Accurate and efficient thermal stress analyses of functionally graded solids using incompatible graded finite elements

Functionally graded materials have found a wide usage in high temperature applications. The smooth transition from one material to another, in graded materials, may reduce thermal stresses, residual stresses and stress concentration factors as well as utilize properties of both materials. To perform accurate and efficient finite element analysis for heat transfer and transient thermal stress analyses in two-dimensional functionally graded materials, incompatible graded finite elements are developed and verified. User-defined subroutines in ABAQUS are developed to address the gradation of material properties within an element. An emphasis is made on an incompatible six-node graded finite element (QM6)which is accurate and efficient compared to linear four-node (Q4)and quadratic eight-node (Q8)elements. With the help of posteriori error estimation, a critical comparison is made among three types of solid elements. Modified 6-node (QM6)incompatible graded elements provide better accuracy than Q4 elements and take less computational time than Q8 elements, thereby showing QM6 as an optimal element for engineering analysis.