Biaxial and shear buckling of laminated composite elliptic paraboloids with cutouts and concentrated mass

The buckling of laminated elliptic paraboloids with cutouts and concentrated mass subjected to the in-plane bi-axial and the shear load is investigated for various boundary conditions using present mathematical model. Transverse shear stresses are represented by a parabolic function across the thickness and the cross curvature effect 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 parabolic distribution of transverse shear strains across the thickness of shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine node curved isoparametric element is used. So far, no solution exists in the literature for dual axis buckling problem of laminated composite elliptic paraboloids with cutouts and concentrated mass. As no result is available for the present problem, the present model is compared with suitable published results and then it is extended to analyze bi-axial and shear buckling of laminated composite elliptic paraboloids. A C° finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, lamination schemes etc.