Course

The course Shape and topology optimization for structures built by additive manufacturing is taught by Prof. Grégoire Allaire.

This series of 6 lectures (1h30) is devoted to the specific models and tools of shape and topology optimization for designing mechanical structures built by additive manufacturing. The focus is on powder bed fusion processes.

After reviewing the classical tools of parametric, geometric and topology optimization, the typical new constraints induced by additive manufacturing are introduced, like overhangs, thermal deformation or residual stresses. New models based on layer-by-layer fabrication or coupled thermo-mechanical equations are discussed.

Finally, two recent issues in additive manufacturing are presented. The first one is the optimal design of so-called lattice materials, i.e., porous structures made of periodically perforated material, where the microscopic periodic cell can be macroscopically modulated and oriented. Lattice materials are becoming increasingly popular since they can be built by additive manufacturing techniques. The second one is the concurrent path planning optimization and shape optimization for a mechanical structure built by melting a metallic powder bed with a traveling laser beam. The goal is to design a structure which has optimal mechanical performance for its final use but is also built in minimal time, corresponding to the shortest laser path.

 

Grégoire Allaire

Ecole Polytechnique de Paris, France

Grégoire Allaire is a Professor of Applied Mathematics at Ecole Polytechnique. He received his PhD from Pierre et Marie Curie (Paris 6) University in 1989.
Professor Allaire’s research focuses on the mathematical modeling, numerical simulation and optimization of physical and mechanical problems. He is a specialist of multi-scale analysis (homogenization) and of shape and topology optimization of structures.