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

Introduction. The notion of a continuous medium. Principles of analysis of statically indeterminate problems. Examples of simple statically indeterminate systems: plane truss, airplane landing gear, beams.
Analysis of deformation. Analysis of infinitesimal motion, the tensors of infinitesimal deformation and rotation. Normal and shear strains. Maximum and minimum normal and shear strains, the principal directions. Change of volume in an infinitesimal material element, the volumetric strain. Plane motion, change of coordinate system, extensiometers, the Mohr circle. Simple states of deformation: pure volumetric deformation, simple shear. The deviatoric strain tensor.The compatibility equations and the calculation of displacement from the strain tensor.
Stresses. External and internal forces in deformable media. The stress vector, the stress tensor, the stress vector on an arbitrary surface. Conservation of linear and angular momentum: the differential equations of equilibrium and the symmetry of the stress tensor. Principal directions and principal stresses. Plane stress states, change of coordinate system, the Mohr circle of the stress tensor. Simple stress states: uniaxial tension/compression, biaxial tension/compression, hydrostatic stress, pure shear. The deviatoric stress tensor.
Elastic constitutive equations. Stress‐strain relations in isotropic linear‐elastic materials. Young’s modulus, Poisson’s ratio, the shear and bulk moduli, the relationships among the elastic constants. Incompressible materials. Thermal strains and the corresponding thermomechanical constitutive equations.
Thin‐walled pressure vessels. Stresses in spherical and cylindrical vessels under internal and external pressure. Stresses in axisymmetric pressure vessels.
The boundary value problem. The general boundary value problem of linear elastostatics: problem formulation, the principle of superposition, the principle of Saint‐Venant. Uniqueness of solution and “ellipticity” of the differential equations.
Analysis of beams (the Saint‐Venant problem). Problem formulation and the Saint‐Venant boundary conditions. Exact solutions: i) tension/compression, ii) torsion of beams with circular and arbitrary cross‐ sections, the warping function and the Prandtl stress‐function, the shear flow, iii) pure bending, symmetrical and non‐symmetrical bending, the neutral axis of bending of the cross‐section, iv) bending by terminal loads, the “shear center” of the cross‐section, the “Jourawski formula”. Approximate calculation of shear stresses for the problem of bending by terminal loads. Eccentric axial loads, the “core” of the cross‐section. Comparison of axial and shear stresses in beams. Design of power‐transmitting shafts, combination of torsional and bending loads. 

• Ν. Αράβας, “Καρτεσιανοί Τανυστές”. Πανεπιστημιακές Εκδόσεις Θεσσαλίας, 2005.
• Ν. Αράβας, “Μηχανική των Υλικών, Τόμος Ι: Εισαγωγή στη Μηχανική των Παραμορφωσίμων Σωμάτων και τη Γραμμική Ελαστικότητα”. Εκδόσεις Τζιόλας, 2014.
• Ν. Αράβας, “Μηχανική των Υλικών, Τόμος ΙΙ: Ανάλυση Ελαστικών Δοκών”. Πανεπιστημιακές Εκδόσεις
  Θεσσαλίας, 2008.
• 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.
•  Ventsel, E. and Krauthammer, T., “Thin Plates and Shells”, Marcel Dekker, Inc., 2001.

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Lectures and Laboratory Exercises