Nonlinear Bending, Buckling and Post-Buckling of Higher-Order Shear Deformable Porous Beams Subjected to Axially Varying Compressions and Linearly Varying Transverse Loadings

Abstract

Porous structural components, especially metal foam-based beams, are increasingly utilized in lightweight and high-performance engineering applications due to their superior energy absorption and weight reduction capabilities. However, their mechanical behavior under nonlinear deformation regimes remains insufficiently explored, particularly under complex loading conditions. This study aims to investigate the nonlinear bending, buckling, and post-buckling responses of porous metal foam beams based on higher-order shear deformation theory (HSDT). The analysis considers both uniform and three non-uniform porosity distributions, including axially varying compressive loadings and linearly varying transverse loads. The governing equations are derived using von K & aacute;rm & aacute;n-type nonlinear strain-displacement relations and solved via Galerkin's method. The results reveal that axially varying loading patterns, especially the A-DTG and A-DTR types, significantly enhance the structural performance across all deformation stages compared to uniform and point loadings. Among the porosity distributions, NUDP1 and NUDP3 generally improve the load-bearing capacity, while NUDP2 has a detrimental effect. Additionally, increasing the porosity coefficient reduces all load capacities, whereas higher slenderness and width-depth ratios yield distinct effects depending on the loading and deformation stage. These findings provide valuable insights for the design and optimization of porous beam elements subjected to nonuniform loading scenarios, highlighting the critical role of porosity distribution and geometrical parameters in determining the nonlinear mechanical response.