Frequency response

Frequency response belongs to the category of problems where mechanical intuition is very limited. Topology optimization can provide great help in the design phase of structures submitted to dynamic excitations. However, conventional adjoint methods lead to prohibiting computational times for industrial applications.

Recent advances in modal approaches for frequency response problems (Allaire,Michailidis and Spillane, 2016) have shown that alternative non-adjoint methods can equally be applied, reducing dramatically the computational time for topology optimization.

Here, we present some recent results for the minimization of the static and the dynamic compliance in an excitation frequency interval. First, a constraint is imposed on the static compliance. We denote the dynamic compliance of the optimized shape as 'Crefdyn'. Then, we further the dynamic compliance by imposing the constraint Cdyn < aCrefdyn, where a belongs to the interval (0,1).

MBB beam: volume minimization under constraints on the static and dynamic compliance.
Boundary conditions. Optimized shape imposing a constraint on the static compliance. Optimized shape imposing a constraint on the static and dynamic compliance (a=0.70). Optimized shape imposing a constraint on the static and dynamic compliance (a=0.50). Optimized shape imposing a constraint on the static and dynamic compliance (a=0.30).

3d bridge: volume minimization under constraints on the static and dynamic compliance.
Boundary conditions. Optimized shape imposing a constraint on the static compliance. Optimized shape imposing a constraint on the static and dynamic compliance (a=0.70). Optimized shape imposing a constraint on the static and dynamic compliance (a=0.50). Optimized shape imposing a constraint on the static and dynamic compliance (a=0.30).