Basic Assumptions
Shape optimization in NX Nastran assumes the engineer is starting with a reasonably good design but would like to investigate ways in which the shape of the part, or even the entire structure, might be modified in order to better meet the design goals.
Although large shape variations can be investigated in NX Nastran, it is important to note that in a practical design environment, shape changes are often limited by numerous design considerations. Manufacturability of the part, interference from neighboring components of the structure, aesthetics, and so on, often limit the degree to which the structural shape can be modified.
Shape optimization in NX Nastran allows you to investigate these “real world” types of shape variations. It will, for example, let you determine the optimum placement and size of cutouts to lighten a structure. What the code will not tell you is how many of these cutouts to start with or whether an alternate method of construction is better. In fact, the latter questions are still active areas of shape optimization research.
Goal of Design Modeling for Shape
Four different modeling methods are available in NX Nastran. The purpose of each method is the same—to define a basis vector (or a set of basis vectors) for shape optimization. The methods only differ in terms of their user interfaces and whether or not the basis vectors are
automatically updated on each design cycle. The following subsections briefly outline each approach, its strong as well as its possible weak points, and its requirements for use.
Manual Grid Variation
This is the most general, as well as perhaps the most tedious, method of generating Shape basis vectors. It is listed first since it can be thought of as the lowest level approach, somewhat analogous to Assembly Language versus FORTRAN programming. A DVGRID Bulk Data entry defines the direction and magnitude of a grid variation for a given change in a design variable.
This relation is shown inFigure 2-15andEq. 2-19. A single DVGRID entry is required for every design variable-grid pair.
Figure 2-15. Grid Point Variation Defined by a DVGRID Entry
Equation 2-19.
DVGRID entries alone can be used to describe shape changes, although the method is probably more useful when combined with the direct input of shapes approach. Its most powerful form, however, is in connection with the geometric shapes approach. (These methods are described later in this section.)
Benefits
Since this can be considered the lowest-level approach, its strength lies in its generality. Using DVGRIDs alone, the designer has direct control over every designed grid point in the model (that is, every grid point whose location is to change during shape optimization.)
Drawbacks
In all but the simplest of problems, the data input can be formidable without a preprocessor.
The resultant basis vectors are treated as constant and not updated with each design cycle, so the risks of mesh distortion are increased.
Checklist
1. Define the shape design variables using DESVAR Bulk Data entries.
2. Establish the corresponding grid variations using DVGRID Bulk Data entries, one entry for every design variable-designed grid pair in the model. This entry ties design variable changes to changes in the structure’s shape. (Of course, this may lead to a large amount of data, up to G*NDV where G is the number of designed grids in the model and NDV is the number of shape design variables. A model with only 100 grids and 2 design variables would thus require on the order of 200 DVGRID entries.)
3. Preview the resultant basis vectors, and modify if necessary.
Direct Input of Shapes
This approach greatly simplifies the process of defining shape basis vectors. With this method, externally-generated vectors are DBLOCATEd and used to define shape basis vectors. An auxiliary model analysis provides these externally-generated vectors.
Benefits
Basis vectors for shape optimization can be generated using an external auxiliary model analysis and DBLOCATEd, allowing for easy generation of shape basis vectors. In theory, any method of external generation is possible, as long as the number of degrees of freedom in the auxiliary model is the same as in the primary structure (i.e., G-sets must be equivalent).
Drawbacks
The process is not fully automatic since an auxiliary model analysis must be performed beforehand, saved on the database, and DBLOCATEd for shape optimization. Since the basis vectors are externally generated, they are not updated for each design cycle. This may cause mesh distortion problems for large shape changes.
Checklist
1. Define an auxiliary model, perform an analysis, and save the results to the database using the SCR=NO option on the NASTRAN job submittal command. This process is the same as a conventional NX Nastran analysis except that the auxiliary model geometry and boundary conditions have been established with consideration given to the shape redesign goals.
