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

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.