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.
Highlights
Topology optimization is conducive to the conceptual design of a structure and enables engineers to find optimal material distribution
There is a significant difference between the formula of design sensitivity and the one employed by solid isotropic material with penalization (SIMP), as the densities defined in this work have been polarized while the avoidance of intermediate densities penalization is utilized
For the compliance minimum problem, we propose an iterative algorithm incorporated with the level set method, design sensitivity, and topological sensitivity
Summary
Topology optimization is conducive to the conceptual design of a structure and enables engineers to find optimal material distribution. Sophisticated methods have emerged to help engineers deal with the topology optimization problem of discrete structures. After almost 30 years of development, four crucial methods have stood out for the topology optimization of the continuum structure, namely, the homogenization method [4], the level set-based methods [5], the evolutionary structural optimization (ESO) approach [6], and the solid isotropic material with penalization (SIMP) scheme [7]. In the early 2000s, the level set-based method was introduced in the topology optimization discipline and became increasingly popular. Topology changes of structures can be made by the level set method. This study proposes a more accurate level set-based topology optimization method. The trapezoidal method is used to solve the Hamilton-Jacobi equation
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