Level set based structural topology optimization for minimizing frequency response

• Published in: Journal of sound and vibration Vol. 330; no. 24; pp. 5820 - 5834
• Main Authors: Shu, Lei, Wang, Michael Yu, Fang, Zongde, Ma, Zhengdong, Wei, Peng
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 21.11.2011; Elsevier
• Subjects: Exact sciences and technology; Frequency response; Fundamental areas of phenomenology (including applications); Mathematical analysis; Optimization; Physics; Sensitivity analysis; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Three dimensional; Topology optimization; Two dimensional; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Geometrical shape; Sensitivity analysis; Vibration; Contour line; Adjoint method; Topology; Optimization; Advection; Equations of state; Vibration control; Frequency response; Structural analysis; eXtended Finite Element Method
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2011.07.026

For the purpose of structure vibration reduction, a structural topology optimization for minimizing frequency response is proposed based on the level set method. The objective of the present study is to minimize the frequency response at the specified points or surfaces on the structure with an excitation frequency or a frequency range, subject to the given amount of the material over the admissible design domain. The sensitivity analysis with respect to the structural boundaries is carried out, while the Extended finite element method (X-FEM) is employed for solving the state equation and the adjoint equation. The optimal structure with smooth boundaries is obtained by the level set evolution with advection velocity, derived from the sensitivity analysis and the optimization algorithm. A number of numerical examples, in the frameworks of two-dimension (2D) and three-dimension (3D), are presented to demonstrate the feasibility and effectiveness of the proposed approach. ► We proposed a structural topology optimization for minimizing frequency response. ► Topology optimization base on the level set method. ► Optimal structure with smooth boundaries is obtained by the level set evolution. ► Frequency response of specified position on the structure is minimized.