Recent Advances in Shape and Topology Optimization via the Level Set Method in an Industrial Context

François Jouve^*, Grégoire Allaire and Georgios Michailidis

Shape and topology optimization via the level set method has started attracting the interest of an increasing number of researchers and industrial designers over the last years. A large number of classical academic problems, using various objective functions and constraints, have been successfully treated with this class of methods, showing its efficiency and flexibility. We present briefly the basic principles of the level set method for structural optimization and some numerical results. \newline But real industrial applications involve more complex and mixed constraints that are less usual, and sometimes not easy to formulate from a mathematical point of view. As examples of unusual constraints, we show how we have been able to deal with cooling and molding constraints, written as geometric constraints over the shape to optimize.

Mathematics Subject Classification: 74P15

Keywords: shape and topology optimization; level set method; industrial constraints

Minisymposion: Material and Topology Optimization: Theory, Methods and Applications