An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Abstract

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

Security Check Mutual Recognition between High-Speed Railway and Urban Rail Transit Based on Variable Fuzzy Set Theory

“…When α � 1, p � 1, the above formula is a fuzzy comprehensive evaluation linear model [33]; when α � 1, p � 2, it is a rational model [34]; when α � 2, p � 1, it is a sigmoid function [35]; when α � 2, p � 2, it is a fuzzy optimal model [36].…”