Code_Aster ®
Version
7.4
Titrate:
Modelings AXIS, PLAN, AXIS_DIAG and PLAN_DIAG

Date:
01/06/05
Author (S):
C. DURAND, F. LEBOUVIER Key
:
U3.23.01-E Page
: 1/4

Organization (S): EDF-R & D/AMA, DeltaCAD
Handbook of Utilization
U3.23 booklet: Thermal finite elements 2D
Document: U3.23.01

Modelings AXIS, PLAN, AXIS_DIAG
and PLAN_DIAG

Summary:

This document describes for modelings of thermics of the axisymmetric and plane elements:

· degrees of freedom carried by the finite elements which support modeling,
· the related meshs supports,
· supported materials and loadings,
· nonlinear possibilities,
· case-tests implementing modelings.

Axisymmetric and plane modelings (Phénomène: THERMIQUE) correspond to finite elements
whose meshs supports are surface.

Modelings AXIS_DIAG and PLAN_DIAG cover the same possibilities as AXIS and PLAN and in
differ that for a calculation from thermics where the thermal matrix of mass is then diagonalisée.
Handbook of Utilization
U3.23 booklet: Thermal finite elements 2D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings AXIS, PLAN, AXIS_DIAG and PLAN_DIAG

Date:
01/06/05
Author (S):
C. DURAND, F. LEBOUVIER Key
:
U3.23.01-E Page
: 2/4

1 Discretization

1.1
Degrees of freedom

Modeling
Degrees of freedom
(with each node node)

AXIS, AXIS_DIAG, PLAN,
TEMP: corresponds to the temperature
PLAN_DIAG

1.2
Net support of the matrices of rigidity

The meshs support of the finite elements can be triangles or quadrilaterals. The elements are
isoparametric.

Modeling Nets
Interpolation
Remarks

AXIS (_DIAG) - PLANE (_DIAG)
TRIA3
Linear
AXIS (_DIAG) - PLANE (_DIAG)
QUAD4
Linear
AXIS (_DIAG) - PLANE (_DIAG)
TRIA6
Quadratic
AXIS - PLAN
QUAD8
Serendip
AXIS (_DIAG) - PLANE (_DIAG)
QUAD9
Quadratic

1.3
Net support of the loadings

Modeling Nets
Interpolation
Remarks

AXIS (_DIAG) - PLANE (_DIAG)
SEG2
Linear
AXIS (_DIAG) - PLANE (_DIAG)
SEG3
Quadratic

2 Loadings
supported

The loadings available are as follows:

· SOURCE
Allows to apply voluminal sources to a field 2D.
Supported modelings: AXIS (_DIAG), PLAN (_DIAG)

· FLUX_REP
Allows to apply normal flows to sides of elements 2D.
Supported modelings: AXIS (_DIAG), PLAN (_DIAG)

· ECHANGE
Allows to apply conditions of exchange with an outside temperature at sides
elements 2D.
Supported modelings: AXIS (_DIAG), PLAN (_DIAG)

· ECHANGE_PAROI
Allows to apply conditions of exchange between two walls.
Supported modelings: AXIS (_DIAG), PLAN (_DIAG)
Handbook of Utilization
U3.23 booklet: Thermal finite elements 2D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings AXIS, PLAN, AXIS_DIAG and PLAN_DIAG

Date:
01/06/05
Author (S):
C. DURAND, F. LEBOUVIER Key
:
U3.23.01-E Page
: 3/4

· GRAD_TEMP_EPSI
Allows to apply a presumedly uniform variation in temperature “initial” in the element.
Supported modelings: AXIS (_DIAG), PLAN (_DIAG)

· CONVECTION
Allows to take into account the terms of transport of heat by convection, for
THER_NON_LINE_MO only.
Supported modelings: AXIS, PLAN

· RAYONNEMENT
Allows to take into account ad infinitum radiated flow.
Supported modelings: AXIS (_DIAG), PLAN (_DIAG)

