Static analyses of FGM beams by various theories and finite elements

Abstract

The 1D Carrera Unified Formulation (CUF) is here used to perform static analyses of functionally graded (FG) structures. The hierarchical feature of CUF allows one to automatically generate an infinite number of displacement theories that may include any kind of functions of the cross-section coordinates (x, z), among which those used to describe the variation of the mechanical properties of FG materials. The governing equations are derived by means of the Principle of Virtual Displacements in a weak form and solved by means of the Finite Element method (FEM). The equations are written in terms of “fundamental nuclei”, whose forms do not depend on the used expansions. Trigonometric, polynomial, exponential and miscellaneous expansions are here used and evaluated for various structural problems. Resulting theories are assessed by considering several aspect-ratios, gradation laws, loading and boundary conditions. The results are compared with 1-, 2- and 3-D solutions both in terms of displacements and stress distributions. The comparisons confirm that the 1D CUF elements are valuable tools for the study of FG structures.