Analysis of three point bending mechanical properties of functionally graded triply periodic minimal surfaces

SHI Yaochen; HAN Jinhu; DUAN Haitao; LU Zhiyi; YANG Fengshuang; DU Yingyu

doi:10.16579/j.issn.1001.9669.2026.04.015

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Analysis of three point bending mechanical properties of functionally graded triply periodic minimal surfaces

·Design·Calculation· | 更新时间：2026-04-15

- Analysis of three point bending mechanical properties of functionally graded triply periodic minimal surfaces
- Journal of Mechanical Strength Vol. 48, Issue 4, Pages: 134-138(2026)
- 作者机构：
  
  1.长春大学机械与车辆工程学院，长春 130022
  2.长春职业技术大学机电学院，长春 130033
- 作者简介：
  
  DU Yingyu, E-mail:1390394015@qq.com
- 基金信息：
  
  Jilin Provincial Natural Science Foundation(YDZJ202601ZYTS142)
- DOI：10.16579/j.issn.1001.9669.2026.04.015
  CLC： TH122
- Received：14 August 2024，
  
  Revised：2024-10-27，
  
  Published：15 April 2026
- 稿件说明：
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史尧臣，韩金虎，段海涛，等. 功能梯度三周期极小曲面的三点弯曲力学性能分析［J］. 机械强度，2026，48（4）：134-138.

SHI Yaochen，HAN Jinhu，DUAN Haitao，et al. Analysis of three point bending mechanical properties of functionally graded triply periodic minimal surfaces［J］. Journal of Mechanical Strength，2026，48（4）：134-138.
史尧臣，韩金虎，段海涛，等. 功能梯度三周期极小曲面的三点弯曲力学性能分析［J］. 机械强度，2026，48（4）：134-138. DOI： 10.16579/j.issn.1001.9669.2026.04.015.

SHI Yaochen，HAN Jinhu，DUAN Haitao，et al. Analysis of three point bending mechanical properties of functionally graded triply periodic minimal surfaces［J］. Journal of Mechanical Strength，2026，48（4）：134-138. DOI： 10.16579/j.issn.1001.9669.2026.04.015.

摘要

目的

针对三周期极小曲面梯度设计中孔隙率单方向线性渐变的局限，基于Primitive曲面多孔结构，开展孔隙率与梯度设计对其三点弯曲力学性能的影响研究，提出适配结构应力分布的孔隙率梯度优化方法。

方法

首先，基于Primitive曲面隐式函数，构建3种孔隙率的均厚多孔结构模型，明确孔隙率对结构力学性能的影响规律；其次，依据均厚结构三点弯曲受载的应力分布特征，提出M形孔隙率梯度设计方案，实现高应力区孔隙率精准调控；然后，采用光固化成形技术制备试件，基于Ansys软件开展三点弯曲工况有限元仿真；最后，通过三点弯曲试验，分析孔隙率及梯度设计对结构弯曲力学性能的影响机制。

结果

结果表明，厚多孔结构抗弯性能与孔隙率呈负相关，孔隙率从35%降至30%时，弯曲刚度提升53.6%；与32.5%孔隙率均厚结构相比，M形梯度结构弯曲刚度提升17.8%、强度提升28.2%，质量仅增加3.7%；该方法可有效缓解应力集中，在轻量化前提下提升多孔结构抗弯性能，为多孔承载结构梯度优化设计提供参考。

Abstract

Objective

TAiming at the limitation of unidirectional linear gradient of porosity in the gradient design of triply periodic minimal surfaces

the influence of porosity and gradient design on the three-point bending mechanical properties of porous structures based on Primitive surface was studied

and a porosity gradient optimization method adapted to the structural stress distribution was proposed.

Methods

Firstly

three uniformly thick porous structure models with different porosities were constructed based on the implicit function of Primitive surface

and the influence law of porosity on the structural mechanical properties was clarified. Secondly

an M-shaped porosity gradient design scheme was proposed according to the stress distribution characteristics of the uniformly thick structure under three-point bending load

to realize precise regulation of porosity in high stress areas. Then

the specimens were fabricated by stereo lithography apparatus technology

and finite element simulation under three-point bending condition was carried out based on Ansys software. Finally

three-point bending tests were conducted to analyze the influence mechanism of porosity and gradient design on the bending mechanical properties of the structure.

Results

Results indicate that the flexural performance of the uniformly thick porous structure is negatively correlated with the porosity. When the porosity decreases from 35% to 30%

the bending stiffness increases by 53.6%. Compared with the uniformly thick structure with 32.5% porosity

the M-shaped gradient structure has a 17.8% increase in bending stiffness

a 28.2% increase in strength

and only a 3.7% increase in mass. This method can effectively alleviate stress concentration

improve the flexural performance of the porous structure under the premise of lightweight

and provide a reference for the gradient optimization design of porous load-bearing structures.

关键词

Keywords

references

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