Advanced Mechanics of Solids and Structures
- 1st Edition - February 2, 2026
- Latest edition
- Author: Dimitrios G. Pavlou
- Language: English
Advanced Mechanics of Solids and Structures provides the classic methods that are essential for a wider audience, but also the advanced techniques based on mechanical behavior,… Read more
World Book Day celebration
Where learning shapes lives
Up to 25% off trusted resources that support research, study, and discovery.
Description
Description
Advanced Mechanics of Solids and Structures provides the classic methods that are essential for a wider audience, but also the advanced techniques based on mechanical behavior, material characterization and anisotropic elasticity with applications to composite materials.
This title provides deep insight on important topics, such as the theory of beams with composite cross sections, slender beams, plates on elastic foundation, Airy’s stress functions, contact stresses and the elastic stability of a variety of structural members.
Mathematical tools, along with advanced methods of integral transforms are provided so the reader can follow along and apply learning.
Therefore, not only is this an essential resource for BSc, MSc, PhD level students, but also a practical guide for researchers, consultants and industrial engineers in the field of mechanical, civil, and structural engineering.
Key features
Key features
- Advanced techniques based on integral transforms
- Generalized functions for solving complex problems
- Mathematical tools
- Step-by-step solutions for real-life engineering problems
- Typical exam exercises
Readership
Readership
Students in BSc, MSc and PhD level, university lecturers and researchers. Engineers in the field of mechanical, civil, and structural engineering, aerospace, biomechanical engineering, offshore and marine structures, naval architecture, and geotechnical engineering
Table of contents
Table of contents
1. Stress
1.1 Definition of stress
1.2 Nomenclature of stresses – stress components of a point
1.3 Stress tensor – symmetry of stresses
1.4 Stresses components on an arbitrary plane ABC
1.5 Normal and shear stress on an arbitrary plane ABC
1.6 Stress vector transformation to a rotated coordinate system
1.7 Stress tensor transformation to a rotated coordinate system
Exercise 1
Exercise 2
1.8 Principal Stresses
1.9 Determination of the orientation l, m, n of the principal planes
1.10 Octahedral stresses
Exercise 3
1.11 Spherical and Deviatoric stress tensor
1.12 Plane stress: stress tensor in rotated coordinate system
Exercise 4
Exercise 5
Exercise 6
1.13 Differential equations of motion in cartesian coordinate system
1.14 Differential equations of motion in polar coordinate system
1.8 References
2. Strain
2.1 Definition of strain
2.1.1 Normal strain
2.1.2 Shear strain
2.2 Strain vector and strain tensor
2.2.1 Transformation of strain vectors
2.2.2 Transformation of strain tensors
2.2.3 Plane strain
2.3 Principal strains
2.4 Compatibility conditions of strains
2.5 Strain-displacement equations
2.6 NDT of strain measurements
2.7 Problems
2.8 References
3. Stress-strain relationships
3.1 Generalized Hooke’s law for isotropic materials
3.2 Strain energy density
3.3 Thermoelasticity
3.4 Problems
3.5 References
4. Mechanical behaviour of materials and material characterization
4.1 Stress-strain curve and basic mechanical properties of materials
4.2 Parameters affecting the stress-strain behaviour
4.2.1 Loading rate effect
4.2.2 Temperature effect
4.2.3 Surface quality effect
4.2.4 Specimen size effect
4.3 Material response in impact loading
4.4 Material response in high temperature – Creep
4.5 Material response in cyclic loading – Fatigue
4.6 Material hardness and hardness measurement
4.7 Corrosion, corrosion measurement, corrosion protection
4.8 Non-destructive evaluation of material properties
4.9 Problems
4.19 References
5. Inelastic material response and yield criteria
5.1 Types of inelastic response under mechanical stresses
5.2 Yield criteria for isotropic materials
5.2.1 Maximum principal stress criterion
5.2.2 Maximum principal strain criterion
5.2.3 Stain energy density criterion
5.2.4 Maximum shear stress criterion (Tresca criterion)
5.2.5 Distortional energy density criterion (von Mises criterion)
5.3 Problems
5.4 References
6. Beam theory – Bending and Torsion
6.1 Kirchhoff’s hypothesis for beam cross sections
6.2 Symmetric and nonsymmetric bending
