# The Open Civil Engineering Journal

ISSN: 1874-1495 ― Volume 13, 2019
RESEARCH ARTICLE

# Revised Level Set-Based Method for Topology Optimization and Its Applications in Bridge Construction

Jing Wu1, 2 , Li Wu1, *
1 Engineering Faculty, China University of Geosciences, Wuhan 430074, China
2 Hubei Engineering University, Xiaogan 432000, China

## Abstract

To cure imperfections such as low accuracy and the lack of ability to nucleate hole in the conventional level set-based topology optimization method, a novel method using a trapezoidal method with discrete design variables is proposed. The proposed method can simultaneously accomplish topology and shape optimization. The finite element method is employed to obtain element properties and provide data for calculating design and topological sensitivities. With the aim of performing the finite element method on a non-conforming mesh, a relation between the level set function and the element densities field has to be clearly defined. The element densities field is obtained by averaging the Heaviside function values. The Lagrange multiplier method is exploited to fulfill the volume constraint. Based on topological and design sensitivity and the trapezoidal method, the Hamilton-Jacobi partial differential equation is updated recursively to find the optimal layout. In order to stabilize the iterations and improve the efficiency of the algorithm, re-initiation of the level set function is necessary. Then, the detailed process of a cantilever design is illustrated. To demonstrate the applications of the proposed method in bridge construction, two numerical examples of a pylon bridge design are introduced. It is shown that the results match practical designs very well, and the proposed method is a helpful tool in bridge design.

Keywords: Level set method, Sensitivity analysis, Topology optimization, Trapezoidal method.

### Article Information

#### Identifiers and Pagination:

Year: 2017
Volume: 11
First Page: 153
Last Page: 166
Publisher Id: TOCIEJ-11-153
DOI: 10.2174/1874149501711010153

#### Article History:

Acceptance Date: 14/10/2016
Electronic publication date: 24/02/2017
Collection year: 2017

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open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Engineering Faculty, China University of Geosciences, Wuhan 430074, China; Tel: 86-02767883428; Fax: 86-02767883507; E-mail: lwu@cug.edu.cn

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