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Structural Engineering and Mechanics
  Volume 74, Number 2, April25 2020, pages 227-241

Bi-axial and shear buckling of laminated composite rhombic hypar shells
Abhay K. Chaubey, Shubham Raj, Pratik Tiwari, Ajay Kumar, Anupam Chakrabarti and K.K. Pathak

    The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C0 finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.
Key Words
    buckling; composite; finite element method; skew hypar shell
Abhay K. Chaubey: Department of Civil Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram-522502, India
Shubham Raj, Ajay Kumar: Department of Civil Engineering, National Institute of Technology Patna, Patna-800005, India
Pratik Tiwari: Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, Kharagpur-721302, India
Anupam Chakrabarti: Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, India
K.K. Pathak: Department of Civil Engineering, Indian Institute of Technology (BHU), Varanasi-221005, India

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