Large deflections of non-linear bi-modulus functionally graded beams under different boundary and loading conditions

Abstract

The use of functionally graded materials (FGMs) is increasing thanks to recent development in manufacturing technologies. FGMs are considered a members of composites families in which material properties vary depending on a specific function through a desired direction. The variation of the material property could be one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D). However, this study examines axial, transverse, and bi-directional material compositions. Moreover, the large deflection of beams made of non-linearly elastic, generalized (or modified) Ludwick type of materials and FGMs have received considerable critical attention in recent years. Generalized Ludwick's constitutive law, an empirical equation derived from Hooke's law, defines the constitutive relation of non-linearly elastic materials. In addition, bi-modulus materials are the materials that respond differently in tension and compression due to having different Young's moduli in tension and compression. Large deflections of generalized Ludwick type non-linearly elastic, bi-modulus, functionally graded, non-prismatic, Euler-Bernoulli cantilever beams subjected to a concentrated force at the free end are examined numerically in this study.