A novel high order theory for static bending of functionally graded (FG) beams subjected to various mechanical loads

Abstract

This study develops a new higher-order shear deformation theory (HSDT) to analyze the static behavior of functionally graded (FG) beams under various mechanical loading conditions. The new theory is meticulously designed to effectively represent complexities in stress, strain, and deformation analysis, with a focus on maintaining or enhancing accuracy while reducing the computational burden for practical applications. The material properties of the FG beams are assumed to vary continuously across the thickness as per a power law distribution (P-FGM). The governing equilibrium equations are derived using the principle of virtual work. Navier’s solution method is then utilized to obtain the analytical solutions. Extensive numerical studies are conducted to study the influences of key geometric and material parameters on the static response. The deflection, axial stress and tangential stress distributions are computed for different combinations of length-to- thickness ratio, material grading index, and applied loads. The results are validated by comparison with existing literature where good agreement is observed, demonstrating the accuracy of the proposed HSDT formulation. Parametric analyses provide useful insights into the individual and coupled effects of beam slenderness, material inhomogeneity and transverse loading on the static performance of P-FGM beams. This study enhances understanding of the structural behavior of FG beams through an efficient and accurate analytical approach.