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.

Biaxial buckling of the laminated composite rhombic (skew) plate with mass variations in the form of openings and adding extra mass at the center of the plate was studied using improved shear deformation theory (ISDT). The ISDT mathematical model incorporates third-degree variation of the thickness coordinate in the displacement formulation. In the presented theory, the use of shear correction factor was eliminated and a second-order variation of transverse shear strains through the plate thickness was implied. A computer-based algorithm based on the $C_0$ finite-element formulation of the mathematical model was developed to analyze the buckling behavior of a laminated composite skew plate with openings and extra mass imposed at the center of the plate. Due to a lack of results in the literature based on the ISDT of the considered problem of biaxial buckling of laminated composite skew plates with openings cutout and extra mass imposed at the center of plate, the present results were validated with the suitable results available for laminated composite plates without openings/extra mass imposed at the center of plate with zero skew angle. The new results were obtained by varying the geometry, boundary conditions, ply orientations, and skew angles.