Journal of Failure Analysis and Prevention

, Volume 12, Issue 2, pp 204–213 | Cite as

Optimization of Cut-Out Shape on Composite Plate Under In-Plane Shear Loading

  • V. Sivakumar
  • R. K. Arjun
  • V. Ishwarya
  • S. Nithya
  • Sreeja Sunder
  • B. N. Thilak
Technical Article---Peer-Reviewed


The wing in flight condition is subjected to heavy aerodynamic loads that in turn lead to a shear flow over the wing ribs that support it. Cut-outs change the mechanical behavior of plates, as they redistribute the stresses and are influenced by the shape of the cut-out. A three-dimensional displacement-based finite element analysis is performed to study the symmetric, laminated composite plate of 20 layers. The analysis is performed to obtain the in-plane and out of plane performances of the laminate. Five basic cut-out geometries, viz., circle, square, diamond, ellipse with major axis along the y-axis, and another ellipse with major axis along the x axis were used for the numerical analysis. A cut-out geometry is generated based on the results of analyses performed on five basic geometries to optimize the performance. The optimized cut-out is associated with the least Tsai-Hill and Hashin failure index as compared with the five basic geometries.


Cut-out Composite Optimization 

List of symbols

X (Xt or Xc)

Normal strength (tensile or compressive, respectively) of lamina in fiber direction-1

Y (Yt or Yc)

Normal strength (tensile or compressive, respectively) of lamina in direction transverse to the fiber direction-1

Z (Zt or Zc)

Normal strength (tensile or compressive, respectively) of lamina in principal material direction-3, i.e., perpendicular to plane of lamina

R, S, and T

Shear strengths of lamina in-planes 2–3, 1–3, and 1–2, respectively

σ1, σ2, and σ3

Normal stress components in principal material directions 1, 2, and 3, respectively (the subscript 1 referring to the fiber direction)

τ12, τ13, and τ23

Shear stress components in principal material planes 1–2, 1–3, and 2–3, respectively

E1, E2, and E3

Principal Young’s moduli in fiber direction and other two transverse directions, respectively

G12, G13, and G23

Shear moduli associated with planes 1–2, 1–3, and 2–3, respectively

ν12, ν13, and ν23

Poisson’s ratios associated with planes 1–2, 1–3, and 2–3, respectively


peel strength equal to the tensile normal transverse strength of lamina


Inter-laminar shear strength equal to transverse shear strength corresponding to the plane 1–3 of lamina


Lift force


Distance of the section from the leading edge


Distance of the aerodynamic centre from the leading edge


Moment at any section from the leading edge


Moment about aerodynamic centre


Slope of the lift curve


Coefficient of moment about aerodynamic centre


Maximum angle of attack


Dynamic pressure


Net shear flow


Planform area of wing

u, v, and w

Displacements in x, y, and z directions respectively

σx, σy, σz

Normal Stress in x, y, and z directions respectively

τxy, τxz, and τyz

Shear Stresses in planes xy, xz, and yz


  1. 1.
    Jafari, M., Rezaeepazhand, J.: Stress concentration in metallic plates with special shaped cut-out. Int. J. Mech. Sci. 52, 96–102 (2010)CrossRefGoogle Scholar
  2. 2.
    Rao, K.P., Pandey, R., Thakur, S., Ramanath, K.S.: Stress Concentration and Stability Studies in Composite Ribs with Flanged Cut-Outs. CAE Group, Infosys Technologies, Bangalore (2001)Google Scholar
  3. 3.
    Guo, S.J.: Stress concentration and buckling behaviour of shear loaded composite panels. Compos. Struct. 80, 1–9 (2007)CrossRefGoogle Scholar
  4. 4.
    Ghannadpour, S.A.M., Najafi, A., Mohammadi, B.: On the buckling behavior of cross-ply laminated composite plates due to circular/elliptical cut-outs. Compos. Struct. 75, 3–6 (2006)CrossRefGoogle Scholar
  5. 5.
    Guo, S., Morishima, R., Zhang, X., Mills, A.: Cut-out shape and reinforcement design for composite c-section beams under shear load. Compos. Struct. 88, 179–187 (2009)CrossRefGoogle Scholar
  6. 6.
    Dinesh Kumar, A., Singh, S.B.: Post-buckling strengths of composite laminate with various shaped cut-outs under in-plane shear. Compos. Struct. 92, 2966–2978 (2010)CrossRefGoogle Scholar
  7. 7.
    Sivakumar, V., Vinesh, D.: Analysis of composite laminated skew plate with elliptical cutout. Proceedings of 5th International Conference on Theoretical, Applied, Computational and Experimental Mechanics (ICTACEM 2010). Department of Aerospace Engineering, IIT Kharagpur, India. Paper No-288, ISBN. 978-93-80813-03-5 (2010)Google Scholar
  8. 8.
    ABAQUS V. 6.10, User’s Manual, Simulia, Dessault Systemes (2010)Google Scholar
  9. 9.
    Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, 2nd edn. CRC press, Boca Raton (2003)Google Scholar
  10. 10.
    Ochoa, O.O., Reddy, J.N.: Finite Element Analysis of Composite Laminate, pp. 125–128. Kluwer, Dordrecht (1992)Google Scholar
  11. 11.
    Nelson, R.C.: Flight Stability and Automatic Control, 2nd edn, pp. 416–417. McGraw Hill, New York (1997)Google Scholar

Copyright information

© ASM International 2012

Authors and Affiliations

  • V. Sivakumar
    • 1
  • R. K. Arjun
    • 1
  • V. Ishwarya
    • 1
  • S. Nithya
    • 1
  • Sreeja Sunder
    • 1
  • B. N. Thilak
    • 1
  1. 1.Department of Aerospace EngineeringAmrita School of Engineering, Amrita Vishwa Vidyapeetham (University)CoimbatoreIndia

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