Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications

In this research, we consider solutions for the Euler-Bernoulli theory (CBT) and the theory of Timoshenko (TBT). It presents an innovative mixed finite element method tailored for analysing beams with functionally graded properties, focusing on their behaviour under bending loads. The method employs an isoparametric formulation in natural coordinates, enabling precise modelling of complex geometries common in structural engineering and materials science. A significant contribution is extending the mixed finite element approach to assess the bending behaviour of functionally graded beams. Hence, it is vital to understand material responses to external forces. To illustrate its effectiveness and versatility, we provide two numerical examples involving cantilever and simply-supported isotropic beams with property variations along the material's thickness, following power-law distributions. Additionally, a third example features a cantilever made from isotropic functionally graded material with quadratic property changes through the thickness. The method's robustness and credibility are established through rigorous validation against numerical and analytical solutions found in existing literature. This validation confirms the accuracy and reliability of the mixed finite element method for assessing functionally graded materials under bending conditions, enhancing its utility in structural analysis. This research introduces a potent numerical tool for investigating the behaviour of functionally graded materials subjected to bending, providing valuable implications for engineering and materials science applications.