Topology
optimization

Topology optimization is considered nowadays as a very consolidated conceptual tool for structural design, not only for pure academic purposes but also for industrial applications.

It solves the basic engineering problem of distributing a limited amount of material in a design space to optimize a certain objective function while some constraints are fulfilled.

At present, to do this in an optimal way is an engineering must. Topology optimization brings together Mathematics, Physics and Engineers in this fascinating and challenging task, which is today present in multiple physical contexts. From a mathematical side, there are many deep questions relevant to the optimal design of structures, as typical optimal solutions of these problems are of microstructural nature, and therefore relaxation via variational techniques and mathematical description of microstructure are of major importance. From a more practical point of view, to device numerical algorithms capable to capture optimal microstructural solutions, or contrary to this, to find classical, black and white (and therefore manufacturable), pseudo-optimal structures are two of the main current interests in this research area.

Our focus is now on the topology optimization of hyperelastic structures (those exhibiting large deformations and displacements) and the development of the topology optimization software Toptimiz3D.