ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Solution to stress intensity factor by weight function method based on deep learning
Received date: 2022-12-06
Revised date: 2023-01-30
Accepted date: 2023-03-02
Online published: 2023-03-10
A deep-learning based multiple reference states weight function method is proposed to address the problems in traditional multiple reference states weight function method for complex geometric configurations. Comparison with the Green's functions at corresponding points of the crack surface shows that the deviation between the Green’s functions of unilateral penetrating crack at the edge of the finite width plate obtained by this method and the Wu-Carlsson analytical weight function method is within 0.4%， verifying the accuracy of the weight function obtained by this method and proving the feasibility of this method. Using this method， we derive the weight function with some geometric dimensions for the edge crack at the off-center hole on the finite plate common in the aerospace field， and compare it with the Green’s function value obtained by the finite element method. The results show that most of the deviations are smaller than 1.5%， with the maximum deviation of 4.8%， further verifying the accuracy of the weight function solution obtained by this method. The proposed method has the potential to be applied to complex geometric crack bodies.
Yunhe ZHAO , Shengnan WANG . Solution to stress intensity factor by weight function method based on deep learning[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(19) : 228367 -228367 . DOI: 10.7527/S1000-6893.2023.28367
| 1 | 崔德刚， 鲍蕊， 张睿， 等. 飞机结构疲劳与结构完整性发展综述［J］. 航空学报， 2021， 42（5）： 524394. |
| CUI D G， BAO R， ZHANG R， et al. Development of aircraft structural fatigue and structural integrity： Review［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（5）： 524394 （in Chinese）. | |
| 2 | 《飞机设计手册》总编委会.飞机设计手册（第9册）［M］. 北京： 航空工业出版社，2001. |
| “Aircraft Design Manual” Editorial Committee. Aircraft design manual （Volume 9） ［M］. Beijing： Aviation Industry Press， 2001 （in Chinese）. | |
| 3 | BUECKNER H F. A novel principle for the computation of stress intensity factors［J］. Zeitschrift fur Angewandte Mathematik und Mechanik， 1970， 50（9）： 529-546. |
| 4 | RICE J R. Some remarks on elastic crack-tip stress fields［J］. International Journal of Solids and Structures， 1972， 8（6）： 751-758. |
| 5 | WU X R， CARLSSON J. Weight functions and stress intensity factor solutions［M］. Oxford： Pergamon Press， 1991. |
| 6 | WU X R. Analytical wide-range weight functions for various finite cracked bodies［J］. Engineering Analysis with Boundary Elements， 1992， 9（4）： 307-322. |
| 7 | FETT T， MUNZ D. Stress intensity factors and weight functions［M］. Southampton： Computational Mechanics Publications， 1997. |
| 8 | FETT T. Direct determination of weight functions from reference loading cases and geometrical conditions［J］. Engineering Fracture Mechanics， 1992， 42（3）： 435-444. |
| 9 | GLINKA G， SHEN G. Universal features of weight functions for cracks in mode I［J］. Engineering Fracture Mechanics， 1991， 40（6）： 1135-1146. |
| 10 | SHEN G， GLINKA G. Weight functions for a surface semi-elliptical crack in a finite thickness plate［J］. Theoretical and Applied Fracture Mechanics， 1991， 15（3）： 247-255. |
| 11 | WU X R， TONG D H. Evaluation of various analytical weight function methods base on exact K-solutions of an edge-cracked circular disc［J］. Engineering Fracture Mechanics， 2018， 189： 64-80. |
| 12 | WU X R， TONG D H， ZHAO X C， et al. Review and evaluation of weight functions and stress intensity factors for edge-cracked finite-width plate［J］. Engineering Fracture Mechanics， 2018， 195： 200-221. |
| 13 | OJDROVIC R P， PETROSKI H J. Weight functions from multiple reference states and crack profile derivatives［J］. Engineering Fracture Mechanics， 1991， 39（1）： 105-111. |
| 14 | BRENNAN F P. Evaluation of stress intensity factors by multiple reference state weight function approach［J］. Theoretical and Applied Fracture Mechanics， 1994， 20（3）： 249-256. |
| 15 | 吴学仁， 童第华， 徐武. 断裂力学的权函数理论与应用［M］. 北京： 航空工业出版社， 2019. |
| WU X R， TONG D H， XU W. Weight function methods in fracture mechanics： Theory and applications［M］. Beijing： Aviation Industry Press， 2019 （in Chinese）. | |
| 16 | FETT T. Stress intensity factors， T-stresses， weight functions［M］. Karlsruhe： Schriftenreihe des Instituts für Keramik im Maschinenbau， 2008. |
| 17 | 王建春， 晋国栋. 机器学习在力学模拟与控制中的应用专题序［J］. 力学学报， 2021， 53（10）： 2613-2615. |
| WANG J C， JIN G D. Application of machine learning in mechanical simulation and control［J］. Chinese Journal of Theoretical and Applied Mechanics， 2021， 53（10）： 2613-2615 （in Chinese）. | |
| 18 | 谢建新， 宿彦京， 薛德祯， 等. 机器学习在材料研发中的应用［J］. 金属学报， 2021， 57（11）： 1343-1361. |
| XIE J X， SU Y J， XUE D Z， et al. Machine learning for materials research and development［J］. Acta Metallurgica Sinica， 2021， 57（11）： 1343-1361 （in Chinese）. | |
| 19 | RAJENDRA P， GIRISHA A， GUNAVARDHANA NAIDU T. Advancement of machine learning in materials science［J］. Materials Today： Proceedings， 2022， 62： 5503-5507. |
| 20 | LIU X， ATHANASIOU C E， PADTURE N P， et al. A machine learning approach to fracture mechanics problems［J］. Acta Materialia， 2020， 190： 105-112. |
| 21 | LIU T W， SUN S W， LIU H， et al. A predictive deep-learning approach for homogenization of auxetic kirigami metamaterials with randomly oriented cuts［J］. Modern Physics Letters： B， 2021， 35（1）： 2150033. |
| 22 | XIAO Q Z， KARIHALOO B L. Approximate Green’s functions for singular and higher order terms of an edge crack in a finite plate［J］. Engineering Fracture Mechanics， 2002， 69（8）： 959-981. |
| 23 | SHIVAKUMAR V， FORMAN R G. Green’s function for a crack emanating from a circular hole in an infinite sheet［J］. International Journal of Fracture， 1980， 16（4）： 305-316. |
| 24 | JIN X C， ZENG Y J， DING S D， et al. Weight function of stress intensity factor for single radial crack emanating from hollow cylinder［J］. Engineering Fracture Mechanics， 2017， 170： 77-86. |
| 25 | 赵晓辰， 吴学仁， 童第华， 等. 无限板孔边裂纹问题的高精度解析权函数解［J］. 航空学报， 2018， 39（9）： 221987. |
| ZHAO X C， WU X R， TONG D H， et al. Accurate analytical weight function solutions for crack at edge of circular hole in infinite plate［J］. Acta Aeronautica et Astronautica Sinica， 2018， 39（9）： 221987 （in Chinese）. |
/
| 〈 |
|
〉 |
CJA