Lezione 7 di Costruzione di macchine

Solidi Assialsimmetrici

• Basic hypotheses: full axisymmetry:
  • Geometrical
  • Loads
  • Material (it has to be also linear elastic)
• State of stress:
  • Plane stress (disks)
  • Plane strain (tubes)
• Coordinate system: cylindrical
  • z axial coordinate
  • r radial coordinate
  • θ circumferential coordinate
• Reference system
  • z axial direction
  • r radial direction
  • c circumferential direction

• If the axisymmetric hypotheses hold, the state of stress only depends on the radial coordinate:
• σ(r, θ, z) = σ(r)
• The state of stress is triaxial
  • Radial stress σ_r = σ_r(r)
  • Circumferential stress σ_c = σ_c(r)
  • Axial stress σ_z = σ_z(r)
• Radial σ_r and circumferential σ_c stresses are independent of end constraints
• Axial stress σ_z depends on end constraints

SOLIDI ASSIALSIMMETRICI

• Basic hypotheses: full axisymmetry: conversioni generali
  • Geometrical
  • Loads
  • Material (it has to be also linear elastic)
• State of stress:
  • Plane stress (disks)
  • Plane strain (tubes)
• Coordinate system: cylindrical
  • z axial coordinate
  • r radial coordinate
  • θ circumferential coordinate
• Reference system sse del pezzo
  • z axial direction
  • r radial direction
  • c circumferential direction

traduco lo sforzo in una direzione (tensione piana)

uso 1 riga uno 1 colonna

• If the axisymmetric hypotheses hold, the state of stress only depends on the radial coordinate:

σ(r, θ, z) = σ(r)

• The state of stress is triaxial non più 1D!
  • Radial stress σ_r = σ(r) → radiale
  • Circumferential stress σ_c = σ(r) → tangenziale
  • Axial stress σ_z = σ(r) → assiale
• Radial σ_r and circumferential σ_c stresses are independent of end constraints vincoli
• Axial stress σ_z depends on end constraints

3 classificazioni

• Tubes:

• Axially much more extended: L >> D
• Thick tube: t / r_i > 0.1 (Lamé)
• Thin tube: t / r_i ≤ 0.1 (Boyle-Mariotte)

• Discs:

• Axially thin: L