Assignment of p-Discretization in StressCheck

p-Discretization enables the user to control the polynomial orders (i.e. p-levels) of individual elements in the mesh. This allows the user to override the default p-levels of the StressCheck Solver input.

To assign p-Discretization to a StressCheck model, select the p-Discretization tab in the Input dialog and change the Object combo-box of the C/A/O/M to the desired object type. Then, select the object(s), specify the desired option and p-level(s) and click Accept.

Note: if the object Element (or All Elements) is selected, then only the p-Discretization: combo-box and p-level(s) are available for input. If the object Face or Face Surface is selected, then the q-Discretization: combo-box and p-level are also available for input. The q-Discretization option is most applicable for ply-by-ply lamina assignments and thin solids.

Specifying Element P-Levels and Spaces

In StressCheck, typically uniform p-extensions are used (i.e. all element p-levels are uniformly increased based on the Solver inputs). Extension means a systematic increase in the number of degrees of freedom on a fixed mesh. It is possible, however, to select any group of elements and limit or fix the polynomial degree for those elements. This is discussed in the following.

Space Options

The options are: Trunk and Product space.

• The Trunk space is the default space and is applicable to all element types. If a uniform p-extension is to be employed, with the Trunk space specified, then nothing needs to be done because this is the default option for StressCheck.
• The Product space is applicable for quadrilateral and hexahedral elements only. The use of product space in 3D is limited to models that have only hexahedral elements. In that case all the elements must be assigned the product space.

For more details consult “Finite Element Spaces” in “Introduction to Finite Element Analysis: Formulation, Verification & Validation” by Drs. Barna Szabó & Ivo Babuška

P-Discretization Input Options

The options are: Variable, Bounded, Fixed, and Uniform.

• Variable means that the p-level is allowed to change from the starting level in the corresponding input field.
• Bounded means that the p-level for any element or group of elements is bounded between a lower and upper limit.
• Fixed means that the p-level of the selected group of elements will remain fixed at the input value during the p-extension.
• Uniform means that during an adaptive p-extension, the p-level of all the selected elements will be set to the same value based on the error indicator reading for the elements.

Q-Discretization Input Options

The only option is Fixed. For Face/Face Surface objects only. Allows to fix the polynomial order (q-level) in one direction for hexahedral and pentahedral elements. Used in connection with ‘thin-solids’ (quadrilateral and triangular elements in the 3D reference), the ‘thin’ direction is determined based on the selected element faces. By selecting the face of an element, the thin direction is understood to be in the direction normal to the selected face. Any fixed value of q between 1 and 8 can be assigned.

Solution Expectations

When a solution is initiated, the initial and final p-levels given in the StressCheck Solver interface are assigned to ALL elements as a default setting. Explicit P-discretization settings may be assigned to individual elements that will override the default settings. Individual elements may be assigned P-discretization attributes that are Variable, Bounded, or Fixed. Any P-discretization attributes that are assigned to ALL elements, will be automatically overridden by the Solver interface.

For an example of using p-Discretization to improve solution efficiency, refer to Helpful Hints and Tips: Case Study on the Influence of Element Mapping and p-Discretization.

Selecting Objects for p-Discretization Assignment

You may select an object (such as a face, surface or element) or a group of objects during p-Discretization assignment. An object is selected from the Model View by pointing to it and clicking on the left mouse button.

• A group of objects can be marquee selected by left-clicking and dragging the cursor until the desired group is completely enclosed in a rectangular box.
• Holding the Shift key down while left-clicking will allow selection of multiple objects for assignment.
• If the group includes objects which were not to be selected then individual objects can be removed from the group by holding the Ctrl key down while clicking on them.
• If you wish to cancel the current selection of objects, simply right-click on the Model View.

Note: assigning to geometric objects, if associated with elements, will result in the associated elements inheriting the assignment. It is recommended to assign p-Discretization to geometry whenever applicable in case the mesh is updated.

Specifying a Set for p-Discretization Assignment

Alternatively, if a there is a set definition containing a list of objects for assignment, the name of this set may be specified in the Set: combo-box instead of selecting the objects from the Model View. Simply select the name of the set, and the objects in the set list will automatically be selected in the Model View.

Adding a p-Discretization Assignment

Once an object or group of objects are selected, and the option(s)/p-level(s) are input, to add the new p-Discretization assignment record simply click the Accept button. Note: if an existing p-Discretization assignment record has already been selected from the record listbox, you first must choose Set: “New set” or re-select the action, object, or method. Then, you are able to create the new p-Discretization assignment record as usual.

Replacing/Deleting a p-Discretization Assignment

If the user wishes to edit the data in an existing p-Discretization assignment record, or delete an existing p-Discretization assignment record, the user first selects the assignment record from the record listbox directly under the C/A/O/M combo-boxes. Once it is selected, the Status column will read “Selected”, signifying the record can be replaced (updated) or deleted.

Replacing a p-Discretization Assignment Record

Once a p-Discretization assignment record is selected, the user may update the data in the p-Discretization tab, and then click Replace to update the p-Discretization assignment record. After clicking Replace, the Accept button will become active and the Replace and Delete buttons will become inactive.

Deleting a p-Discretization Assignment Record

Once a p-Discretization assignment record is selected, the user may click Delete to delete the p-Discretization assignment record. After clicking Delete, the Accept button will become active and the Replace and Delete buttons will become inactive.

Removing All p-Discretization Assignment Records

To remove all p-Discretization assignment records, regardless of p-Discretization ID, click the Purge button.