Multi-phase Optimization

We are working on shape and topology optimization of multiple phases using a level-set method for the description of the phases' interface. A complete description of the method can be found in our paper "Multi-phase optimization via a level set method". The method is appropriate both for materials with a "sharp" or a "functionally graded" interface.

Structural Optimization (with G. Allaire, C. Dapogny and G. Delgado)

The minimization of the compliance (work done by the loads) of a structure, under some volume constraint for the material used, is a benchmark problem in shape and topology optimization. For reasons of economy, it can be preferable to combine several materials and impose a volume constraint to each one separately. The "strong" material will then be placed to regions of high stress and the rest of the structure will be dominated by "weaker" phases (see "Multi-phase optimization via a level set method").

Long cantilever using two phases and void.
Boundary conditions. Initialization. Optimized shape.

3-force bridge using two phases and void.
Boundary conditions.

 

Initialization.

 

Optimized shape.

3-force bridge using three phases and void.
Boundary conditions.

 

Initialization.

 

Optimized shape.

L-beam using two phases and void.
Boundary conditions.

Initialization.

Optimized shape.

Multi-functional Optimization

Phases with different properties can be used in order to construct multi-functional structures, e.g. stiff and thermally isolating structures (see "Structural and multi-functional optimization using multiple phases and a level-set method").

 

 

Boundary conditions.

Optimized shape for "off-plane" flux. Optimized shape for "in-plane" flux.