# Advanced Mechanics of Solids by Otto T. Bruhns

# Advanced Mechanics of Solids by Otto T. Bruhns

Book Title : Advanced Mechanics of Solids

Author(s) : Otto T. Bruhns

Publisher : Springer

Edition : First

Pages : 110

Size : 57 Mb

Author(s) : Otto T. Bruhns

Publisher : Springer

Edition : First

Pages : 110

Size : 57 Mb

Book Description:

**Advanced Mechanics of Solids**by Otto T. Bruhns eBook is for advanced students who already are familiar with the elementary concepts of statics and the strength of materials. The principles of linear continuum mechanics and linear elastic material behavior are presented. This book build readers the foundation for the later treatment of structures such as beams, bars, plates and shells. Particular attention is paid to the respective thin-walled cases. The eBook also contains some chapters on the more and more important topic of dynamics of structures. Moreover, it provides the fundamental principles underlying modern computer methods. The book is structured such that in each chapter the theoretical considerations are accompanied by several illustrative examples demonstrating the application of these results.
Contents of the book:

1. Basic Concepts of Continuum Mechanics

1.1 General Remarks

1.2 Stresses

1.3 Strains

1.4 Compatibility Conditions

1.5 Equations of Motion

1.6 Energy

1.7 Principle of Virtual Work

1.8 Exercises to Chapter 1

2. Elastic Material

2.1 Hooke’s Law

2.2 Strain Energy, Complementary Energy

2.3 Fundamental Equations

2.4 Influence of Temperature

2.5 Hooke’s Law in Two Dimensions

2.6 Strength Criteria

2.7 Principle of Complementary Virtual Work

2.8 Exercises to Chapter 2

3. The Theory of Simple Beams I

3.1 General, Normal Stresses

3.2 Shear Stresses

3.3 Shear Center of Thin-Walled Open Sections

3.4 Influence of Distributed Loads

3.5 Stresses in Non-prismatic Beams

3.6 Deflections of Beams

3.7 Exercises to Chapter 3

4. Torsion of Prismatic Bars

4.1 Solid Cross Sections

4.2 Thin-Walled Closed Cross Sections

4.3 Thin-Walled Open Sections

4.4 Influence of Restrained Warping

4.4.1 Closed profiles

4.4.2 Open profiles

4.5 Exercises to Chapter 4

5. Curved Beams

5.1 General, Statics

5.2 Large Curvature

5.3 Small Curvature

5.4 Deflections of Curved Beams

5.5 Exercises to Chapter 5

6. Simple Beams II: Energy Principles

6.1 Reciprocity Theorems of Betti and Maxwell

6.2 Theorems of Engesser and Castigliano

6.3 Statically Indeterminate Systems

6.4 The Complementary Energy of Beams

6.5 Strain Energy of Beams

6.6 Application to Beams

6.7 Exercises to Chapter 6

7. Two-dimensional Problems

7.1 Plane Stress and Plane Strain

7.2 Body Forces Derived From a Potential

7.3 Plane Problems in Polar Coordinates

7.4 Exercises to Chapter 7

8. Plates and Shells

8.1 General Remarks

8.2 Disks

8.3 Thin Plates

8.3.1 Fundamental equations

8.3.2 Kirchhoff’s theory

8.3.3 Boundary conditions

8.3.4 Axially symmetric bending of circular plates

8.3.5 Elastic energy of plates

8.4 Membrane Theory of Shells of Revolution

8.5 Exercises to Chapter 8

9. Stability of Equilibrium

9.1 General Remarks

9.2 Bifurcation Problems with Finite Degrees of Freedom

9.3 A Snap-Through Problem

9.4 Column Buckling

9.5 Exercises to Chapter 9

10. Some Basic Concepts of Dynamics

10.1 Principle of Virtual Work

10.2 Hamilton’s Principle

10.3 The Euler-Lagrange Equations

10.4 The Lagrangian Multiplier Method

11. Oscillators With One Degree of Freedom

11.1 Undamped Free Vibration

11.2 Damped Free Vibration

11.3 Forced Vibration with Harmonic Excitation

11.4 Vibration Isolation

11.5 Exercises to Chapter 11

12. Systems of Several Degrees of Freedom

12.1 A Typical Example

12.2 General Equations and Solution

12.3 Forced Vibration with Harmonic Excitation

12.4 Exercises to Chapter 12

13. Answers to the Exercises

1. Basic Concepts of Continuum Mechanics

1.1 General Remarks

1.2 Stresses

1.3 Strains

1.4 Compatibility Conditions

1.5 Equations of Motion

1.6 Energy

1.7 Principle of Virtual Work

1.8 Exercises to Chapter 1

2. Elastic Material

2.1 Hooke’s Law

2.2 Strain Energy, Complementary Energy

2.3 Fundamental Equations

2.4 Influence of Temperature

2.5 Hooke’s Law in Two Dimensions

2.6 Strength Criteria

2.7 Principle of Complementary Virtual Work

2.8 Exercises to Chapter 2

3. The Theory of Simple Beams I

3.1 General, Normal Stresses

3.2 Shear Stresses

3.3 Shear Center of Thin-Walled Open Sections

3.4 Influence of Distributed Loads

3.5 Stresses in Non-prismatic Beams

3.6 Deflections of Beams

3.7 Exercises to Chapter 3

4. Torsion of Prismatic Bars

4.1 Solid Cross Sections

4.2 Thin-Walled Closed Cross Sections

4.3 Thin-Walled Open Sections

4.4 Influence of Restrained Warping

4.4.1 Closed profiles

4.4.2 Open profiles

4.5 Exercises to Chapter 4

5. Curved Beams

5.1 General, Statics

5.2 Large Curvature

5.3 Small Curvature

5.4 Deflections of Curved Beams

5.5 Exercises to Chapter 5

6. Simple Beams II: Energy Principles

6.1 Reciprocity Theorems of Betti and Maxwell

6.2 Theorems of Engesser and Castigliano

6.3 Statically Indeterminate Systems

6.4 The Complementary Energy of Beams

6.5 Strain Energy of Beams

6.6 Application to Beams

6.7 Exercises to Chapter 6

7. Two-dimensional Problems

7.1 Plane Stress and Plane Strain

7.2 Body Forces Derived From a Potential

7.3 Plane Problems in Polar Coordinates

7.4 Exercises to Chapter 7

8. Plates and Shells

8.1 General Remarks

8.2 Disks

8.3 Thin Plates

8.3.1 Fundamental equations

8.3.2 Kirchhoff’s theory

8.3.3 Boundary conditions

8.3.4 Axially symmetric bending of circular plates

8.3.5 Elastic energy of plates

8.4 Membrane Theory of Shells of Revolution

8.5 Exercises to Chapter 8

9. Stability of Equilibrium

9.1 General Remarks

9.2 Bifurcation Problems with Finite Degrees of Freedom

9.3 A Snap-Through Problem

9.4 Column Buckling

9.5 Exercises to Chapter 9

10. Some Basic Concepts of Dynamics

10.1 Principle of Virtual Work

10.2 Hamilton’s Principle

10.3 The Euler-Lagrange Equations

10.4 The Lagrangian Multiplier Method

11. Oscillators With One Degree of Freedom

11.1 Undamped Free Vibration

11.2 Damped Free Vibration

11.3 Forced Vibration with Harmonic Excitation

11.4 Vibration Isolation

11.5 Exercises to Chapter 11

12. Systems of Several Degrees of Freedom

12.1 A Typical Example

12.2 General Equations and Solution

12.3 Forced Vibration with Harmonic Excitation

12.4 Exercises to Chapter 12

13. Answers to the Exercises

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