Axisymmetric-Harmonic 4-Node Thermal Solid

Compatible Products: – | – | – | Enterprise | Ent PP | Ent Solver | –

PLANE75 Element Description

PLANE75 is used as an axisymmetric ring element with a 3-D 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 Harmonic Axisymmetric Elements with Nonaxisymmetric Loads.

The element is applicable to an axisymmetric geometry for steady-state or transient thermal analyses. See PLANE75 in the Mechanical APDL 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 midside node capability is PLANE78.

Figure 75.1:  PLANE75 Geometry

PLANE75 Geometry

PLANE75 Input Data

The geometry, node locations, and the coordinate system for this axisymmetric thermal solid element are shown in Figure 75.1: PLANE75 Geometry. The data input is essentially the same as for PLANE55 and is described in "PLANE55 Input Data". 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 similarly to the axisymmetric case of PLANE55. The MODE and ISYM parameters describe the type of temperature distribution and are discussed in detail in Harmonic Axisymmetric Elements with Nonaxisymmetric Loads.

Element loads are described in Nodal Loading. Harmonically varying bulk temperatures or heat fluxes (but not both) may be input as surface loads on the element faces as shown by the circled numbers on Figure 75.1: PLANE75 Geometry. 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 "PLANE75 Input Summary". A general description of element input is given in Element Input.

PLANE75 Input Summary


I, J, K, L

Degrees of Freedom


Real Constants


Material Properties

MP command: 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

Number of harmonic waves around the circumference (MODE)

Loading Condition

Symmetry condition (MODE)

Special Features

Birth and death



PLANE75 Output Data

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

Convection heat flux is positive out of the element; applied heat flux is positive into the element. 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 Harmonic Axisymmetric Elements with Nonaxisymmetric Loads. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 75.1:  PLANE75 Element Output Definitions

ELElement numberYY
NODESNodes - I, J, K, LYY
MATMaterial numberYY
XC, YCLocation where results are reportedY3
HGENHeat generations HG(I), HG(J), HG(K), HG(L)Y-
MODENumber of waves in loadingY-
TG:X, Y, SUM, ZThermal gradient components and vector sum (X and Y) at centroid11
TF:X, Y, SUM, ZThermal flux (heat flow rate/cross-sectional area) components and vector sum (X and Y) at centroid11
FACEFace label2-
NODESFace nodes2-
AREAFace area22
TAVG, TBULKAverage of the two end nodal temperatures evaluated at peak value, fluid bulk temperature evaluated at peak value22
HEAT RATEHeat flow rate across face by convection22
HEAT RATE/AREAHeat flow rate per unit area across face by convection2-
HFAVGAverage film coefficient of the face-2
TBAVGAverage face bulk temperature-2
HFLXAVGHeat flow rate per unit area across face caused by input heat flux-2
HFLUXHeat flux at each node of face2-

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

  2. Output if a surface load is input

  3. Available only at centroid as a *GET item.

Table 75.2: PLANE75 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 75.2: PLANE75 Item and Sequence Numbers:


output quantity as defined in the Table 75.1: PLANE75 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for solution items for element Face n

Table 75.2:  PLANE75 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

PLANE75 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 75.1: PLANE75 Geometry 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 Degenerated Shape Elements.

  • 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 (that is, 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.

PLANE75 Product Restrictions

There are no product-specific restrictions for this element.

Release 18.2 - © ANSYS, Inc. All rights reserved.