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A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

Xiaoyan Teng1, Qiang Li1, Xudong Jiang2,*
1 Institute of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, 150001, China
2 Institute of Mechanical Power Engineering, Harbin University of Science and Technology, Harbin, 150080, China
* Corresponding Author: Xudong Jiang. Email:
(This article belongs to this Special Issue: Computer Modeling in Ocean Engineering Structure and Mechanical Equipment)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2479-2496.

Received 10 April 2022; Accepted 08 July 2022; Issue published 23 November 2022


A smooth bidirectional evolutionary structural optimization (SBESO), as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load. A weighted function is introduced to regulate the mass and stiffness matrix of an element, which has the inefficient element gradually removed from the design domain as if it were undergoing damage. Aiming at maximizing the natural frequency of a structure, the frequency optimization formulation is proposed using the SBESO technique. The effects of various weight functions including constant, linear and sine functions on structural optimization are compared. With the equivalent static load (ESL) method, the dynamic stiffness optimization of a structure is formulated by the SBESO technique. Numerical examples show that compared with the classic BESO method, the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function. It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.


Topology optimization; smooth bi-directional evolutionary structural optimization (SBESO); eigenfrequency optimization; dynamic stiffness optimization

Cite This Article

Teng, X., Li, Q., Jiang, X. (2023). A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance. CMES-Computer Modeling in Engineering & Sciences, 135(3), 2479–2496.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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