A finite element formulation for creep buckling analysis of Al–SiC functionally graded beams

A geometrically nonlinear finite element formulation is applied for the creep buckling analysis of Al–SiC functionally graded beam-type structures. The formulation is based on a co-rotational beam finite element, enabling the local evaluation of elastic and creep material properties according to the prescribed material gradation. The time-dependent material behaviour is described by the Norton creep law, while the corresponding creep parameters are evaluated locally using experimentally validated constitutive relations available in the literature. The proposed formulation is validated through benchmark problems involving functionally graded beams and frames subjected to sustained mechanical loading. Buckling predictions are compared with MSC Nastran benchmark solutions, demonstrating the accuracy and robustness of the proposed formulation. The results demonstrate that both the magnitude and the spatial distribution of ceramic reinforcement strongly influence the long-term stability of functionally graded structures. Increasing the SiC volume fraction enhances both the elastic buckling resistance and the creep buckling lifetime, whereas increasing the material gradation index reduces the critical load and accelerates creep-induced instability. The proposed formulation provides a robust computational framework for predicting the long-term stability of functionally graded beam-type structures under sustained loading.