Coupled thermo-mechanical bending and vibration responses of Porous Multidirectional Circular Functionally graded (PMCF) plate: An isogeometric analysis

Multidirectional structural analysis plays a critical role in meeting performance requirements such as temperature distribution, vibration control, and stress management in multiple directions, particularly for advanced engineering applications. This work investigates the bending and vibration responses of a porous multidirectional circular functionally graded (PMCF) plate using the Isogeometric analysis (IGA) framework. The spatial variation of the material properties within the plate is modeled using a modified power-law distribution, enabling accurate representation of the gradation in both radial and thickness directions. The equations that govern the system are formulated based on the Mindlin–Reissner plate theory using energy principles. To satisfy the continuity requirements inherent to the FSDT model, improved inter-element continuity properties of Non-Uniform Rational B-Spline (NURBS) basis functions are leveraged within the IGA framework. The proposed numerical formulation is validated through comprehensive convergence and verification studies, confirming its effectiveness and accuracy. The Structural behavior in static and vibratory conditions of the PMCF plate is thoroughly investigated for a range of boundary conditions, porosity levels, material gradation profiles, and thermal loading cases. This work advances the analysis of functionally graded structures with complex, multidirectional property variations, providing a robust numerical tool for engineering design.