Isogeometric analysis in simulation of bending response multi-directional functionally graded variable-thickness porous plates

This study presents a powerful isogeometric analysis (IGA) framework for studying bending analysis of multi-directional functionally graded (MDFG) porous plates. For the first time, three distinct material distribution patterns, including power-law and two trigonometric functions, are employed to model MDFG porous variable-thickness plates of square, circular, and elliptical geometries. The methodology integrates the third-order shear deformation theory (TSDT) with isogeometric analysis (IGA), utilizing its ability to smoothly model complex geometries and efficiently handle thickness variations through parametric space mapping. Material properties are determined using the mixture rule and Mori–Tanaka method. The governing equations are derived via Hamilton’s principle. The proposed model and solution methodology are validated against existing literature and have a good agreement. Computational results confirm that material gradation patterns critically influence bending response. The investigation comprehensively studied the impact of varying gradation indices, porosity, and thickness on bending performance under fully clamped and fully simply supported boundary conditions. Numerical investigations demonstrate that placing the stiff ceramic precisely at the mid-regions of the top and bottom surfaces achieves best bending performance and lightweight. These results provide a powerful design blueprint. Practically, it sets a clear target for advanced manufacturing to achieve lighter, stiffer, and potentially more functionally versatile FGM plates. The proposed model is applicable to a range of engineering components including civil infrastructure, automotive sector, biomedical implants, sports equipment, and marine and aerospace structures.