Nonlinear Bending Analysis of Functionally Graded Beams with Spring Constraints and Thermal Effects

Abstract The nonlinear bending behavior of beams made up of functionally graded materials (FGM) is heavily influenced by boundary flexibility and thermo-mechanical coupling. However, most existing models assume conventional end conditions such as simply supported, clamped, or cantilevered beams, which may often be difficult to achieve in practice. This research presents the nonlinear static bending analysis of FGM beams with elastic boundary conditions that permit both translation and rotation, subjected to combined transverse loads and uniform heating. The governing equations are derived using von Karman geometric nonlinearity combined with first-order shear deformation theory, incorporating material gradation through a power law across the thickness. Effective properties are calculated using both the rule of mixtures and the Mori-Tanaka method. The results show how boundary stiffness, material gradation, and thermal effects influence the nonlinear load-deflection response, revealing differences from standard simply-supported and clamped boundary conditions. The comparison of the two material models illustrates variations in nonlinear behavior, especially under combined thermo-mechanical loading. Selected findings are verified through finite element simulations in ABAQUS, which agree well with the analytical results. The study underscores the importance of accurate boundary modeling and appropriate material homogenization for reliable nonlinear thermo-mechanical analysis of FGM beams.