Shape preserving design of vibrating structures using topology optimization

In several engineering components, the shape of some functional surfaces needs to be preserved in order to avoid losing performance or even its functionality when subjected to loads. This is particularly important when tight tolerances are required for operational conditions in some regions. If the deformation significantly affects product functionality, it is interesting to use a shape preserving design technique. This will often reduce deformation in a local region. To achieve that, we deal with topology optimization of elastic, continuum structures with Rayleigh damping, subjected to time-harmonic, design-independent external dynamic loading with prescribed excitation frequency, amplitude and spatial distribution. In topology optimization for vibrating structures, the obtained design should often have its resonance frequencies driven far away from the given excitation frequency in order to avoid resonance and to reduce vibration levels. In this work, we explore harmonic vibration problems with the excitation frequency lower than the first resonance frequency of the initial structure. Dynamic compliance minimization is used to improve dynamic response of the structure. An additional local dynamic compliance constraint is used to define the shape preserving problem, thus, reducing deformation in specific regions of a part named shape preserving region (SPR). A commercial FE code (ANSYS (R)) is used to solve the finite element problem. The optimization Method of Moving Asymptotes (MMA) is used with the modified Solid Isotropic Material with Penalization (SIMP) material interpolation scheme. The effectiveness of this technique is presented using 2D plane structures. Coherent results were achieved using the proposed optimization formulation. It is possible to observe significant decrease on local deformation, at expense of little increase on global dynamic compliance.