Multi-material topology optimization of viscoelastically damped structures using a parametric level set method

Abstract

The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design practices typically rely on informed trial and error based modifications to improve dynamic performance. In this article, a multi-material topology optimization approach is presented as a systematic methodology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric, level set-based topology optimization to simultaneously distribute structural and viscoelastic material to optimize damping characteristics. The viscoelastic behavior is represented by a complex-valued material modulus resulting in a complex-valued eigenvalue problem. The structural loss factor is used as objective function during the optimization and is calculated using the complex-valued eigenmodes. An adjoint sensitivity analysis is presented that provides an analytical expression for the corresponding sensitivities. Multiple numerical examples are treated to illustrate the effectiveness of the approach and the influence of different viscoelastic material models on the optimized designs is studied. The optimization routine is able to generate designs for a number of eigenmodes and to attenuate a resonant mode of an existing structure.

Design of Viscoelastic Damped Plate Structures with a Multi-Material Topology Optimization Method

“…[1] took the classical level set topology optimization to determine the distribution for constrained damping patches attached to the board, aiming at maximizing loss factors. And later, Kolk et al [2] simultaneously optimized the distribution scheme of the substrate and the viscoelastic material layer together, for maximum modal loss factors at target frequencies.…”

Topology optimization of frequency dependent viscoelastic structures via a level-set method

“…Yun et al [9] performed multimaterial topology optimization to maximize energy dissipation of viscoelastically damped structures subjected to unsteady loads using SIMP and MMA. Ansari et al [10] used a level set method to perform topology optimization of viscoelastic UCLD plate whereas van der Kolk et al [11] used a parametrized level set based method for multi-material topology optimization of beams.…”

Multi-material topology optimization for automotive design problems

“…Liu et al 28 extended Wang's research by considering the cohesive constitutive relationship of the materials. Van der Kolk et al 29 used the level-set method of multi-material topology optimization to attenuate the resonance of a structure. Previous studies were intensively concentrated on solving simple twodimensional classical problems, such as the 2D cantilever or 2D Messerschmitt-Bo¨lkow-Blohm (MBB) beams, based on the assumption of plane stress and using a limited numbers of design variables.…”