Static and dynamic analysis of engineering structures : incorporating the boundary element method / Levon G. Petrosian, Professor of Structural Engineering and Structural Mechanics, Moscow University of Engineering and Building Structures, Doctor of Science, Doctorate in Structural Engineering and Structural Mechanics, Ph.D. in Civil Engineering, Master of Civil Engineering, University of Architecture & Construction, Vladimir A. Ambartsumian, Professor of Structural Engineering and Structural Mechanics, Armenian National University of Architecture & Construction.

ABOUT THE AUTHOR
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.

Includes bibliographical references and index.

TABLE OF CONTENTS
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

ABOUT

"This book examines static and dynamic analysis of engineering structures for methodological and practical purposes. The first chapter solves problems using traditional techniques. Next, boundary element methods are introduced. Vibrations of discrete and continuous systems are then discussed. The final chapters offer solutions for more complex systems, such as elastic waves in inhomogeneous media, frequency-dependent damping, and membranes of arbitrary shape. The aim of this book is to provide the readers with a guide to analyzing static and dynamic structures using traditional and advanced approaches with real-world, practical examples. Analysis of static and dynamic structures lies at the heart of mechanical engineering, and many techniques and approaches have been developed over the years to improve modeling and prediction of the performance of such structures. Typically, one of the most difficult aspects to model are the boundaries and discontinuities of a structure, and it is research in this area that led to one of the most established techniques employed today known as the Boundary Element Method"-- Provided by publisher.

An authoritative guide to the theory and practice of static and dynamic structures analysis

Static and Dynamic Analysis of Engineering Structures examines static and dynamic analysis of engineering structures for methodological and practical purposes. In one volume, the authors – noted engineering experts – provide an overview of the topic and review the applications of modern as well as classic methods of calculation of various structure mechanics problems. They clearly show the analytical and mechanical relationships between classical and modern methods of solving boundary value problems.

The first chapter offers solutions to problems using traditional techniques followed by the introduction of the boundary element methods. The book discusses various discrete and continuous systems of analysis. In addition, it offers solutions for more complex systems, such as elastic waves in inhomogeneous media, frequency-dependent damping and membranes of arbitrary shape, among others. Static and Dynamic Analysis of Engineering Structures is filled with illustrative examples to aid in comprehension of the presented material. The book:

Illustrates the modern methods of static and dynamic analysis of structures;
Provides methods for solving boundary value problems of structural mechanics and soil mechanics;
Offers a wide spectrum of applications of modern techniques and methods of calculation of static, dynamic and seismic problems of engineering design;
Presents a new foundation model.
Written for researchers, design engineers and specialists in the field of structural mechanics, Static and Dynamic Analysis of Engineering Structures provides a guide to analyzing static and dynamic structures, using traditional and advanced approaches with real-world, practical examples.