Figure. Constraint enforcement accuracy depends heavily on the fineness of the FE mesh.
ProTOp can handle the most important technological (geometrical) constraints. These constraints can be classified into three main categories, as follows:
All technological constraints are enforced by mapping material parameters on a discrete FE mesh. This automatically means that the mapping accuracy heavily depends on the fineness of the mesh. Namely, when a material parameter from a particular node is mapped to another location, the error introduced depends on the distances from the mapped location to the neighboring nodes. These distances, and consequently the error, obviously decrease as the mesh becomes finer.
Figure. Constraint enforcement accuracy depends heavily on the fineness of the FE mesh.
Obviously, the fineness of the mesh has to be set carefully when technological constraints are enforced on a part. Failure to do so escalates especially in situations where the optimizer generates slender regions of less than 2~3 finite elements thickness. In such regions, technological constraints enforcement may cause the element switching problem, where finite elements switch from material to void and vice versa in sequential optimization cycles.
Figure. Technological constraint enforcement on slender regions will result in the element switching problem.
Accuracy of constraint enforcement is improved by improving the FE mesh fineness. Apart from this, however, this process can also be made much more accurate by
A constraints consistent FE mesh is a mesh that reflects the geometrical properties of the constraint. For example, for a plane symmetry constraint, a mesh exhibiting the same symmetry (each node has a symmetric counterpart) would be perfect. It should be noted, however, that in practice constraints consistent meshes often can not be generated easily (or at all) by available meshers.
Constraints consistent loads are loads that reflect the geometrical properties of the constraint. To achieve this, the introduction of additional load cases might be necessary. For example, for a plane symmetry constraint, additional load cases that introduce the symmetry into the set of all load cases are typically highly recommended.