Design Variables for Shape Optimization

In finite elements, the shape of a structure is defined by the vector of nodal coordinates (x). In order to avoid mesh distortions due to shape changes, changes of the shape of the structural boundary must be translated into changes of the interior of the mesh.

The two most commonly used approaches to account for mesh changes during a shape optimization are the basis vector approach and the perturbation vector approach. Both approaches refer to the definition of the structural shape as a linear combination of vectors.

Using the basis vector approach, the structural shape is defined as a linear combination of basis vectors. The basis vectors define nodal locations.

where x is the vector of nodal coordinates, is the basis vector associated to the design variable .

Using the perturbation vector approach, the structural shape change is defined as a linear combination of perturbation vectors. The perturbation vectors define changes of nodal locations with respect to the original finite element mesh.

where x is the vector of nodal coordinates, is the vector of nodal coordinates of the initial design, is the perturbation vector associated to the design variable.

The initial nodal coordinates are those defined with the GRID entity. The perturbation vectors are defined on the DVGRID statement, which is referenced by the design variable entity DESVAR.

If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced on the DESVAR bulk data entry for the design variable values.

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Shape Optimization