The dual-axis buckling of Laminated composite skew hyperbolic paraboloid with cutouts subjected to the in-plane biaxial and the shear load is investigated for various boundary conditions using the present mathematical model. Variation of transverse shear stresses is represented by a second-order function across the thickness, and the cross-curvature effect is also included via strain relations. The transverse shear stress-free condition at the shell top and bottom surfaces is also satisfied. This mathematical model (having a realistic second-order 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 skew hyperbolic paraboloids with cutouts. 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 biaxial and shear buckling of laminated composite skew hyperbolic paraboloids. A C 0 finite element coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc.

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Motivated by the works on non-gradient techniques in the domain of shape optimization of the structure, the present work intends to suggest a novel non-gradient procedure for shape optimization of structures and compare it to an existing gradient-based method. The presented technique optimizes the shape of structural parts using a fuzzy controlled integrated zero-order methodology incorporating the notion of design elements and automated mesh construction with mesh refinement at each iteration. The movement of nodes and convergence monitoring is taken care of using the triangular fuzzy membership function. The changes in shape occur according to the selected target maximum shear stress (σt) with a view of reaching as near to the target as possible at all the points. The present methodology is packaged in a piece of software termed GSO (Gradientless shape optimization) coded in FORTRAN language. To explain the efficacy of the current approach, a few basic structural shapes have been optimized under various constraints, and the results of the same are compared to those obtained using Optistruct (a part of software suite HyperWorks from Altair engineering), which works on gradient descent method. The proposed approach works well and produces more industry fabricable results than what is produced by the gradient descent method in Optistruct.

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