# Integration in diffusive heat transfer elements In all of the first-order elements (2-node links, 3-node triangles, 4-node quadrilaterals, 4-node tetrahedra, 6-node triangular prisms, and 8-node bricks) the internal energy storage term (associated with specific heat and latent heat storage) is integrated at the nodes. This integration scheme gives a diagonal internal energy matrix and improves the accuracy for problems with latent heat effects. Conduction contributions in these elements and all contributions in second-order elements use conventional Gauss schemes. Second-order elements are preferable for smooth problems without latent heat effects. The one-dimensional element cannot be used in a mass diffusion analysis. # Forced convection heat transfer elements These elements are available with linear interpolation only. They use an “upwinding” (Petrov-Galerkin) method to provide accurate solutions for convection-dominated problems (see “Convection/diffusion,” Section 2.11.3 of the Abaqus Theory Guide). Consequently, the internal energy (associated with specific heat storage) is not integrated at the nodes, which yields a consistent internal energy matrix and may cause oscillatory temperatures if strong temperature gradients occur along boundaries that are parallel to the flow direction. # Electromagnetic elements These elements are available with linear edge-based interpolation only. The user-defined nodes define the geometry of the element but do not directly participate in the interpolation of the electromagnetic or, in the case of a magnetostatic analysis, the magnetic fields. However, temperature and predefined field variables are defined at the user-defined nodes and are interpolated to the integration points for evaluating material properties that are temperature and predefined field variable dependent. # Using element types C3D6 and C3D6T in Abaqus/Explicit analyses When element types C3D6 and C3D6T are used in Abaqus/Explicit analyses, they appear in the output database (.odb) file as C3D6R and C3D6RT, respectively. In the data (.dat) file, C3D6 is referred to as C3D6R. You cannot specify C3D6R or C3D6RT as an element type for input. # 28.1.2 ONE-DIMENSIONAL SOLID (LINK) ELEMENT LIBRARY Products: Abaqus/Standard Abaqus/CAE # References • “Solid (continuum) elements,” Section 28.1.1 • \*SOLID SECTION # Overview This section provides a reference to the one-dimensional solid (link) elements available in Abaqus/Standard. For structural link (truss) elements, refer to “Truss elements,” Section 29.2.1. # Element types # Diffusive heat transfer elements

DC1D2	2-node link
DC1D3	3-node link

Active degree of freedom 11 Additional solution variables None. # Forced convection heat transfer elements

DCC1D2	2-node link
DCC1D2D	2-node link with dispersion control

Active degree of freedom 11 Additional solution variables None. # Coupled thermal-electrical elements

DC1D2E	2-node link
DC1D3E	3-node link

Active degrees of freedom 9, 11 Additional solution variables None. Acoustic elements

AC1D2	2-node link
AC1D3	3-node link

Active degree of freedom 8 Additional solution variables None. Nodal coordinates required

X, Y, Z

Element property definition You must provide the cross-sectional area of the element; by default, unit area is assumed. Input File Usage: \*SOLID SECTION Abaqus/CAE Usage: Property module: Create Section: select Beam as the section Category and Truss as the section Type Element-based loading Distributed heat fluxes Distributed heat fluxes are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

Load ID(*DFLUX)	Abaqus/CAELoad/Interaction	Units	Description
BF	Body heat flux	$JL^{-3} \ T^{-1}$	Heat body flux per unit volume.
BFNU	Body heat flux	$JL^{-3} \ T^{-1}$	Nonuniform heat body flux per unit volume with magnitude supplied via user subroutine DFLUX.
S1	Surface heat flux	$JL^{-2} \ T^{-1}$	Heat surface flux per unit area into the first end of the link (node 1).

Load ID(*DFLUX)	Abaqus/CAELoad/Interaction	Units	Description
S2	Surface heat flux	$JL^{-2}$ $T^{-1}$	Heat surface flux per unit area into the second end of the link (node 2 or node 3).
S1NU	Not supported	$JL^{-2}$ $T^{-1}$	Nonuniform heat surface flux per unit area into the first end of the link (node 1) with magnitude supplied via user subroutine DFLUX.
S2NU	Not supported	$JL^{-2}$ $T^{-1}$	Nonuniform heat surface flux per unit area into the second end of the link (node 2 or node 3) with magnitude supplied via user subroutine DFLUX.

# Film conditions Film conditions are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

Load ID (*FILM)	Abaqus/CAE Load/Interaction	Units	Description
F1	Not supported	$JL^{-2}T^{-1}\theta^{-1}$	Film coefficient and sink temperature (units of $\theta$ ) at the first end of the link (node 1).
F2	Not supported	$JL^{-2}T^{-1}\theta^{-1}$	Film coefficient and sink temperature (units of $\theta$ ) at the second end of the link (node 2 or node 3).
F1NU	Not supported	$JL^{-2}T^{-1}\theta^{-1}$	Nonuniform film coefficient and sink temperature (units of $\theta$ ) at the first end of the link (node 1) with magnitude supplied via user subroutine FILM.
F2NU	Not supported	$JL^{-2}T^{-1}\theta^{-1}$	Nonuniform film coefficient and sink temperature (units of $\theta$ ) at the second end of the link (node 2 or node 3) with magnitude supplied via user subroutine FILM.

