Level Set function-based Functionally Graded Material for the reduction of maximum stresses around a pair of inclined unequal circular holes

Abstract

OBJECTIVE: The aim of this work is to present the methodology for grading the Functionally Graded Material (FGM) using Level Set (LS) sign distance function around the multiple holes and parametrically analyse the maximum stresses for a pair of inclined unequal circular holes surrounded by the FGM layer in an infinite plate subjected to uniaxial tensile load using the Extended Finite Element Method (XFEM). METHODS: The LS method has the ability to represent the multiple geometrical boundaries with a single sign distance function which can be effectively used for grading the FGM around the multiple discontinuities such as holes, inclusions, cracks, etc. When dealing with FGM material grading around multiple discontinuities, it is important to have smooth grading to minimise the stress concentration. The grading of the material with multiple functions may result in sharp changes in the material properties at the interference region which may lead to high stresses. The LS function-based FGM material grading eliminates such sharp changes as it uses a single function. RESULTS: The parametric analysis shows that applying the LS function-based power law FGM layer of Titanium – Titanium Mono Boride (Ti-TiB) around the pair of inclined unequal circular holes significantly reduces the values of maximum tensile as well as compressive hoop stresses when compared with the homogeneous material case.