Courses

Theory of Elasticity

General

Course Contents

• Stresses. Normal and shear stress. Stress tensor. Equations of equilibrium.
• Basic principles of elasticity – plasticity. Continuous media. Homogeneous – isotropic materials.
Small and large deformations. Second-order phenomena. Static and dynamic loads.
• Change of coordinate system. Transformation of stresses.
• Principal stresses – principal axes. Mohr’s circles. Invariants of stresses. Three-dimensional and
plane stress state.
• Deformations. Strain tensor. Laws of material behavior, stress-strain relationship. Compatibility
equations.
• Linear elasticity. Constitutive equations. Mechanical characteristics of materials. Hooke’s law.
Modulus of elasticity. Poisson’s ratio. Shear modulus. Elasto-plastic materials.
• Properties of fluids. Viscosity.
• Boundary conditions. Principle of superposition. Saint Venant’s principle. Plane stress state. Plane
strain state.
• Airy stress function. Solving two-dimensional problems in orthogonal and polar coordinates.
Boundary conditions.
• Lamé’s constants. Elasticity equations. P and S wave velocities. Speeds of propagation.
• Energy methods. Strain energy. Maxwell – Betti reciprocity theorem. Castigliano’s theorem.

Educational Goals

The familiarization of students with the concepts of stress and strain in continuous elastic media and
the stress-strain relationship in the elastic region. Understanding the equilibrium and compatibility
equations. The use of boundary conditions. The ability to apply analytical, energy, and numerical
methods to determine deformations in truss and solid structures.

General Skills

– Search for, analysis and synthesis of data and information, with the use of the necessary technology
– Adapting to new situations
– Decision-making
– Working independently
– Team work
– Working in an interdisciplinary environment
– Project planning and management
– Criticism and self-criticism
– Production of free, creative and inductive thinking

Teaching Methods

Face to face

Teaching Organization

ActivitySemester workload
Lectures52
Individual study78
TOTAL130
Total260

Students Evaluation

1. Assignment of tasks aimed at exploring the understanding
of the concepts taught.
2. Final written exam at the end of the semester (in Greek).

3. Each student is given the opportunity to review their
written exam and have their mistakes analyzed.

Recommended Bibliography

  • Γδούτου Ε. «Θεωρία Ελαστικότητας», Εκδόσεις Συμμετρία 2003.
  • http://eclass.opencourses.teicm.gr/eclass/modules/document/file.php/TMB111/FULL.pdf
  • Timoshenko S, Goodier G.N. «Theory of Elasticity», McGraw-Hill, 1969.
  • Timoshenko S, «Theory of Elasticity», McGraw-Hill, 1987.
  • L. D. Landau, E. M. Lifshitz, «Theory of Elasticity», Pergamon Press, 1989.
  • A.I. Lurie, «Theory of Elasticity», Springer Science & Business Media, 2010.
  • Gdoutos E. «Theory of Elasticity», Symmetria publications 2003 (in Greek)
    http://eclass.opencourses.teicm.gr/eclass/modules/document/file.php/TMB111/FULL.pdf
    Timoshenko S, Goodier G.N. «Theory of Elasticity», McGraw-Hill, 1969.
    Timoshenko S, «Theory of Elasticity», McGraw-Hill, 1987.
    L. D. Landau, E. M. Lifshitz, «Theory of Elasticity», Pergamon Press, 1989.
    A.I. Lurie, «Theory of Elasticity», Springer Science Business Media, 2010