3-D 10-Node
Tetrahedral Thermal Solid
SOLID87 Element Description
SOLID87 is well suited to model irregular meshes (such as produced from various CAD/CAM systems). The element has one degree of freedom, temperature, at each node.
The element is applicable to a 3-D, steady-state or transient thermal analysis. See SOLID87 in the Mechanical APDL Theory Reference for more details about this element. If the model containing this element is also to be analyzed structurally, the element should be replaced by the equivalent structural element (such as SOLID187). A 20-node thermal solid element, SOLID90, is also available.
SOLID87 Input Data
The geometry, node locations, and the coordinate system for this element are shown in Figure 87.1: SOLID87 Geometry.
Orthotropic material directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. Specific heat and density are ignored for steady-state solutions. Properties not input default as described in the Material Reference.
Element loads are described in Nodal Loading. Convection or heat flux (but not both) and radiation may be input as surface loads at the element faces as shown by the circled numbers on Figure 87.1: SOLID87 Geometry. 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). If all corner node heat generation rates are specified, each midside node heat generation rate defaults to the average heat generation rate of its adjacent corner nodes.
For phase change problems, use KEYOPT(1) = 1 (diagonalized specific heat matrix). For convection regions with strong thermal gradients, use KEYOPT(5) = 1 (consistent convection matrix).
A summary of the element input is given in "SOLID87 Input Summary". A general description of element input is given in Element Input.
SOLID87 Input Summary
- Nodes
I, J, K, L, M, N, O, P, Q, R
- Degrees of Freedom
TEMP
- Real Constants
None
- Material Properties
MP command: KXX, KYY, KZZ, DENS, C, ENTH
- Surface Loads
- Convection or Heat Flux (but not both) and Radiation (using Lab = RDSF) --
face 1 (J-I-K), face 2 (I-J-L), face 3 (J-K-L), face 4 (K-I-L)
- Body Loads
- Heat Generations --
HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P), HG(Q), HG(R)
- Special Features
- KEYOPT(1)
Specific heat matrix:
- 0 --
Consistent specific heat matrix
- 1 --
Diagonalized specific heat matrix
- KEYOPT(5)
Surface convection matrix:
- 0 --
Diagonalized convection matrix
- 1 --
Consistent convection matrix
SOLID87 Output Data
The solution output associated with the element is in two forms:
Nodal temperatures included in the overall nodal solution
Additional element output as shown in Table 87.1: SOLID87 Element Output Definitions.
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. 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 87.1: SOLID87 Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element Number | Y | Y |
| NODES | Nodes - I, J, K, L, M, N, O, P, Q, R | Y | Y |
| MAT | Material number | Y | Y |
| VOLU: | Volume | Y | Y |
| XC, YC, ZC | Location where results are reported | Y | 2 |
| HGEN | Heat generations HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P), HG(Q), HG(R) | Y | - |
| TG:X, Y, Z, SUM | Thermal gradient components and vector sum at centroid | Y | Y |
| TF:X, Y, Z, SUM | Thermal flux (heat flow rate/cross-sectional area) components and vector sum at centroid | Y | Y |
| FACE | Convection face label | 1 | - |
| NODES | Convection face corner nodes | 1 | - |
| AREA | Convection face area | 1 | 1 |
| HFILM | Film coefficient | 1 | - |
| TAVG | Average face temperature | 1 | 1 |
| TBULK | Fluid bulk temperature | 1 | - |
| HEAT RATE | Heat flow rate across face by convection | 1 | 1 |
| HEAT RATE/AREA | Heat flow rate per unit area across face by convection | 1 | - |
| HFAVG | Average film coefficient of the face | - | 1 |
| TBAVG | Average face bulk temperature | - | 1 |
| HFLXAVG | Heat flow rate per unit area across face caused by input heat flux | - | 1 |
| HFLUX | Heat flux at each node of face | 1 | - |
Available only at centroid as a *GET item.
Table 87.2: SOLID87 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See Creating an Element Table 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 87.2: SOLID87 Item and Sequence Numbers:
- Name
output quantity as defined in the Table 87.1: SOLID87 Element Output Definitions
- Item
predetermined Item label for ETABLE command
- FCn
sequence number for solution items for element Face n
SOLID87 Assumptions and Restrictions
The element must not have a zero volume.
Elements may be numbered either as shown in Figure 87.1: SOLID87 Geometry or may have node L below the IJK plane.
An edge with a removed midside node implies that the temperature varies linearly, rather than parabolically, along that edge.
See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for more information about the use of midside nodes.
The specific heat and enthalpy are evaluated at each integration point to allow for abrupt changes (such as melting) within a coarse grid of elements.
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.
SOLID87 Product Restrictions
When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.
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