0
Research Papers

Local Stress-Field Reconstruction Around Holes in a Plate Using Strain Monitoring Data and Stress Function

[+] Author and Article Information
Toshiya Nakamura

Structures and Advanced Composite
Research Unit,
Aeronautical Technology Directorate,
Japan Aerospace Exploration Agency (JAXA),
Osawa, Mitaka 1810015, Tokyo, Japan
e-mail: nakamura.toshiya@jaxa.jp

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 25, 2018; final manuscript received November 30, 2018; published online December 24, 2018. Assoc. Editor: Junlan Wang.

J. Appl. Mech 86(3), 031005 (Dec 24, 2018) (8 pages) Paper No: JAM-18-1605; doi: 10.1115/1.4042135 History: Received October 25, 2018; Revised November 30, 2018

This study reconstructs a two-dimensional stress field from measured strain data. The advantage of using stress functions is that the stress equilibrium and strain compatibility are automatically satisfied. We use the complex stress functions given by the finite series of polynomials. Then, we find the proper set of coefficients required to make the best fit to the measured strain data. Numerical examples represent the stress concentration problems around a hole(s) in a plate. It is demonstrated that the present method reconstructs the stress field around the hole(s), and the estimated stress agrees with the finite element (FE) analysis result.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Murayama, H. , Tachibana, K. , Hirano, Y. , Igawa, H. , Kageyama, K. , Uzawa, K. , and Nakamura, T. , 2012, “ Distributed Strain and Load Monitoring of 6m Composite Wing Structure by FBG Arrays and Long-Length FBGs,” Proc. SPIE, 8421, p. 84212D.
Igawa, H. , Murayama, H. , Kasai, T. , Yamaguchi, I. , Kageyama, K. , and Ohta, K. , 2005, “ Measurements of Strain Distributions With a Long Gauge FBG Sensor Using Optical Frequency Domain Reflectometry,” Proc. SPIE, 5855, pp. 547–550.
Igawa, H. , Ohta, K. , Kasai, T. , Yamaguchi, I. , Murayama, H. , and Kageyama, K. , 2008, “ Distributed Measurements With a Long Gauge FBG Sensor Using Optical Frequency Domain Reflectometry (1st Report, System Investigation Using Optical Simulation Model),” J. Solid Mech. Mater. Eng., 2(9), pp. 1242–1252. [CrossRef]
Wada, D. , Igawa, H. , and Kasai, T. , 2016, “ Vibration Monitoring of a Helicopter Blade Model Using the Optical Fiber Distributed Strain Sensing Technique,” Appl. Opt., 55(25), pp. 6953–6959. [CrossRef] [PubMed]
Wada, D. , Igawa, H. , Tamayama, M. , Kasai, T. , Arizono, H. , Murayama, H. , and Shiotsubo, K. , 2018, “ Flight Demonstration of Aircraft Fuselage and Bulkhead Monitoring Using Optical Fiber Distributed Sensing System,” Smart Mater. Struct., 27(2), p. 025014. [CrossRef]
Wada, D. , Igawa, H. , Tamayama, M. , Kasai, T. , Arizono, H. , and Murayama, H. , “ Flight Demonstration of Aircraft Wing Monitoring Using Optical Fiber Distributed Sensing System,” Smart Mater. Struct., (in press). http://iopscience.iop.org/article/10.1088/1361-665X/aae411
Nakamura, T. , Igawa, H. , and Kanda, A. , 2012, “ Inverse Identification of Continuously Distributed Loads Using Strain Data,” Aerosp. Sci. Technol., 23(1), pp. 75–84. [CrossRef]
Nakamura, T. , 2016, “ Estimation of Dynamic Load on a Beam Using Central-Difference Scheme and FEM,” AIP Conf. Proc., 1798, p. 020108.
Maniatty, A. , Zabaras, N. , and Stelson, K. , 1989, “ Finite Element Analysis of Some Inverse Elasticity Problems,” J. Eng. Mech., 115(6), pp. 1303–1317. [CrossRef]
Maniatty, A. , and Zabaras, N. , 1994, “ Investigation of Regularization Parameters and Error Estimating in Inverse Elasticity Problems,” Int. J. Numer. Methods Eng., 37(6), pp. 1039–1052. [CrossRef]
Schnur, D. S. , and Zabaras, N. , 1990, “ Finite Element Solution of Two-Dimensional Inverse Elastic Problems Using Spatial Smoothing,” Int. J. Numer. Methods Eng., 30(1), pp. 57–75. [CrossRef]
Shkarayev, S. , Krashantisa, R. , and Tessler, A. , 2004, “ An Inverse Interpolation Method Utilizing In-Flight Strain Measurements of Determining Loads and Structural Response of Aerospace Vehicles,” NASA Langley Research Center, Hampton, VA, Report No. 20040086071. https://ntrs.nasa.gov/search.jsp?R=20040086071
Coates, C. W. , and Thamburaj, P. , 2008, “ Inverse Method Using Finite Strain Measurements to Determine Flight Load Distribution Functions,” AIAA J. Aircr., 45(2), pp. 366–370. [CrossRef]
Kirby, G. C. , Lim, T. W. , Weber, R. , Bosse, A. B. , Povich, C. , and Fisher, S. , 1997, “ Strain Based Shape Estimation Algorithms for Cantilever Beam,” Proc. SPIE, 3041, pp. 788–798.
Tessler, A. , and Spangler, J. , 2003, “ A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells,” NASA Langley Research Center, Hampton, VA, Report No. NASA/TM-2003-212445. https://ntrs.nasa.gov/search.jsp?R=20030068121
Tessler, A. , and Spangler, J. , 2004, “ Inverse FEM for Full-Field Reconstruction of Elastic Deformation in Shear Deformable Plates and Shells,” Second European Workshop on Structural Health Monitoring, Munich, Germany, July 7–9.
Vazquez, S. L. , Tessler, A. , Parks, J. , and Spangler, J. , 2005, “ Structural Health Monitoring Using High-Density Fiber Optic Strain Sensor and Inverse Finite Element Methods,” NASA Langley Research Center, Hampton, VA, Report No. NASA/TM-2005-213761. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050185211.pdf
Kefal, A. , Tessler, A. , and Oterkus, E. , 2018, “ An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells,” NASA Langley Research Center, Hampton, VA, Report No. NASA/TP-2018-220079. https://ntrs.nasa.gov/search.jsp?R=20180004525
Sadd, M. H. , 2014, Elasticity, 3rd ed., Academic Press, Cambridge, MA.
Sokolnikoff, I. S. , 1955, Mathematical Theory of Elasticity, 2nd ed., McGraw-Hill, New York.
Savin, G. N. , 1970, “ Stress Distribution Around Holes,” NASA, NASA Langley Research Center, Hampton, VA, Report No. NASA TT F-607. https://archive.org/details/nasa_techdoc_19710000647
Woo, C. W. , and Chan, L. W. S. , 1992, “ Boundary Collocation Method for Analyzing Perforated Plate Problems,” Eng. Fract. Mech., 43(5), pp. 757–768. [CrossRef]
Sobey, A. J. , 1964, “ The Estimation of Stresses Around Unreinforced Holes in Infinite Elastic Sheets,” Aeronautical Research Council/Ministry of Aviation, London, Reports No. 3354. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.227.1892&rep=rep1&type=pdf
Newman, J. C. , 1971, “ An Improved Method of Collocation for the Stress Analysis of Cracked Plates With Various Shaped Boundaries,” NASA Langley Research Center, Hampton, VA, Report No. NASA TN D-6376. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710022830.pdf
Wu, B. , Cartwright, D. J. , and Collins, R. A. , 1994, “ The Boundary Collocation Method for Stress Intensity Factors of Cracks at Internal Boundaries in a Multiply Stiffened Sheet,” Trans. Eng. Sci., 6, pp. 497–504.
Sharma, D. S. , 2011, “ Stress Concentration Around Circular/Elliptical/Triangular Cutouts in Infinite Composite Plate,” World Congress on Engineering, Vol. III, London, July 6–8, pp. 2626–2631.
Pan, Z. , Cheng, Y. , and Liu, J. , 2013, “ Stress Analysis of a Finite Plate With a Rectangular Hole Subjected to Uniaxial Tension Using Modified Stress Functions,” Int. J. Mech. Sci., 75, pp. 265–277. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

