The Mechanical APDL program's element library includes two basic types of area and volume elements: linear (with or without extra shapes), and quadratic. These basic element types are represented schematically in Figure 2.1: Area and Volume Types. Let's examine some of the considerations involved in choosing between these two basic element types:
- Basic area and volume types available in the Mechanical APDL program
(a) Linear isoparametric (b) Linear isoparametric with extra shapes (c) Quadratic
For structural analyses, these corner node elements with extra shape functions will often yield an accurate solution in a reasonable amount of computer time. When using these elements, it is important to avoid their degenerate forms in critical regions. That is, avoid using the triangular form of 2D linear elements and the wedge or tetrahedral forms of 3D linear elements in high results-gradient regions, or other regions of special interest. You should also take care to avoid using excessively distorted linear elements. In nonlinear structural analyses, you will usually obtain better accuracy at less expense if you use a fine mesh of these linear elements rather than a comparable coarse mesh of quadratic elements.
Examples of (a) linear and (b) quadratic elements are shown in Figure 2.2: Comparable Grids.
When modeling a curved shell, you must choose between using curved (that is, quadratic) or flat (linear) shell elements. Each choice has its advantages and disadvantages. For most practical cases, the majority of problems can be solved to a high degree of accuracy in a minimum amount of computer time with flat elements. You must take care, however, to ensure that you use enough flat elements to model the curved surface adequately. Obviously, the smaller the element, the better the accuracy. It is recommended that the 3D flat shell elements not extend over more than a 15° arc. Conical shell (axisymmetric line) elements should be limited to a 10° arc (or 5° if near the Y axis).
For most non-structural analyses (thermal, magnetic, etc.), the linear elements are nearly as good as the higher order elements, and are less expensive to use. Degenerate elements (triangles and tetrahedra) usually produce accurate results in non-structural analyses.
For linear structural analyses with degenerate element shapes (that is, triangular 2D elements and wedge or tetrahedral 3D elements), the quadratic elements will usually yield better results at less expense than will the linear elements. However, in order to use these elements correctly, you need to be aware of a few peculiar traits that they exhibit:
Distributed loads and edge pressures are not allocated to the element nodes according to "common sense," as they are in the linear elements. (See Figure 2.3: Equivalent Nodal Allocations.) Reaction forces from midside-node elements exhibit the same nonintuitive interpretation.
3D thermal elements with midside nodes subject to convection loading inherently distribute the heat flow such that it flows in one direction at the midside node and in the other direction at the corner nodes.
Mass at the midside nodes is greater than at the corner nodes. When selecting master degrees of freedom in a substructure (or CMS) generation, you must include midside nodes as master nodes in order to achieve better mass or surface load representation.
Equivalent nodal allocations of a unit uniform surface load are shown in Figure 2.3: Equivalent Nodal Allocations. The following scenarios are depicted:
(a) 2D elements (b) 3D elements (c) triangular 3D elements In dynamic analyses where wave propagation is of interest, midside-node elements are not recommended because of the nonuniform mass distribution.
Do not define nodal-based contact elements (such as COMBIN40, CONTA175, and CONTA178) at, or connect gap elements to, faces with midside nodes. Similarly for thermal problems, do not apply radiation links or nonlinear convection surfaces to edges with midside nodes. Where nodal-based contact is necessary on surfaces with midside nodes, the midside nodes should be removed, if possible. This caution does not apply to the surface-to-surface and line-to-surface contact elements (TARGE169, TARGE170, CONTA172, CONTA174, and CONTA177). Meshing of solid models provides ways to omit certain midside nodes.
When constraining degrees of freedom at an element edge (or face), all nodes on the face, including the midside nodes, must be constrained.
The corner node of an element should only be connected to the corner node, and not the midside node of an adjacent element. Adjacent elements should have connected (or common) midside nodes.
For elements having midside nodes, it is generally preferred that each such node be located at the straight-line position halfway between the corresponding corner nodes. There are, however, situations where other locations may be more desirable:
Nodes following curved geometric boundaries will usually produce more accurate analysis results - and all Mechanical APDL meshers place them there by default.
Even internal edges in some meshes may have to curve to prevent elements from becoming inverted or otherwise overly distorted. Mechanical APDL meshers sometimes produce this type of curvature.
It is possible to mimic a crack-tip singularity with "quarter point" elements, with midside nodes deliberately placed off-center. You can produce this type of specialized area mesh in Mechanical APDL by using the KSCON command.
Midside node positions are checked by the element shape test described below. (For information about controlling element shape checking, see Generating the Mesh of this manual.)
All solid and shell elements except 3-node triangles and 4-node tetrahedra are tested for uniformity of the mapping between "real" 3D space and the element's own "natural" coordinate space. A large Jacobian ratio indicates excessive element distortion, which may or may not be caused by poorly located midside nodes. For details about Jacobian ratio tests, refer to Element Shape Testing in the Theory Reference.
If you do not assign a location for a midside node, the program will automatically place that node midway between the two corner nodes, based on a linear Cartesian interpolation. Nodes located in this manner will also have their nodal coordinate system rotation angles linearly interpolated.
Connecting elements should have the same number of nodes along the common side. When mixing element types it may be necessary to remove the midside node from an element. For example, node N of the 8-node element shown below should be removed (or given a zero-node number when the element is created (E)) when the element is connected to a 4-node element.
Note: The program will automatically remove midside nodes along the common sides of linear and quadratic elements in the following situation: one area (or volume) is meshed (AMESH, VMESH, FVMESH) with linear elements, then an adjacent area (or volume) is meshed with quadratic elements. Midside nodes will not be removed if the order of meshing is reversed (quadratic elements followed by linear elements).
A removed midside node implies that the edge is and remains straight, resulting in a corresponding increase in the stiffness. It is recommended that elements with removed nodes be used only in transition regions and not where simpler linear elements with added shape functions will do. If necessary, use the EMID or EMODIF command to add or remove nodes after an element is generated.
A quadratic element has no more integration points than a linear element. For this reason, linear elements will usually be preferred for nonlinear analyses.
One-element meshes of higher-order quadrilateral elements such as PLANE183 may produce a singularity due to zero energy deformation.
In postprocessing, the program uses only corner nodes for section and hidden line displays. Similarly, nodal stress data for printout and postprocessing are available only for the corner nodes.
In graphics displays, midside-node elements, which actually use a curved edge in the element formulation, are displayed with straight-line segments (unless PowerGraphics is used). Models will therefore look "cruder" than they actually are.