# Radiation types Radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

Load ID(*RADIATE)	Abaqus/CAELoad/Interaction	Units	Description
R1	Surface radiation	Dimensionless	Emissivity and sink temperature (units of θ) at the first end of the link (node 1).
R2	Surface radiation	Dimensionless	Emissivity and sink temperature (units of θ) at the second end of the link (node 2 or node 3).

# Distributed impedances Distributed impedances are available for elements with acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” Section 34.4.6.

Load ID(*IMPEDANCE)	Abaqus/CAE Load/Interaction	Units	Description
I1	Not supported	None	Name of the impedance property that defines the impedance at the first end of the link (node 1).
I2	Not supported	None	Name of the impedance property that defines the impedance at the second end of the link (node 2 or node 3).

# Distributed electric current densities Distributed electric current densities are available for coupled thermal-electrical elements. They are specified as described in “Coupled thermal-electrical analysis,” Section 6.7.3.

Load ID(*DECURRENT)	Abaqus/CAELoad/Interaction	Units	Description
CBF	Body current	$CL^{-3}T^{-1}$	Volumetric current source density.
CS1	Surface current	$CL^{-2}T^{-1}$	Current density at the first end of the link (node 1).
CS2	Surface current	$CL^{-2}T^{-1}$	Current density at the second end of the link (node 2 or node 3).

# Element output # Heat flux components Available for elements with temperature degrees of freedom. HFL1 Heat flux along the element axis. # Electrical potential gradient Available for coupled thermal-electrical elements. EPG1 Electrical potential gradient along the element axis. # Electrical current density components Available for coupled thermal-electrical elements. ECD1 Electrical current density along the element axis. # Node ordering and face numbering on elements 

text_image

1 end 1 2 end 2

2 - node element 

flowchart

```mermaid graph TD A["1"] --> B["2"] B --> C["3"] A -->|end 1| B C -->|end 2| B ```

3 - node element # Numbering of integration points for output 

text_image

1 + 1 2

2 - node element 

flowchart

```mermaid graph TD 1["1"] -->|×| 1 1 -->|×| 2["2"] 2 -->|×| 2 2 -->|×| 3["3"] ```

3 - node element # 28.1.3 TWO-DIMENSIONAL SOLID ELEMENT LIBRARY Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE # References • “Solid (continuum) elements,” Section 28.1.1 • \*SOLID SECTION # Overview This section provides a reference to the two-dimensional solid elements available in Abaqus/Standard and Abaqus/Explicit. # Element types Plane strain elements

CPE3	3-node linear
CPE3H(S)	3-node linear, hybrid with constant pressure
CPE4(S)	4-node bilinear
CPE4H(S)	4-node bilinear, hybrid with constant pressure
CPE4I(S)	4-node bilinear, incompatible modes
CPE4IH(S)	4-node bilinear, incompatible modes, hybrid with linear pressure
CPE4R	4-node bilinear, reduced integration with hourglass control
CPE4RH(S)	4-node bilinear, reduced integration with hourglass control, hybrid with constant pressure
CPE6(S)	6-node quadratic
CPE6H(S)	6-node quadratic, hybrid with linear pressure
CPE6M	6-node modified, with hourglass control
CPE6MH(S)	6-node modified, with hourglass control, hybrid with linear pressure
CPE8(S)	8-node biquadratic
CPE8H(S)	8-node biquadratic, hybrid with linear pressure
CPE8R(S)	8-node biquadratic, reduced integration
CPE8RH(S)	8-node biquadratic, reduced integration, hybrid with linear pressure

Active degrees of freedom 1, 2 Additional solution variables The constant pressure hybrid elements have one additional variable relating to pressure, and the linear pressure hybrid elements have three additional variables relating to pressure. Element types CPE4I and CPE4IH have five additional variables relating to the incompatible modes. Element types CPE6M and CPE6MH have two additional displacement variables. Plane stress elements

CPS3	3-node linear
CPS4(S)	4-node bilinear
CPS4I(S)	4-node bilinear, incompatible modes
CPS4R	4-node bilinear, reduced integration with hourglass control
CPS6(S)	6-node quadratic
CPS6M	6-node modified, with hourglass control
CPS8(S)	8-node biquadratic
CPS8R(S)	8-node biquadratic, reduced integration

Active degrees of freedom 1, 2 Additional solution variables Element type CPS4I has four additional variables relating to the incompatible modes. Element type CPS6M has two additional displacement variables. Generalized plane strain elements

CPEG3(S)	3-node linear triangle
CPEG3H(S)	3-node linear triangle, hybrid with constant pressure
CPEG4(S)	4-node bilinear quadrilateral
CPEG4H(S)	4-node bilinear quadrilateral, hybrid with constant pressure
CPEG4I(S)	4-node bilinear quadrilateral, incompatible modes
CPEG4IH(S)	4-node bilinear quadrilateral, incompatible modes, hybrid with linear pressure
CPEG4R(S)	4-node bilinear quadrilateral, reduced integration with hourglass control
CPEG4RH(S)	4-node bilinear quadrilateral, reduced integration with hourglass control, hybrid with constant pressure