### International Journal of Mathematical, Engineering and Management Sciences

#### ISSN: 2455-7749 . Open Access

Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer

#### Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer

Pushpa Rani
Department of Mathematics, NIILM University, Kaithal, Haryana, India.

Dinesh Verma
Department of Mathematics, NIILM University, Kaithal, Haryana, India.

Gyander Ghangas
Department of Mechanical Engineering, SRM Institute of Science and Technology, Delhi NCR Campus, Ghaziabad, Uttar Pradesh, India.

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Accepted on January 02, 2023

Abstract

The aim of the present work is to model and analyze stresses around rounded rectangular inclusion enclosed with functionally graded material (FGM) layer. The inclusion has been considered in an infinite plate which is subjected to far-field tensile stress. The extended finite element method (XFEM) has been used to model the inclusion with non-conformal mesh. The level set functions of circular and rectangular shapes have been used to trace the inclusion boundary with mesh. The FGM has been considered as continuous varying mixture of inclusion and plate materials with power law function along normal direction to the inclusion interface. Young's modulus has been assumed to vary within FGM layer, whereas Poisson's ratio is kept constant. The stress distribution and stress concentration factor (SCF) have been analyzed for different geometrical and FGM parameters. It has been observed that XFEM with level set method efficiently model the difficult shape inclusions such as rounded rectangle. Applying the FGM layer smoothens the stress distribution around rounded rectangular inclusion and significantly reduces SCF. The position of maximum stress shifted from the inclusion interface toward the FGM layer interface. The least SCF has been noted with power law index n = 0.5 and FGM layer thickness t = r.

Keywords- Inclusion, Functionally graded material, Extended finite element method, Level-set method.

Citation

Rani, P., Verma, D., & Ghangas, G. (2023). Modeling and Stress Analysis of Rounded Rectangular Inclusion Enclosed by FGM Layer. International Journal of Mathematical, Engineering and Management Sciences, 8(2), 282-293. https://doi.org/10.33889/IJMEMS.2023.8.2.017.