3 Possibilities
non-linear

Two operators are available for the study of non-linear behaviors:

· THER_NON_LINE [U4.54.02]: this operator allows, in hover or in transient, of
to solve the problems of:
­ Thermique non-linear standard: material depend on the temperature, conditions with
limits (radiation and nonlinear imposed flow),
­ Non-linear Thermique with calculation of the hydration of the concrete,
­ Séchage of the concrete.
· THER_NON_LINE_MO [U4.54.03]: this operator allows to solve the equation of heat
stationary in a mobile reference frame related to a loading and moving in a direction
and at a given speed.

4
Examples of implementation: case-tests

4.1 Thermics

· AXIS
­ Stationary linear Thermique
TPLA07A [V4.01.007]: Analyze thermal of an orthotropic hollow roll subjected to different
boundary conditions (imposed flow, convection, linear variation of the temperatures
external).
­ Stationary non-linear Thermique
TPNA01A [V4.41.001]: Analyze thermal of a hollow roll subjected to a convectif exchange
on the interior wall and with a radiation ad infinitum on the external wall.
­ Thermique linear transient
TTLV01B [V4.25.001]: Analyze thermal linear transient of a full sphere subjected to
a heat transfer by convection.
­ Thermique non-linear transient
TTNA200A: case-test of not-regression
· PLAN
­ Stationary linear Thermique
TPLL100B [V4.02.100]: Analyze thermal of an anisotropic plane wall subjected to one
temperature imposed and on a flow.
­ Stationary non-linear Thermique
TPNL300A [V4.42.300]: Analyze thermal unidimensional of a wall subjected to one
temperature imposed on the internal wall and on an exchange by radiation on the wall
external (Test NAFEMS).
Handbook of Utilization
U3.23 booklet: Thermal finite elements 2D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings AXIS, PLAN, AXIS_DIAG and PLAN_DIAG

Date:
01/06/05
Author (S):
C. DURAND, F. LEBOUVIER Key
:
U3.23.01-E Page
: 4/4

­ Thermique linear transient
TTLP100B [V4.23.100]: Calculate linear transitory thermal response of two plates
separated by a play in which a transfer of heat between the walls is carried out.
­ Thermique non-linear transient
TTNL02A [V4.22.002]: Simulation of a liquid/solid phase shift while introducing
via the voluminal enthalpy latent heat of fusion.
­ Nonlinear stationary Thermique with mobile loading
TPLV102A [V4.04.102]: Transport of heat by convection and conduction in one
square cavity.
· AXIS_DIAG
­ Thermique linear transient
TTLV100A [V4.25.100]: Analyze thermal linear transient of a presumedly infinite pipe in
which one imposes a cold thermal shock using a limiting condition of exchange.
· PLAN_DIAG
­ Thermique linear transient
TTLL100A [V4.21.100]: Analyze thermal linear transient of an infinite plane wall to which one
impose a cold thermal shock using a limiting condition of exchange.
­ Thermique non-linear transient
TTNL02C [V4.22.002]: Simulation of a liquid/solid phase shift while introducing
via the voluminal enthalpy latent heat of fusion.

4.2 Hydration

· AXIS
TTNL03B [V4.22.003]: simulation of an adiabatic test: analyze behavior
thermo hydrating of freshly-mixed a concrete sample plunged in a calorimeter, the catch being carried out
with release of heat.

4.3 Drying

· AXIS
HSNA102A [V7.20.102]: Validation of the calculation of the drying of the concrete, it acts of a case test
axisymmetric where the water concentration is applied directly to the external wall.

· AXIS_DIAG
HSNA102D [V7.20.102]: Validation of the calculation of the drying of the concrete, it acts of a case test
axisymmetric where the water concentration is applied directly to the external wall.

Handbook of Utilization
U3.23 booklet: Thermal finite elements 2D
HT-66/05/004/A

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