An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Xingfa Yang,Jie Liu,Yin Yang,Qixiang Qing,Guilin Wen

doi:10.1155/2018/3653817

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.

Highlights

In the field of structural optimization, topology optimization has gained more and more attention
They first apply an explicit jump immersed interface method to compute the structural stresses for a given design domain discretized by finite differences, and the level set method, which represents the design structure through an embedded topology implicit function (TDF), is used to alter the structural shape, with velocities depending on the stresses in the current design; criteria are provided for advancing the shape and introducing holes in an appropriate direction
Notice that the classical solid isotropic material with penalization (SIMP) and bidirectional evolutionary structural optimization (BESO) methods are taken as benchmarks in the following examples, and the computational time by using these two approaches will not be considered as their efficiency is varied with different unfixed parameters

Summary

Introduction

In the field of structural optimization, topology optimization has gained more and more attention. Node-based topology optimization method is developed to overcome the disadvantages of element-based topology optimization, for the zigzag boundaries issues It can produce solutions with crisp and smooth edges that require little postprocessing effort to interpret results before they can be manufactured, which is due to the fact that it employs an implicit function to describe the shape and topology of the structure. The implicit function is called topology description function (TDF) in node-based topology optimization method, which is first proposed by Sethian and Wiegmann [22] In their article, they first apply an explicit jump immersed interface method to compute the structural stresses for a given design domain discretized by finite differences, and the level set method, which represents the design structure through an embedded topology implicit function (TDF), is used to alter the structural shape, with velocities depending on the stresses in the current design; criteria are provided for advancing the shape and introducing holes in an appropriate direction.

Smooth the Heaviside Function

Topology-Description-Function-Based Method

Remarks on the Merits of Proposed TDFM

Numerical Examples

Findings

Concluding Remarks