Incompatible Graded Finite Elements for Orthotropic Nonhomogeneous Media

Orthotropic materials or composites are challenging to model due to different elastic properties in two in-plane directions, which requires sufficient mesh refinement to attain desired accuracy. In this regard, an accurate and efficient incompatible graded element is developed for modeling orthotropic functionally graded materials. Properties of Graded finite elements such as Young’s moduli (E11, E22), shear modulus (G12) and Poisson’s ratio (v12) vary. A new incompatible graded element is developed using user subroutines in Abaqus and are compared to available exact solutions. In this study, performance (QM6) graded element is compared with lower-order and higher-order compatible elements (Q4 and Q8) as well as linear triangular (T3) and quadratic triangular (T6) elements with aid of several numerical examples. Additionally, orthotropic graded plate with carbon fibers properties as well as a circular disc with orthotropic properties under internal pressure is included. Furthermore, a curved beam with radially graded properties under the bending moment is studied. Additionally, the performance of various graded elements is compared with analytical solutions using Russell error.