2. DBLOCATE the results for shape optimization using the following FMS section commands (assuming the master file is file1.MASTER):
ASSIGN FILE1 = “file1.MASTER”
DBLOCATE DATABLK=(UG/UGD,GEOM1/GEOM1D,GEOM2/GEOM2D), LOGICAL=FILE1
Note: The data blocks UG, GEOM1, and GEOM2, are DBLOCATEd and renamed to UGD, GEOM1D, and GEOM2D, respectively. The data block names UGD, GEOM1D, and GEOM2D cannot be changed.
3. Define shape design variables using DESVAR entries, and correlate these to the DBLOCATEd basis vectors using DVSHAP Bulk Data entries.
4. Preview the resultant shape basis vectors to check for modeling errors.
Geometric Boundary Shapes
This method defines allowable shape variations using only the boundary of the structure. These shape variations can be supplied manually or with a geometry-based preprocessor. Either approach relies on BNDGRD Bulk Data entries to define the structure’s boundaries and DVGRID entries to furnish the shape variations over these boundaries.
Shape basis vectors are automatically generated by the code through a process of interpolation of the boundary shape changes to the interior of the structure. Additionally, the shape basis vectors are updated on every design cycle, minimizing the problems associated with mesh distortion for large shape changes.
Benefits
Since grid variations need only be specified over the boundaries, data preparation is greatly simplified. In fact, since DVGRID entries are only written for the boundaries, many real-world problems can be effectively solved without geometry-based preprocessors. Internal computation of the shape basis vectors means that these can be recomputed (updated) for every design cycle, reducing the problems associated with mesh distortion for large shape changes.
Drawbacks
Describing grid variations over the boundaries may still require a lot of DVGRID information, even though orders of magnitude less than the manual grid variation method.
Checklist
1. Define the shape design variables using DESVAR Bulk Data entries.
2. Define corresponding shape variations over the structure’s boundaries using DVGRID entries.
3. Define the shape boundary conditions using BNDGRID Bulk Data entries. The
BNDGRID-DVGRID entry combination is analogous to the use of SPCDs to impose enforced boundary displacements. The DVGRID entry supplies the enforced variation, much like an SPCD, to the boundary grids specified on the BNDGRID entry (similar to an SPC entry).
Analytic Boundary Shapes
This approach is similar to the geometric boundary shapes method but avoids having to use DVGRID entries on the boundary. Instead, the designer provides an auxiliary model over the boundaries of the structure that are to be changed. This may be a collection of BAR elements along the edges of a two-dimensional structure or a “skin” of plate elements over a three-dimensional part. We often refer to this model over the boundaries as an auxiliary boundary model. The designer then constrains and statically loads the model to produce a shape variation over the boundary, which the code then interpolates to the interior of the structure.
The result is a shape basis vector for optimization.
Benefits
The method is very general, and does not require a geometry-based pre- and postprocessor.
The user interface is entirely within the NX Nastran environment. Shape basis vectors are updated on every design cycle, reducing the problems associated with mesh distortion for large shape changes.
Drawbacks
Some creativity is often required in the selection of loads and boundary conditions for the auxiliary boundary models. However, any combination of static loading available in NX Nastran can be used; point loads (FORCE), enforced displacements (SPCD), thermal loads (TEMP), pressure loads (PLOAD), and so on, can all be used to generate the desired shapes.
Checklist
1. Define auxiliary boundary models using one additional Bulk Data Section for each model.
These sections are identified with the command, BEGIN BULK AUXMODEL = n where n is the auxiliary boundary model ID.
2. Select loading and boundary conditions in Case Control using AUXCASE and AUXMODEL = n to define the auxiliary boundary model Case Control Sections.
3. Define the shape boundary conditions on the actual structure using BNDGRID Bulk Data entries. (The actual structure is often referred to as the primary structure.) In addition to defining the connection points with the auxiliary boundary model, the BNDGRID entries define those boundaries that are invariant during shape optimization.
4. Define the shape design variables using DESVAR entries, and relate these to the shape basis vectors (which the code will compute) with DVSHAP entries.