4.75 PLANE75 Axisymmetric-Harmonic Thermal Solid

4.75 PLANE75 Axisymmetric-Harmonic Thermal Solid (UP19980821 ) PLANE75 is used as an axisymmetric ring element with a three-dimensional thermal conduction capability. The element has four nodes with a single degree of freedom, temperature, at each node. The element is a generalization of the axisymmetric version of PLANE55 in that it allows nonaxisymmetric loading. Various loading cases are described in Section 2.10.

The element is applicable to a two-dimensional, axisymmetric, steady-state or transient thermal analysis. See Section 14.75 of the ANSYS Theory Reference for more details about this element. If the model containing the element is also to be analyzed structurally, the element should be replaced by the equivalent structural element (such as PLANE25). A similar thermal element, with mid-side node capability (PLANE78), is described in Section 4.78.

Figure 4.75-1 PLANE75 Axisymmetric-Harmonic Thermal Solid



4.75.1 Input Data

The geometry, node locations, and the coordinate system for this axisymmetric thermal solid element are shown in Figure 4.75-1. The data input is essentially the same as for PLANE55 and is described in Section 4.55.1. The element input data also includes the number of harmonic waves (MODE) and the symmetry condition (ISYM) on the MODE command. If MODE=0 and ISYM=1, the element behaves similar to the axisymmetric case of PLANE55. The MODE and ISYM parameters describe the type of temperature distribution and are discussed in Section 2.10.

Element loads are described in Section 2.7. Harmonically varying convections or heat fluxes (but not both) may be input as surface loads on the element faces as shown by the circled numbers on Figure 4.75-1. Harmonically varying heat generation rates may be input as element body loads at the nodes. If the node I heat generation rate HG(I) is input and all others are unspecified, they default to HG(I).

A summary of the element input is given in Table 4.75-1. A general description of element input is given in Section 2.1.

Table 4.75-1 PLANE75 Input Summary

Element Name

PLANE75

Nodes

I, J, K, L

Degrees of Freedom

TEMP

Real Constants

None

Material Properties

KXX, KYY, KZZ, DENS, C, ENTH

Surface Loads

Convections:
face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)
Heat Fluxes:
face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)

Body Loads

Heat Generations: HG (I), HG (J), HG (K), HG (L)

Mode Number

Input mode number on MODE command

Loading Condition

Input for ISYM in MODE command
1 Symmetric loading
-1 Antisymmetric loading

Special Features

Stress stiffening (MODE,0 only), Birth and death

4.75.2 Output Data

The solution output associated with the element is in two forms:

Heat flowing out of the element is considered to be positive. The element output directions are parallel to the element coordinate system. The face area and the heat flow rate are on a full 360° basis. For more information about harmonic elements, see Section 2.9. A general description of solution output is given in Section 2.2. See the ANSYS Basic Analysis Procedures Guide for ways to view results.

The following notation is used in Table 4.75-2:

A colon (:) in the Name column indicates the item can be accessed by the Component Name method [ETABLE, ESOL] (see Section 2.2.2). The O and R columns indicate the availability of the items in the file Jobname.OUT (O) or in the results file (R), a Y indicates that the item is always available, a number refers to a table footnote which describes when the item is conditionally available, and a - indicates that the item is not available.

Table 4.75-2 PLANE75 Element Output Definitions

Name

Definition

O

R

EL

Element number

Y Y
NODES

Nodes - I, J, K, L

Y Y
MAT

Material number

Y Y
VOLU:

Volume

Y Y
CENT: X, Y

Center location XC, YC

- Y
HGEN

Heat generations HG(I), HG(J), HG(K), HG(L)

Y -
MODE

Number of waves in loading

Y -
TG: X, Y, SUM, Z

Thermal gradient components and vector sum (X and Y) at centroid

1 1
TF: X, Y, SUM, Z

Thermal flux (heat flow rate/cross-sectional area) components and vector sum (X and Y) at centroid

1 1
FACE

Face label

2 -
NODES

Face nodes

2 -
AREA

Face area

2 2
TAVG, TBULK

Average of the two end nodal temperatures evaluated at peak value, fluid bulk temperature evaluated at peak value

2 2
HEAT RATE

Heat flow rate across face by convection

2 2
HEAT RATE/AREA

Heat flow rate per unit area across face by convection

2 -
HFAVG

Average film coefficient of the face

- 2
TBAVG

Average face bulk temperature

- 2
HFLXAVG

Heat flow rate per unit area across face caused by input heat flux

- 2
HFLUX

Heat flux at each node of face

2 -
1. Gradient and flux peak at THETA = 0 and THETA =90MODE degrees

2. Output if a surface load is input

Table 4.75-3 lists output available through the ETABLE command using the Sequence Number method. See Chapter 5 of the ANSYS Basic Analysis Procedures Guide and Section 2.2.2.2 of this manual for more information. The following notation is used in Table 4.75-3:

Table 4.75-3 PLANE75 Item and Sequence Numbers for the ETABLE and ESOL Commands

Name

Item

FC1

FC2

FC3

FC4

AREA

NMISC

1 7 13 19
HFAVG

NMISC

2 8 14 20
TAVG

NMISC

3 9 15 21
TBAVG

NMISC

4 10 16 22
HEAT RATE

NMISC

5 11 17 23
HFLXAVG

NMISC

6 12 18 24

4.75.3 Assumptions and Restrictions

The element must not have a negative or a zero area. The element must lie in the global X-Y plane as shown in Figure 4.75-1 and the Y-axis must be the axis of symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.

A triangular element may be formed by defining duplicate K and L node numbers as described in Section 2.8. If the thermal element is to be replaced by the analogous structural element (PLANE25) with surface stresses requested, the thermal element should be oriented so that face I-J (and also face K-L, if applicable) is a free surface.

A free surface of the element (i.e., not adjacent to another element and not subjected to a boundary constraint) is assumed to be adiabatic. Thermal transients having a fine integration time step and a severe thermal gradient at the surface will also require a fine mesh at the surface.

Temperature dependent material properties (including the film coefficient) are assumed to be axisymmetric even if the temperature varies harmonically. If MODE=0, properties are evaluated at the temperatures calculated in the previous substep (or at TUNIF if for the first substep). If MODE>0, properties are evaluated at temperatures calculated from the previous MODE=0 substep; if no MODE=0 substep exists, then evaluation is done at 0.0 degrees.

4.75.4 Product Restrictions

There are no product restrictions for this element.