Structural health monitoring of precracked structures using an in-plane inverse crack-tip element

Abstract

This study investigates the application of the inverse finite element method (iFEM) in fracture mechanics by developing a novel two-dimensional six-node triangular inverse crack-tip element. With its simplified formulation, the proposed inverse element is computationally efficient and ensures strain singularity at the crack tip by repositioning midside nodes. Its displacement-based stress intensity factor (SIF) computation methodology integrates seamlessly with the existing iFEM framework, making it highly suitable for real-time health assessment of structures with preexisting cracks. The inverse element has been rigorously validated for shape-sensing and mixed-mode SIF calculations by considering various crack geometries and mixed-mode loading conditions. The triangular inverse element demonstrates superior flexibility in handling structured and unstructured discretizations in mapping regular and complex geometries, particularly high-stress gradient areas like crack tips. The study also explores the variational least squares method for optimal sensor placement within the inverse element domain, ensuring accurate shape-sensing and SIF computations with fewer onboard strain sensors. The proposed inverse formulation, with its accurate shape-sensing capabilities and precise reconstruction of fracture parameters, represents a significant advancement in the real-time Structural Health Monitoring of engineering structures with pre-existing cracks.

Keywords

structural health monitoring / stress intensity factor / shape-sensing / crack tip / iFEM

References

[1] Hassani S, Dackermann U. A systematic review of advanced sensor technologies for non-destructive testing and structural health monitoring. Sensors. 2023;23(4):2204.

[2] Ko WL, Richards WL, Tran VT. Displacement Theories for In-flight Deformed Shape Predictions of Aerospace Structures. NASA;2007.

[3] Ko WL, Richards WL, Fleischer VT. Applications of Ko DIsplacement Theory to the Deformed Shape Predictions of the Doubly-Tapered Ikhana Wing. NASA;2009.

[4] Gopinathan M, Pajunen GA, Neelakanta P, Arockaisamy M. Recursive estimation of displacement and velocity in a cantilever beam using a measured set of distributed strain data. J Intell Mater Syst Struct. 1995;6(4):537-549.

[5] Manola M, Koumousis V. Ultimate state of plane frame structures with piecewise linear yield conditions and multi-linear behavior: a reduced complementarity approach. Comput Struct. 2014;130:22-33.

[6] Foss G, Haugse E. Using modal test results to develop strain to displacement transformations. In: Proceedings of the 13th International Modal Analysis Conference. Vol 2460. NASA;1995:112.

[7] Pisoni AC, Santolini C, Hauf DE, Dubowsky S. Displacements in a vibrating body by strain gage measurements. Proceedings-SPIE the International Society for Optical Engineering. Citeseer;1995:119.

[8] Shkarayev S, Krashantisa R, Tessler A. An Inverse Interpolation Method Utilizing In-flight Strain Measurements for Determining Loads and Structural Response of Aerospace Vehicles. NASA Technical Reports Server (NTRS);2004.

[9] Tessler A, Spangler JL. A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells. NASA;2003.

[10] Kefal A, Oterkus E, Tessler A, Spangler JL. A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring. Eng Sci Technol Int J. 2016;19(3):1299-1313.

[11] Kefal A. An efficient curved inverse-shell element for shape sensing and structural health monitoring of cylindrical marine structures. Ocean Eng. 2019;188:106262.

[12] Kefal A, Oterkus E. Isogeometric iFEM analysis of thin shell structures. Sensors. 2020;20(9):2685.

[13] Dirik Y, Oterkus S, Oterkus E. Isogeometric Mindlin-Reissner inverse-shell element formulation for complex stiffened shell structures. Ocean Eng. 2024;305:118028.

[14] You R, Ren L, Yuan C, Song G. Two-dimensional deformation estimation of beam-like structures using inverse finite-element method: theoretical study and experimental validation. J Eng Mech. 2021;147(5):04021019.

[15] De Mooij C, Martinez M, Benedictus R. iFEM benchmark problems for solid elements. Smart Mater Struct. 2019;28(6):065003.

[16] Kefal A, Tessler A, Oterkus E. An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures. Compos Struct. 2017;179:514-540.

[17] Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Methods Eng. 1999;46(1):131-150.

[18] Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng. 2004;61(13):2316-2343.

[19] Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng. 2007;196(29-30):2777-2799.

[20] Jirásek M, Zimmermann T. Embedded crack model: I. Basic formulation. Int J Numer Methods Eng. 2001;50(6):1269-1290.

[21] Bai J, Rabczuk T, Gupta A, Alzubaidi L, Gu Y. A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics. Comput Mech. 2023;71(3):543-562.

[22] Nguyen-Thanh VM, Zhuang X, Rabczuk T. A deep energy method for finite deformation hyperelasticity. Eur J Mech-A/Solids. 2020;80:103874.

[23] Zargar SA, Yuan F-G. Physics-informed deep learning for scattered full wavefield reconstruction from a sparse set of sensor data for impact diagnosis in structural health monitoring. Struct Health Monit. 2024;23(5):2963-2979.

[24] Li M, Oterkus E, Oterkus S. A two-dimensional four-node quadrilateral inverse element for shape sensing and structural health monitoring. Math Mech Solids. 2024;29(7):1364-1378.

[25] Barsoum RS. Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int J Numer Methods Eng. 1977;11(1):85-98.

[26] Zhu N, Oterkus E. Calculation of stress intensity factor using displacement extrapolation method in peridynamic framework. J Mech. 2020;36(2):235-243.

[27] Timoshenko S, Goodier J. Theory of elasticity. Inc New York. 1951;1:35-39.

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2024 2024 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.