Figure 5: PlaneStress2d element. Node numbering, edge numbering and definition of local edge c.s.(a).
Represents isoparametric four-node quadrilateral plane-stress finite element. Each node has 2 degrees of freedom. Structure should be defined in x,y plane. The nodes should be numbered anti-clockwise (positive rotation around z-axis). The element features are summarized in Table 7.
| Keyword | planestress2d |
| Description | 2D quadrilateral element for plane stress analysis |
| Specific parameters | [NIP #(in)] |
| Parameters | NIP: allows to set the number of integration points |
| Unknowns | Two dofs (u-displacement, v-displacement) are required in each node. |
| Approximation | Linear approximation of displacements and geometry. |
| Integration | Integration of membrane strain terms using Gauss integration formula in 1, 4 (default), 9 or 16 integration points. The default number of integration points used can be overloaded using NIP parameter. Reduced integration for shear terms is employed. Shear terms are always integrated using the 1-point integration rule. |
| Features | Nonlocal constitutive support, Geometric nonlinearity support. |
| CS properties | cross section thickness is required. |
| Loads | Body loads are supported. Boundary loads are supported and computed using numerical integration. The side numbering is following. Each i-th element side begins in i-th element node and ends on next element node (i+1-th node or 1-st node, in the case of side number 4). The local positive edge x-axis coincides with side direction, the positive local edge y-axis is rotated 90 degrees anti-clockwise (see fig. (5)). |
| Nlgeo | 0, 1. |
| Status | Reliable |
Implementation of quadratic isoparametric eight-node quadrilateral plane-stress finite element. Each node has 2 degrees of freedom. The node numbering is anti-clockwise and is explained in fig. (6). The element features are summarized in Table 8.
| Keyword | qplanestress2d |
| Description | 2D quadratic isoparametric plane stress element |
| Specific parameters | [NIP #(in)] |
| Parameters | NIP: allows to set the number of integration points |
| Unknowns | Two dofs (u-displacement, v-displacement) are required in each node. |
| Approximation | Quadratic approximation of displacements and geometry. |
| Integration | Full integration using Gauss integration formula in 4 (the default), 9 or 16 integration points. The default number of integration points used can be overloaded using NIP parameter. |
| Features | Adaptivity support. |
| CS properties | Cross section thickness is required. |
| Loads | Body and boundary loads are supported. |
| Nlgeo | 0, 1. |
| Status | Stable |
Implements an triangular three-node constant strain plane-stress finite element. Each node has 2 degrees of freedom. The node numbering is anti-clockwise. The element features are summarized in Table 9.
| Keyword | trplanestress2d |
| Description | 2D linear triangular isoparametric plane stress element |
| Specific parameters | - |
| Unknowns | Two dofs (u-displacement, v-displacement) are required in each node. |
| Approximation | Linear approximation of displacements and geometry. |
| Integration | Integration of membrane strain terms using one point gauss integration formula. |
| Features | Nonlocal constitutive support, Edge load support, Geometric nonlinearity support, Adaptivity support. |
| CS properties | Cross section thickness is required. |
| Loads | Body loads are supported. Boundary loads are supported and are computed using numerical integration. The side numbering is following. Each i-th element side begins in i-th element node and ends on next element node (i+1-th node or 1-st node, in the case of side number 3). The local positive edge x-axis coincides with side direction, the positive local edge y-axis is rotated 90 degrees anti-clockwise (see fig. (7)). |
| Nlgeo | 0, 1. |
| Status | Reliable |
Implementation of quadratic six-node plane-stress finite element. Each node has 2 degrees of freedom. Node numbering is anti-clockwise and is shown in fig. (8). The element features are summarized in Table 10.
| Keyword | qtrplstr |
| Description | 2D quadratic triangular plane stress element |
| Specific parameters | [NIP #(in)] |
| Parameters | NIP: allows to set the number of integration points |
| Unknowns | Two dofs (u-displacement, v-displacement) are required in each node. |
| Approximation | Quadratic approximation of displacements and geometry. |
| Integration | Full integration using gauss integration formula in 4 points (the default) or in 7 points (using NIP parameter). |
| Features | Adaptivity support (error indicator). |
| CS properties | Cross section thickness is required. |
| Loads | Boundary loads are supported. |
| Nlgeo | 0, 1. |
| Status | - |
Implementation of triangular three-node plane-stress finite element with independent rotation field. Each node has 3 degrees of freedom. The element features are summarized in Table 11.
| Keyword | trplanestrrot |
| Description | 2D linear triangular plane stress element with rotational DOFs |
| Specific parameters | [NIP #(in)] [NIPRot #(in)] |
| Parameters | NIP: allows to set the number of integration points for integration of membrane terms. |
NIPRot: allows to set the number of integration points for integration of terms associated to rotational field. |
|
| Unknowns | Three dofs (u-displacement, v-displacement, z-rotation) are required in each node. |
| Approximation | Linear approximation of displacements and geometry. |
| Integration | Integration of membrane strain terms using gauss integration formula in 4 points (default) or using 1 or 7 points (using NIP parameter). Integration of strains associated with rotational field integration using 1 point is default (4 and 7 points rules can be specified using NIPRot parameter). |
| Features | - |
| CS properties | Cross section thickness is required. |
| Loads | - |
| Nlgeo | 0. |
| Status | - |