A plate with L contours

Grahic Jump Location
Fig. 2

Plate with a square hole (solid points show the measurement points)

Grahic Jump Location
Fig. 3

Effect of size of sensor circle on RMSPE

Grahic Jump Location
Fig. 4

Effect of the max. exponent of ϕ on RMSPE

Grahic Jump Location
Fig. 5

Estimation of Mises stress (square hole)

Grahic Jump Location
Fig. 6

Reconstruction of Mises stress distribution (square hole)

Grahic Jump Location
Fig. 7

Reconstruction of local Mises stress distribution (square hole): (a) finite element analysis (FEA) result and (b) reconstructed result

Grahic Jump Location
Fig. 8

Estimation of stresses on outer boundary (square hole)

Grahic Jump Location
Fig. 9

Plate with two holes (solid points are the measurement points)

Grahic Jump Location
Fig. 10

Estimation of Mises stress (two holes)

Grahic Jump Location
Fig. 11

Reconstruction of Mises stress distribution (two holes)

Grahic Jump Location
Fig. 12

Reconstruction of local Mises stress distribution around the right hole: (a) FEA result and (b) reconstructed result

Grahic Jump Location
Fig. 13

Estimation of stresses on outer boundary (two holes)

Grahic Jump Location
Fig. 14

Estimation of Mises stresses at all nodes (the edges of two holes are fixed)

Grahic Jump Location
Fig. 15

Reconstruction of Mises stress distribution (the edges of two holes are fixed)

Grahic Jump Location
Fig. 16

Reconstruction of local Mises stress distribution around the right hole): (a) FEA result and (b) reconstructed result

Grahic Jump Location
Fig. 17

Estimation with measurement error (Monte Carlo simulation)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In