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

2021 ◽  
pp. 1-17
Author(s):  
Vikas Goyat ◽  
Suresh Verma ◽  
R.K. Garg

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.

2017 ◽  
Vol 20 (K3) ◽  
pp. 119-125
Author(s):  
Bang Kim Tran ◽  
Huy The Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong

Functionally graded material is of great importance in many engineering problems. Here the effect of multiple random inclusions in functionally graded material (FGM) is investigated in this paper. Since the geometry of entire model becomes complicated when many inclusions with different sizes appearing in the body, a methodology to model those inclusions without meshing the internal boundaries is proposed. The numerical method couples the level set method to the extended finite-element method (X-FEM). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of random inclusions. Numerical examples are presented to demonstrate the accuracy and potential of this technique. The obtained results are compared with available refered results and COMSOL, the finite element method software.


2015 ◽  
Vol 137 (6) ◽  
Author(s):  
M. Jabbari ◽  
A. R. Barati

An analytical study of the piezothermoelastic behavior of a functionally graded material (FGM) hollow sphere with integrated piezoelectric layers as a sensor and actuator under the effect of radially symmetric thermo-electro-mechanical loading is carried out. The material properties of the FGM layer are assumed to be graded in the radial direction according to a power law function. Governing differential equations are developed in terms of the components of the displacement field, the electric potential and the temperature of each layer of the smart FGM hollow sphere. The resulting differential equations are solved analytically. Numerical examples are given and discussed to show the significant influence of grading index of material properties and feedback gain on the mechanical–electrical responses. This will be useful for modern engineering design.


2016 ◽  
Vol 58 (3) ◽  
pp. 260-268 ◽  
Author(s):  
Hassan S. Hedia ◽  
Saad M. Aldousari ◽  
Noha Fouda

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