Shape optimization is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being solved depends on the solution of a given partial differential equation defined on the variable domain.
Topology optimization is, in addition, concerned with the number of connected components/boundaries belonging to the domain. Such methods are needed since typically shape optimization methods work in a subset of allowable shapes which have fixed topological properties, such as having a fixed number of holes in them. Topological optimization techniques can then help work around the limitations of pure shape optimization.
Read more about Shape Optimization: Definition, Examples, Techniques
Famous quotes containing the word shape:
“Fortuitous circumstances constitute the moulds that shape the majority of human lives, and the hasty impress of an accident is too often regarded as the relentless decree of all ordaining fate.”
—Augusta Evans (1835–1909)