Thermo-mechanics

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					Thermo-mechanics

J. Cugnoni, LMAF / EPFL 2009
Three kind of « thermo-mechanics »
1.    Un-coupled: Known temperature field => mechanical
      model (linear statics + th. expansion)
       u   el   th ;  th   T ;   C  el  C (u  T )
       (C (u  T ))  f  0
2.    One way coupling: solve thermal problem =>
      temperature field => solve mechanical problem
             T
         cp       ( T )  s    (C (u  T ))  f  0
             t
3.    Fully coupled: solve at the same time temperature &
      displacement field (includes mechanical dissipation)
                           T
                    c p          ( T )  s  0
                           t
                      (C (u  T ))  f  0
                   
Thermal problem
   Variables
       Essential variable: Temperature field T              q
       Natural variable: heat flux q

   Material                                        Text
       Conductivity 
       Density  & specific heat cp if transient
                                                           T, , , cp, s
   Boundary conditions:
       Temperature: Tsurf = f(t) if transient
       Surface heat fluxes:
            Imposed heat flux qsurf=f(t)
            Convection: qsurf = h (T –Text(t))
       Volume heat source: s = f(t)
Thermal problem in Abaqus
   Select Step = Heat transfer
       Choose steady state or transient
       If transient: set time period, set small initial increment, set max
        T per increment (<1/10 of max T)
   In Mesh:
       select element type: Heat transfer, linear
   Loading:
       Need to impose at least one temp. (rigid body)
       Adiabatic interface: leave free = no flux!
       Flux = load, Temperature = BC
       Convection: in interaction module, create Surface Film condition,
        enter h and Text
       If transient: define an amplitude curve (tool => amplitude), need
        to start at zero for t=0,
Coupled Thermo mechanics in Abaqus

   Select Step = Coupled Temp-Displacement
       Choose steady state or transient
       If transient: set time period, set small initial increment, set max
        T per increment (<1/10 of max T)
   In Mesh:
       select element type: Coupled Temp.-Displacement, quadratic
   Loading:
       Need to impose at least one temp. & block 6 rigid body motions
       Adiabatic interface: leave free = no flux!
       Flux = load, Temperature = BC
       Convection: in interaction module, create Surface Film condition,
        enter h and Text
       If transient: define an amplitude curve (tool => amplitude), need
        to start at zero for t=0
Démos
   Bi-material beam: Thermal switch
     Coupled  Thermo-mechanical problem
     Transient analysis
     Heat transfer & expansion properties
     Heat transfer BC:
          Temperature
          Convection
          Heat Flux
          Time dependent boundary conditions
Demo: thermal switch
   Block: clamped, T= 0°C



                                                         Beam dimensions 60 x 5 x 1 mm

                                                                                       Invar, 0.5 mm




                            Water

Prop.                         Steel         Invar                                      Steel, 0.5 mm
Young’s                       210 GPa       141 GPa
modulus                                                           T water = f(time)
Poisson ratio                 0.3           0.3                                       T=100°C
Th. Expansion                 1e-5          1e-6

Density                       7800 kg/m3    8000 kg/m3

Conductivity                  30 W/m/K      10 W/m/K

Specific heat                 1000 J/kg/K   500 J/kg/K
                                                          T=0°C
                                                                          1           Time (s)         60

				
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posted:10/13/2011
language:English
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