Thermal and uncoupled thermo-mechanicalapplications

c©ZACE Services Ltd

25.08.2009

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Notation

T temperature, [oK ]t time, [day ]λ heat conductivity, [kN/(oK · day)]c∗ = cρ heat capacity, [kN/(m2 ·o K )]c specific heat, [kN ·m/(kg ·o K )]ρ mass density, [kg/m3]q external heat flux, [kN/(m · day)]Te ambient temperature, [oK ]h heat convection coefficient, [kN/(m ·o K · day)]H heat source [kN/m2]

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Problem of heat transfer

Fourier equation (transient case):

(λ T ,i ),i +∂H

∂t= c∗

∂T

∂ton Ω

Boundary conditions:

Temperature BC, with prescribed temperature T :T = T on ΓT

Heat flow BC, with prescribed heat flux q:λ∂T

∂n = −q on Γq

Convective BC, with prescribed ambient temperature Te :λ∂T

∂n = −h(T − Te) on Γc

Note: (Γq ∪ Γc) ∪ ΓT = Γ; but (Γq ∪ Γc) ∩ ΓT = ∅

Initial condition:Known temperature field T0 at time t = 0:T (x,0) = T0(x) on Ω

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Source term (designed for ”young” concrete)

Heat source as a function of maturity M

H(t,T ) = H∞aM

1 + aM

Maturity M as a function of absolute temperature and time

M(t,T ) =

t∫td

exp

[Q

R

(1

Tf− 1

T

)]dt

where:H∞ total value of concrete hydration heat per unit volume [kJ/m3],a heat source parameter [1/day ]Q/R activation energy/universal gas constant [oK ]Tf reference temperature, normally 20oC=293oK [oK ]td dormant period [day ]

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Solving heat transfer problems: Preselection menu.

Heat mode can be set inthe preselection dialog juston start or by invoking itfrom menu Control/Projectpreselection

Heat mode can be modifiedin the Analysis & Driversdialog invoked from mainmenu Control/Analysis &Drivers

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Obligatory and optional components of the model.

1 Obligatory components:Geometrical model (mesh)Boundary conditions (imposed temp./flux/convection)Driver(s)Material definition (properties)

2 Optional components:

Load time functions video

to handle evolution of imposed temperatures ambienttemperature but also material properties in time

Existence functions video

(associated with elements/boundary conditions) to handleexcavation/stage construction or

Initial conditions video

to set initial temperature field in explicit manner

Data super-elements video

to handle spatial variation of the data e.g. λ coefficient

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Drivers

1 Drivers give an instruction to the program what is to becomputed and in which order

2 By default the Initial State driver is set up as the first andthe only one in the list for execution(it is equivalent to the steady state run at time t = 0)

3 Available drivers:

Initial stateTime Dependent Steady stateTime Dependent Transient

NB. Time Dependent/Transient driver activates integration intime hence time stepping plays an important role

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Structure types/Material formulations

NB. Only Continuum or Continuum for structures is allowedbut then all available constitutive models can be applied for heattransfer analysis

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Heat Open data group

A

B

C

NB. Solid and fluid thermal dilatancy have no meaning for heattransfer analyses

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Initial conditions for transient case

1 Definition 1:

2 Definition 2:

Next slide

Defined through preliminary Steady stateanalysis (Initial state=Steady state att=0)

NB. Parameters describing Initial state driver(steady state in this case) have no meaning

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Initial conditions for transient case

1 Definition 1:

2 Definition 2:

Next slide

Analysis starts directly from Transientdriver

Initial pressures must be defined in the preproces-sor using FE model/Initial conditions/Initialtemperature option (same as Initial pressure)

video

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Thermo-mechanical analysis

1 Solve transient heat problem first to obtain T (x, t)2 Solve single-phase or two-phase problem with imposed strainsεo(t)

σ = σo + De (εe − εo − εCR)εo = α (T (tN+1)− T (t0)) 1

Remarks

Meshes for thermal and mechanical analyzes can be different

All items meaningful for mechanical analysis but not for thethermal one may appear in the thermal model (and vice versa)

Time stepping can be different for thermal and mechanicalanalysis (usually time steps for mechanical analysis are larger)

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Sequence of analyzes

Heat transfer project

Mechanical analysiswith nonstationary temperature field

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Example: Tunnel lining subject to heating

5.65

0.47.80.91.0 2.0

12.1

0.4

2.6

6.0

53.9

512.6

ROAD

T3 (t)

T2 (t)

AMBIENTTEMPERATURE Ta= 20 C

T1 (t)

MAT-1MAT-1

MAT-4FILLMAT-3

MAT-2

A BC D

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Building the model for both thermal and mechanicalanalysis

1 Edit load time function video

2 Edit materials video

3 Create skeleton model video

4 Create macro-model video

5 Create mesh video

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Customizing the model for thermal analysis

File: tunnelheat.inp

Set drivers video

Results video

Temperature distribution at t=20hc©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Customizing the model for mechanical analysis with aidof continuum elements

File: tunnelmech.inp

Drivers video

Results video

Recovered bending moment in lining at t=20h

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Customizing the model for mechanical analysis (beamelements are used for lining)

To handle spatial distribution of the temperature field thelayered beam model must be used (button Nonlinearmust be switched ON in material definition for the beam

Beam offset option must be used to shift the centroid of thebeam with respect to the master nodes (offset option)

The aim of setting the offset is to position properly the crosssection of the beam with respect to the cross section designedby the continuum elements used in thermal project

`

h

Lining zone in the thermalproject (continuum elements)

Lining zone in the mechanicalproject (beam elements (layered))must coincide with the excavation

contour

Beam centroids

h/2 (offset)

c©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications

Customizing the model for mechanical analysis (beamelements are used for lining)

Add new material for lining (beam) video

Results video

Bending moment in lining at t=20hc©ZACE Services Ltd Thermal and uncoupled thermo-mechanical applications