6.3 Bending stresses of straight beams
6.3.1 Normal stresses
6.3.2 Shear stress
6.3.3 Neutral line
6.4 Deflection of straight beams
6.5 Curved beams
6.5.1 Circumferential stresses
6.5.2 Radial stresses
6.5.3 Bleich’s factors
6.5.4 Deflections
6.5.5 Closed rings
6.6 Torsion of beams with compact cross section
6.7 Torsion of hollow thin-walled beams with closed cross section
6.8 Torsion of hollow thin-walled beams with open cross section
6.9 Shear center
6.10 Torsion of beams with composite cross section
6.11 Bending-Torsion interaction
6.12 Elastoplastic bending – Residual stresses
6.13 Problems
6.14 References
7. Energy methods
7.1 Thermodynamics of material response under mechanical loads
7.2 Principle of minimum potential energy
7.3 Stain energy of members under axial, shear, bending and torsion loading
7.4 Castigliano’s theorem
7.5 Applications on statically indeterminate beams, trusses, and frames
7.6 Problems
7.7 References
8. Beams on elastic foundation and application in thin-walled cylinders
8.1 Infinite beams on elastic foundation under concentrated load
8.2 Infinite beams on elastic foundation under distributed load
8.3 Semi-infinite and finite beams on elastic foundation
8.4 Short beams on elastic foundation
8.5 The method of integral transforms
8.6 Application in thin-walled cylinders
8.7 Problems
8.8 References
9. Flat plates
9.1 Kirchhoff’s assumption for plates
9.2 Equilibrium equations of stresses
9.3 Strain-displacement relations
9.4 Stress-strain relations
9.5 Boundary conditions
9.6 The biharmonic equation of plate bending
9.7 Westergaard approximate solution for rectangular plates
9.8 Circular plates
9.8.1 Symmetric bending of circular plates
9.8.2 Non-symmetric bending of circular plates
9.9 Problems
9.10 References
10. Plates on elastic foundation
10.1 Infinite plates on elastic foundation
10.2 Finite plates on elastic foundation
10.3 The method of integral transforms
10.4 Problems
10.5 References
11. Airy’s stress function – Stress concentration – Thick-walled cylinders
11.1 Equilibrium equations, compatibility conditions, and biharmonic equation
11.2 Stress concentration
11.2.1 Circular hole in infinite flat plate under in-plane loads
11.2.2 Elliptical hole in infinite flat plate under in-plane loads
11.2.3 Hole in finite flat plate under in-plane loads
11.2.4 Crack in infinite flat plate under in-plane loads
11.3 Thick-walled cylinders
11.3.1 Open cylinder
11.3.2 Cylinder with closed ends
11.3.3 Compound cylinder
11.3.4 Temperature effect
11.3.5 Rotating disks
11.4 Problems
11.5 References
12. Contact stresses
12.1 Deformation of contact surface
12.2 Fundamental equations of bodies under contact
12.3 Approximate results
12.4 Bodies in point contact
12.4.1 Contact between two spheres
12.4.2 Contact between a sphere and a flat or a curved surface
12.5 Bodies in line contact
12.5.1 Contact between two cylinders
12.5.2 Contact between a cylinder and a flat or a curved surface
12.6 Elastic half-space under point load
12.7 Elastic half-space under uniform surface pressure
12.8 Problems
12.9 References
13. Elastic stability
13.1 Buckling of columns
13.1.1 Euler column under axial load
13.1.2 Euler column with a rotational restrained junction
13.1.3 Euler column with continuous elastic restrain
13.1.4 Euler column with distributed load
13.2 Buckling of beams
13.2.1 Flexural-Torsional buckling of beams of rectangular cross section
13.2.2 Flexural-Torsional buckling of beams of I cross section
13.3 Buckling of arches and rings
13.4 Buckling of plates
13.4.1 Rectangular plates
13.4.2 Circular plates
13.5 Problems
13.6 References
14. Elements of anisotropic elasticity – Composite materials
14.1 Anisotropic materials
14.2 Coordinate systems – Principal directions
14.3 Stiffness matrix of anisotropic layer
14.4 Transformation of stress and strain components of anisotropic layer
14.5 Transformation of engineering properties of anisotropic layer
14.6 Anisotropic laminates
14.7 Classical lamination theory
14.8 Kirchhoff’s assumption – Laminate strains and stresses
14.9 Laminate stiffness matrix
14.10 Failure criteria
14.11 Problems
14.12 References
Appendixes
I. Elements from mathematics
I1 Vectors
I2 Tensors
I3 Integral transforms
II Geometrical Properties of cross-sections
II1 Centroid
II2 Moments of inertia of cross sections
II3 Transformation of moments of inertia
II4 Principal axes
II5 Tables of properties of usual cross sections
III. Mechanical properties of selected materials
