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First-ply Failure Analysis of Delaminated Rotating Composite Conical Shells: A Finite Element Approach

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Abstract

The present analysis evaluates the first-ply failure load of delaminated composite conical shells. Single and multiple delamination is considered across the thickness of the conical shell. The dynamic equilibrium equation considers only moderate rotational speeds for which Coriolis effect is neglected. Convergence studies are performed in respect of mesh sizes, and comparisons of the present solutions and those reported in open literature are provided to verify the accuracy of the present finite element formulation. Computer codes are developed to obtain the numerical results for the failure loads of delaminated composite conical shells. The first-ply failure load considering different failure criteria namely Maximum stress (independent), Tsai-Hill, Tsai-Wu-Hahn and Tsai-Hill-Hoffman are evaluated. The variation of the failure loads with the position of delamination across the thickness as well as along longitudinal direction are illustrated and presented.

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Abbreviations

[A], [B] and [D]:

Extension, bending extension coupling and bending stiffness coefficients matrix, respectively

{k}:

Curvature vectors

L, b0, h0 :

Length, reference width and thickness of the Conical shell, respectively

{N}, {M}:

In plane stress resultants and moment resultants, respectively

[Q]:

Transformed reduced stiffness matrix

Rx, Ry :

Radius of curvature in x and y direction, respectively

Rxy :

Radius of twist

S:

Slant length

\({\rm u}_{\rm j}^0, {\rm v}_{\rm j}^0, {\rm w}_{\rm j}^0\) :

Mid plane displacements of element j

α, β:

Minor and major radii at any cross section parallel to the reference ellipse, respectively

α0, β0 :

Minor and major radius of the reference ellipse, respectively

θv, θ0 :

Vertex angle and base subtended angle of cone, respectively

ξ, η:

Non dimensional coordinate systems

{ε0}:

Normal strain vector

Ω:

Non dimensional rotational speed

Ψ:

Twist angle

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Agartala, 799046, Tripura, India

    Ankuran Saha

  2. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, West Bengal, India

    Apurba Das & Amit Karmakar

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  1. Ankuran Saha
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Correspondence to Ankuran Saha.

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Saha, A., Das, A. & Karmakar, A. First-ply Failure Analysis of Delaminated Rotating Composite Conical Shells: A Finite Element Approach. J. Inst. Eng. India Ser. C 99, 657–672 (2018). https://doi.org/10.1007/s40032-017-0373-y

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