 455
B.2 Contact Stresses on the Sole of the Plane Die. 457
References 459
Index 483