1.1 Definition of stress
1.2 Nomenclature of stresses – stress components of a point
1.3 Stress tensor – symmetry of stresses
1.4 Stresses components on an arbitrary plane ABC
1.5 Normal and shear stress on an arbitrary plane ABC
1.6 Stress vector transformation to a rotated coordinate system
1.7 Stress tensor transformation to a rotated coordinate system
Exercise 1
Exercise 2
1.8 Principal Stresses
1.9 Determination of the orientation l, m, n of the principal planes
1.10 Octahedral stresses
Exercise 3
1.11 Spherical and Deviatoric stress tensor
1.12 Plane stress: stress tensor in rotated coordinate system
Exercise 4
Exercise 5
Exercise 6
1.13 Differential equations of motion in cartesian coordinate system
1.14 Differential equations of motion in polar coordinate system
1.8 References
2. Strain
2.1 Definition of strain
2.1.1 Normal strain
2.1.2 Shear strain
2.2 Strain vector and strain tensor
2.2.1 Transformation of strain vectors
2.2.2 Transformation of strain tensors
2.2.3 Plane strain
2.3 Principal strains
2.4 Compatibility conditions of strains
2.5 Strain-displacement equations
2.6 NDT of strain measurements
2.7 Problems
2.8 References
3. Stress-strain relationships
3.1 Generalized Hooke’s law for isotropic materials
3.2 Strain energy density
3.3 Thermoelasticity
3.4 Problems
3.5 References
4. Mechanical behaviour of materials and material characterization
4.1 Stress-strain curve and basic mechanical properties of materials
4.2 Parameters affecting the stress-strain behaviour
4.2.1 Loading rate effect
4.2.2 Temperature effect
4.2.3 Surface quality effect
4.2.4 Specimen size effect
4.3 Material response in impact loading
4.4 Material response in high temperature – Creep
4.5 Material response in cyclic loading – Fatigue
4.6 Material hardness and hardness measurement
4.7 Corrosion, corrosion measurement, corrosion protection
4.8 Non-destructive evaluation of material properties
4.9 Problems
4.19 References
5. Inelastic material response and yield criteria
5.1 Types of inelastic response under mechanical stresses
5.2 Yield criteria for isotropic materials
5.2.1 Maximum principal stress criterion
5.2.2 Maximum principal strain criterion
5.2.3 Stain energy density criterion
5.2.4 Maximum shear stress criterion (Tresca criterion)
5.2.5 Distortional energy density criterion (von Mises criterion)
5.3 Problems
5.4 References
6. Beam theory – Bending and Torsion
6.1 Kirchhoff’s hypothesis for beam cross sections
6.2 Symmetric and nonsymmetric bending
6.3 Bending stresses of straight beams
6.3.1 Normal stresses
6.3.2 Shear stress
6.3.3 Neutral line
6.4 Deflection of straight beams
6.5 Curved beams
6.5.1 Circumferential stresses
6.5.2 Radial stresses
6.5.3 Bleich’s factors
6.5.4 Deflections
6.5.5 Closed rings
6.6 Torsion of beams with compact cross section
6.7 Torsion of hollow thin-walled beams with closed cross section
6.8 Torsion of hollow thin-walled beams with open cross section
6.9 Shear center
6.10 Torsion of beams with composite cross section
6.11 Bending-Torsion interaction
6.12 Elastoplastic bending – Residual stresses
6.13 Problems
6.14 References
7. Energy methods
7.1 Thermodynamics of material response under mechanical loads
7.2 Principle of minimum potential energy
7.3 Stain energy of members under axial, shear, bending and torsion loading
7.4 Castigliano’s theorem
7.5 Applications on statically indeterminate beams, trusses, and frames
7.6 Problems
7.7 References
8. Beams on elastic foundation and application in thin-walled cylinders
8.1 Infinite beams on elastic foundation under concentrated load
8.2 Infinite beams on elastic foundation under distributed load
8.3 Semi-infinite and finite beams on elastic foundation
8.4 Short beams on elastic foundation
8.5 The method of integral transforms
8.6 Application in thin-walled cylinders
8.7 Problems
8.8 References
9. Flat plates
9.1 Kirchhoff’s assumption for plates
9.2 Equilibrium equations of stresses
9.3 Strain-displacement relations
9.4 Stress-strain relations
9.5 Boundary conditions
9.6 The biharmonic equation of plate bending
9.7 Westergaard approximate solution for rectangular plates
9.8 Circular plates
9.8.1 Symmetric bending of circular plates
9.8.2 Non-symmetric bending of circular plates
9.9 Problems
9.10 References
10. Plates on elastic foundation
10.1 Infinite plates on elastic foundation
10.2 Finite plates on elastic foundation
10.3 The method of integral transforms
10.4 Problems
10.5 References
