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In the presented paper, a study of bi-axial buckling of the laminated composite plate with mass variation through the cutout and additional mass is carried out using the improved shear deformation theory (ISDT). The ISDT mathematical model employs a cubic variation of thickness co-ordinates in the displacement field. A realistic parabolic distribution of transverse shear strains through the plate thickness is assumed and the use of shear correction factor is avoided. A C° finite element formulation of the mathematical model is developed to analyze the buckling behavior of laminated composite plate with cutout and additional mass. As no results based on ISDT for the considered problem of bi-axial buckling of the laminated composite plate with mass variation are available in the literature, the obtained results are validated with the data available for a laminated composite plate without cutout and additional mass. Novel results are obtained by varying geometry, boundary conditions and ply orientations.

The present paper is the first study on the hygrothermal analysis (i.e., effect of temperature and moisture loadings) of laminated composite skew conoids with reasonable depth and thickness. In order to solve the hygrothermal problem of laminated composite skew conoids, the cubic variation in displacement field, along with cross curvature effects of the shell, were considered. In the present analysis, the shear correction factor is not needed due to the parabolic variation of transverse shear strain. The zero transverse shear stress conditions at the top and bottom of the shell were imposed in the mathematical model. The novelty of our model is reflected by the simultaneous addition of twist curvature in the strain field, as well as the curvature in the displacement field allowing the reasonably thick and deep laminated composite rhombic conoid. The conoid behavior differs from the usual shells, like cylindrical or spherical ones, due to its inherent twist curvature with the complex geometry and different location of maximum deflection. The finite element (FE) implementation of the present realistic mathematical model was carried out using a nine-noded curved isoparametric element with seven unknowns at each node. The C⁰ FE implementation of the present mathematical model was done and coded in FORTRAN. The present model results were compared and found in good agreement with other solutions published in the literature. Hygrothermal analysis was performed for skew conoids having a different skew angle, temperature, moisture concentration, curvatures, ply orientation, thickness ratio, and boundary conditions.