Objective of the course is to introduce the student το advanced concepts of stress analysis. After completing the course, the student should be able to carry out advanced calculations of elastic stress analysis of mechanical engineering components.

Deflection of beams. Differential equation of the deflection curve, the effect of transverse shear forces, the boundary conditions, discontinuity functions. Statically indeterminate beams. The “three‐ moment equation” (Clapeyron).
The plane problem. Plane strain, plane stress, and generalized plane stress. The plane boundary value problem in linear elastostatics. The problem in terms of stress. The Airy stress function, polynomial stress functions. Applications. Cylindrical coordinates, the general variable‐separable solution of the biharmonic equation in polar coordinates. Axisymmetric plane problems, hollow cylinder under internal and external pressure. Infinite plate with a hole. Use of Mathematica for the solution of plane problems.
Energy methods. General results: statically admissible stress fields and kinematically admissible displacement fields, the principle of virtual work, the principle of virtual work as a sufficient condition for equilibrium, alternative formulations of the boundary value problem in a deformable continuum, the method of “unit load”. Elastic materials (linear or non‐linear): the elastic strain energy and the complementary elastic strain energy, work and elastic energy, the theorems of Castigliano and Engesser. Linear elastic materials: the “Betti” reciprocity theorem, elastic strain energy in simple structures, solution of statically indeterminate problems by using Castigliano’s theorem, the theorems of minimum potential and minimum complementary energy, approximate solutions, the finite element method. Use of the general purpose finite element program ABAQUS for the solution of various elasticity problems.
Buckling. The effect of geometry change on equilibrium. Linear‐elastic cantilever under axial force. Imperfect slender columns. Column buckling as an eigenvalue problem. Column buckling under various support conditions.
Nonlinear materials. Plastic deformations and creep. Introduction to the theories of
plasticity and viscoelasticity.

PROPOSED BIBLIOGRAPHY:
• Beer F., Johnston R., DeWolf J., Mazurek D., Sanghi S. “ΜΗΧΑΝΙΚΗ ΤΩΝ ΥΛΙΚΩΝ”, 8η Έκδοση, Εκδόσεις Τζιόλα, 2023 [IN GREEK].
• Cook, R. and Young, W., “Advanced Mechanics of Materials”, 2nd edition, Prentice Hall, 1998.
• Hjelmstad, K.D., “Fundamentals of Structural Mechanics”, 2nd edition, Academic Press, 2005.Boresi, A.P., Schmidt, R.J., and Sidebottom, O.M., “Advanced Mechanics of Materials”, 5th edition, John Wiley & Sons, 1993.
• Ugural, A.C. and Fenster, S.K., “Advanced Strength and Applied Elasticity”, 4th edition, Prentice‐Hall, 2003.
• Shames, I.H. and Cozzarelli, F.A., “Elastic and Inelastic Stress Analysis”, Taylor & Francis, 1997.
• Αράβας Ν., “Μηχανική των Υλικών, Τόμος ΙΙ: Ανάλυση Ελαστικών Δοκών”. Πανεπιστημιακές Εκδόσεις Θεσσαλίας, 2008 [IN GREEK].
RELEVANT SCIENTIFIC JOURNALS:
• International Journal of Solids and Structures
• ASME Journal of Applied Mechanics
• ASCE Journal of Engineering Mechanics
• Mechanics of Materials
• ASME Journal of Pressure Vessel Technology
• Mechanics and Physics of Solids

Greek

Lectures, Practical Exercises, Laboratory Exercises