Influences of Porosity Distribution and Size-Dependent on Bending, Buckling, and Free Vibration of Bi-Directional FG Porous Microbeams With Variable Thickness and MLSPs Using the MSGT and IGA

Abstract

In this study, the bending, buckling, and free vibration analysis of bi-directional functionally graded porous microbeams with variable thickness are investigated. By utilizing the modified strain gradient theory (MSGT) in conjunction with a sinusoidal shear deformation theory, governing equations are derived using Hamilton's principle within the framework of the non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA). In addition, the C2-continuity requirement can be easily achieved by increasing the order of the NURBS basis functions. The MLSPs and the material properties of microbeams vary along with both thickness and axial directions based on the rule of mixture scheme. To consider the effects of porosity, two even and uneven distributions are considered. After verifying the accuracy of the presented approach, the influence of the aspect ratio, gradient indices, different boundary conditions, porosity parameters, variable MLSPs, and thickness on the bending, buckling, and free vibration characteristics of microbeams are investigated. © 2025 John Wiley & Sons Ltd.