Elasticity and Strength of Materials

Subject 1: Equilibrium in deformable bodies
- Body and surface forces
- Concept of stress
- Stress tensor
- Stress equations of equilibrium
- Stationary stresses
Subject 2: Kinematic of deformable bodies
- Motion: Basic concepts
- Strain Tensor
- Infinitesimal strain
- Geometrical meaning of the components of infinitesimal strain tensor
- Principal Strains
- Equations of compatibility
Subject 3: Constitutive equations
- Behaviour laws
- Hyperelastic behaviour
- Linear elastic behaviour
- Material symmetries
- Physical meaning of the constants
Subject 4: Differential formulation
- Elasticity equations
- Boundary and contact conditions
- Displacement (Navier) formulation
- Stress (Michell-Beltrami) formulation
Subject 5: Integral formulation and principles (I)
- Theorem of Virtual Works
- Clapeyron theorem
- Theorem of Minimum Potential Energy
Subject 6: Integral formulation and principles (II)
- Reciprocity Theorems
- General Principles
Subject 7: Failure criteria
- Failure by yielding
- Haig-Westergaard representation
- Von Mises-Hencky-Nadai yield criterion
- Tresca-Guest yield criterion
- Alternate yield criteria
- Equivalent stress and safety factor
Subject 8: Two dimensional theory of Elasticity (I)
- Plain Stress and Plain Strain
- Plane Elasticity in term of displacement
- Plane Elasticity in terms of stresses
- Methods of solutions
- Mohr¿s circle in 2D
Subject 9: Two dimensional theory of Elasticity (II)
- Elasticity in polar coordinates
- Plane Elasticity in term of displacement
- Plane Elasticity in terms of stresses
Subject 10: Bending in beams
- Kinematic hypotheses
- Normal stresses in beams
- Neutral axis
Subject 11: Torsion
- Kinematic hypotheses
- Displacement formulation
- Stress formulation
- Circular cross sections
CHAPTER 5. DEFLECTIONS OF BEAMS (Nºof sessions: 3)
Subject 12: Deflections of beams (I)
- Equilibrium equations of beams
- Internal forces and moments equations
- Deflections by integration of the internal forces- and moment-equations (Navier-Bresse equations)
Subject 13: Deflections of beams (II)
- Moment-area method(Mohr¿s theorems)
- Differential equation of the deflection curve (Euler and Timoshenko beams)
- Kinematic definitions
- Static definitions
- Introduction to the displacement (or stiffness) method