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

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Abstract

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.

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Abbreviations

X (X t or X c):

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

Y (Y t or Y c):

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

Z (Z t or Z c):

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

E 1, E 2, and E 3 :

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

G 12, G 13, and G 23 :

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

σDN :

peel strength equal to the tensile normal transverse strength of lamina

σDS :

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

L :

Lift force

X 0 :

Distance of the section from the leading edge

X ac :

Distance of the aerodynamic centre from the leading edge

M :

Moment at any section from the leading edge

M ac :

Moment about aerodynamic centre

C lα :

Slope of the lift curve

C mac :

Coefficient of moment about aerodynamic centre

αmax :

Maximum angle of attack

q :

Dynamic pressure

q′:

Net shear flow

S :

Planform area of wing

u, v, and w :

Displacements in x, y, and z directions respectively

σ x , σ y , σ z :

Normal Stress in x, y, and z directions respectively

τ xy , τ xz , and τ yz :

Shear Stresses in planes x–y, x–z, and y–z

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Authors and Affiliations

  1. Department of Aerospace Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham (University), Amrita Nagar P.O., Ettimadai, Coimbatore, 641112, Tamil Nadu, India

    V. Sivakumar, R. K. Arjun, V. Ishwarya, S. Nithya, Sreeja Sunder & B. N. Thilak

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  1. V. Sivakumar
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  2. R. K. Arjun
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  3. V. Ishwarya
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  4. S. Nithya
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  5. Sreeja Sunder
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  6. B. N. Thilak
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Correspondence to V. Sivakumar.

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Sivakumar, V., Arjun, R.K., Ishwarya, V. et al. Optimization of Cut-Out Shape on Composite Plate Under In-Plane Shear Loading. J Fail. Anal. and Preven. 12, 204–213 (2012). https://doi.org/10.1007/s11668-012-9553-5

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  • DOI: https://doi.org/10.1007/s11668-012-9553-5

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