Reliability-based topology optimization for fundamental frequency maximization with frequency band constraints

Abstract

Resonance can be avoided by preventing the structural natural frequencies from falling within the operating frequency range. However, structural natural frequencies are influenced by uncertain parameters, such as material properties and geometric sizes. Therefore, it is essential to consider these uncertainties during the conceptual design phase. To address this problem, a novel reliability-based eigenvalue topology optimization model under frequency-band constraints is established, in which the uncertainties of the material properties and structural size are considered. Owing to the high computational costs of dealing with frequency-band reliability constraints, a frequency-band constraint shifting method (FBCSM) is proposed to ease the heavy computational burden without sacrificing accuracy. In addition, the sensitivities of simple and multiple eigenfrequencies with respect to the design and random variables are derived. The “bound formulation” and “robust formulation” are used to reduce the gray elements and checkerboard phenomenon. Four examples are used to determine the effectiveness of the proposed reliability-based eigenvalue topology model and FBCSM. The results confirmed their superiority in terms of validity and efficiency.