11. Airy’s stress function – Stress concentration – Thick-walled cylinders
11.1 Equilibrium equations, compatibility conditions, and biharmonic equation
11.2 Stress concentration
11.2.1 Circular hole in infinite flat plate under in-plane loads
11.2.2 Elliptical hole in infinite flat plate under in-plane loads
11.2.3 Hole in finite flat plate under in-plane loads
11.2.4 Crack in infinite flat plate under in-plane loads
11.3 Thick-walled cylinders
11.3.1 Open cylinder
11.3.2 Cylinder with closed ends
11.3.3 Compound cylinder
11.3.4 Temperature effect
11.3.5 Rotating disks
11.4 Problems
11.5 References
12. Contact stresses
12.1 Deformation of contact surface
12.2 Fundamental equations of bodies under contact
12.3 Approximate results
12.4 Bodies in point contact
12.4.1 Contact between two spheres
12.4.2 Contact between a sphere and a flat or a curved surface
12.5 Bodies in line contact
12.5.1 Contact between two cylinders
12.5.2 Contact between a cylinder and a flat or a curved surface
12.6 Elastic half-space under point load
12.7 Elastic half-space under uniform surface pressure
12.8 Problems
12.9 References
13. Elastic stability
13.1 Buckling of columns
13.1.1 Euler column under axial load
13.1.2 Euler column with a rotational restrained junction
13.1.3 Euler column with continuous elastic restrain
13.1.4 Euler column with distributed load
13.2 Buckling of beams
13.2.1 Flexural-Torsional buckling of beams of rectangular cross section
13.2.2 Flexural-Torsional buckling of beams of I cross section
13.3 Buckling of arches and rings
13.4 Buckling of plates
13.4.1 Rectangular plates
13.4.2 Circular plates
13.5 Problems
13.6 References
14. Elements of anisotropic elasticity – Composite materials
14.1 Anisotropic materials
14.2 Coordinate systems – Principal directions
14.3 Stiffness matrix of anisotropic layer
14.4 Transformation of stress and strain components of anisotropic layer
14.5 Transformation of engineering properties of anisotropic layer
14.6 Anisotropic laminates
14.7 Classical lamination theory
14.8 Kirchhoff’s assumption – Laminate strains and stresses
14.9 Laminate stiffness matrix
14.10 Failure criteria
14.11 Problems
14.12 References
Appendixes
I. Elements from mathematics
I1 Vectors
I2 Tensors
I3 Integral transforms
II Geometrical Properties of cross-sections
II1 Centroid
II2 Moments of inertia of cross sections
II3 Transformation of moments of inertia
II4 Principal axes
II5 Tables of properties of usual cross sections
III. Mechanical properties of selected materials
Product details
Product details
- Edition: 1
- Latest edition
- Published: April 2, 2026
- Language: English
About the author
About the author
DP
Dimitrios G. Pavlou
Dimitrios Pavlou is Professor of Mechanics at University of Stavanger in Norway, and Elected Academician of the Norwegian Academy of Technological Sciences. He has had over twenty-five years of teaching and research experience in the fields of Theoretical and Applied Mechanics, Fracture Mechanics, Finite and Boundary Elements, Structural Dynamics, Anisotropic Materials, and their applications in Engineering Structures.
Professor Pavlou is the author of titles, "Essentials of the Finite Element Method" (Elsevier) and "Composite Materials in Piping Applications" (Destech Publications), and guest co-editor of several international journal Special Issues and conference proceedings.
His research portfolio includes over 120 publications in the areas of Applied Mechanics and Engineering Mathematics (majority as single or first author). Since January 2020, Professor Pavlou joined the Editorial Board of the journal "Computer-Aided Civil and Infrastructure Engineering" (IF=11.775, 1st of 134 journals in Civil Engineering – 2020 Journal Citation Reports).
He works as Editor for the journals “Maritime Engineering” (IF=5.952); “Nondestructive Testing and Evaluation” (IF=2.098); “Advances in Civil Engineering” (IF= 1.843); “Aerospace Technology and Management” (IF= 0.713);
“Dynamics”; “Aeronautics and Aerospace Open Access Journal” and “Journal of Materials Science and Research”.
He is also an Editorial Board Member for the “International Journal of Structural Integrity,” the “International Journal of Ocean Systems Management” and “Journal of Materials Science and Research”.
Affiliations and expertise
Professor, University of Stavanger, Stavanger, NorwayView book on ScienceDirect
View book on ScienceDirect
Read Advanced Mechanics of Solids and Structures on ScienceDirect