| Matrix or Vector | Base Element | Shape Functions (for each layer) | Integration Points |
|---|---|---|---|
| Stiffness and Stress Stiffness Matrices and Thermal Load Vector | Linear 3D solid or shell | Equation 11–70, Equation 11–71, and Equation 11–72 |
In-plane: 1 x 1 |
| Quadratic 3D solid or shell | Equation 11–82, Equation 11–83, and Equation 11–84 |
In-plane: 2 x 2 | |
| Mass Matrix | Same as stiffness matrix | Same as stiffness matrix | |
| Pressure Load Vector | N/A | N/A | |
| Load Type | Distribution |
|---|---|
| Element Temperature | Bilinear in plane of each reinforcing layer, constant through-the-thickness of each layer. |
| Nodal Temperature | N/A |
| Pressure | N/A |
| Matrix or Vector | Base Element | Shape Functions (for each layer) | Integration Points |
|---|---|---|---|
| Conductivity Matrix and Heat Generation Load Vector | Linear 3D solid | Equation 11–77 |
In-plane: 2 x 2 Through-the-thickness: 1 |
| Quadratic 3D solid | Equation 11–86 |
In-plane: 3 x 3 Through-the-thickness: 1 | |
| Specific Heat Matrix | Same as conduction matrix | ||
| Load Type | Distribution |
|---|---|
| Element HGEN | Bilinear in plane of each reinforcing layer, constant through-the-thickness of each layer. |
Structures describes the derivation of element matrices and load vectors as well as stress evaluations. General Element Formulations gives the general structural element formulations used by this element. Similar formulations can be derived for thermal analysis.
Each layer of reinforcing fibers is simplified as a membrane with unidirectional stiffness. The equivalent membrane thickness h is given by:
 | (13–383) |
where:
| A = cross-section area of each fiber (input on SECDATA command) |
| S = distance between two adjacent fibers (input on SECDATA command) |
We assume that the reinforcing fibers are firmly attached to the base element (that is, no relative movement between the base element and the fibers is allowed). Therefore, the degrees of freedom (DOF) of internal layer nodes (II, JJ, KK, LL, etc.) can be expressed in terms of DOFs of the external element nodes (I, J, K, L, etc.). Taking a linear 3D solid base element as the example, the DOFs of an internal layer node II can be shown as:
 | (13–384) |
where:
| {uII, vII, wII} = displacements of internal layer node II |
| {ui, vi, wi} = displacements of base element node i |
| Ni (ξII, ηII, ζII) = value of trilinear shape function of node i at the location of internal node II |
Similar relationships can be established for other type of base elements. The stiffness and mass matrices of each reinforcing layer are first evaluated with respect to internal layer DOFs. The equivalent stiffness and mass contributions of this layer to the element is then determined through relationship (Equation 13–384).