Search results for: EFGM

Authors: Azher Jameel, Ghulam Ashraf Harmain

Abstract:

In the recent years, the enriched techniques like the extended finite element method, the element free Galerkin method, and the Coupled finite element-element free Galerkin method have found wide application in modeling different types of discontinuities produced by cracks, contact surfaces, and bi-material interfaces. The extended finite element method faces severe mesh distortion issues while modeling large deformation problems. The element free Galerkin method does not have mesh distortion issues, but it is computationally more demanding than the finite element method. The coupled FE-EFGM proves to be an efficient numerical tool for modeling large deformation problems as it exploits the advantages of both FEM and EFGM. The present paper employs the coupled FE-EFGM to model large elastoplastic deformations in bi-material engineering components. The large deformation occurring in the domain has been modeled by using the total Lagrangian approach. The non-linear elastoplastic behavior of the material has been represented by the Ramberg-Osgood model. The elastic predictor-plastic corrector algorithms are used for the evaluation stresses during large deformation. Finally, several numerical problems are solved by the coupled FE-EFGM to illustrate its applicability, efficiency and accuracy in modeling large elastoplastic deformations in bi-material samples. The results obtained by the proposed technique are compared with the results obtained by XFEM and EFGM. A remarkable agreement was observed between the results obtained by the three techniques.

Keywords: XFEM, EFGM, coupled FE-EFGM, level sets, large deformation

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Authors: A. Jameel, G. A. Harmain, Y. Anand, J. H. Masoodi, F. A. Najar

Abstract:

The present study investigates the effect of inclusions on the shape and size of crack tip plastic zones in engineering materials subjected to static loads by employing the element free Galerkin method (EFGM). The modeling of the discontinuities produced by cracks and inclusions becomes independent of the grid chosen for analysis. The standard displacement approximation is modified by adding additional enrichment functions, which introduce the effects of different discontinuities into the formulation. The level set method has been used to represent different discontinuities present in the domain. The effect of inclusions on the extent of crack tip plastic zones is investigated by solving some numerical problems by the EFGM.

Keywords: EFGM, stress intensity factors, crack tip plastic zones, inclusions

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Authors: Rama Bhargava

Abstract:

In the current paper, numerical simulation has been performed for the two-dimensional time dependent Pennes’ heat transfer model which is solved for irregular diseased tumor cells. An elliptic cryoprobe of varying sizes is taken at the center of the computational domain in such a manner that the location of the probe is fixed throughout the computation. The phase transition occurs due to the effect of probe with infusion of different nanoparticles Au, Al₂O₃, Fe₃O₄. The cooling performance of these nanoparticles injected at very low temperature, has been studied by implementing a hybrid FEM/EFGM method in which the whole domain is decomposed into two subdomains. The results are shown in terms of temperature profile inside the computational domain. Rate of cooling is obtained for various nanoparticles and it is observed that infusion of Au nanoparticles is very much efficient in increasing the heating rate than other nanoparticles. Such numerical scheme has direct applications where the domain is irregular.

Keywords: cryosurgery, hybrid EFGM/FEM, nanoparticles, simulation

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Authors: S. Nandal, R. Bhargava

Abstract:

The paper contains a numerical study of the unsteady magneto-hydrodynamic natural convection flow of nanofluids within a symmetrical wavy walled trapezoidal enclosure. The length and height of enclosure are both considered equal to L. Two-phase nanofluid model is employed. The governing equations of nanofluid flow along with boundary conditions are non-dimensionalized and are solved using one of Meshfree technique (EFGM method). Meshfree numerical technique does not require a predefined mesh for discretization purpose. The bottom wavy wall of the enclosure is defined using a cosine function. Element free Galerkin method (EFGM) does not require the domain. The effects of various parameters namely time t, amplitude of bottom wavy wall a, Brownian motion parameter Nb and thermophoresis parameter Nt is examined on rate of heat and mass transfer to get a visualization of cooling and heating effects. Such problems have important applications in heat exchangers or solar collectors, as wavy walled enclosures enhance heat transfer in comparison to flat walled enclosures.

Keywords: heat transfer, meshfree methods, nanofluid, trapezoidal enclosure

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Authors: Rama Bhargava, Surabhi Nishad

Abstract:

The infusion of nanofluids has dramatically enhanced the heat-carrying capacity of the fluids, applicable to many engineering and medical process where the temperature below freezing is required. Cryosurgery is an efficient therapy for the treatment of cancer, but sometimes the excessive cooling may harm the nearby healthy cells. Efforts are therefore done to develop a model which can cause to generate the low temperature as required. In the present study, a mathematical model is developed based on the bioheat transfer equation to simulate the heat transfer from the probe on a tumor (with irregular domain) using the hybrid technique consisting of element free Galerkin method with αα-family of approximation. The probe is loaded will nano-particles. The effects of different nanoparticles, namely Al₂O₃, Fe₃O₄, Au on the heat-producing rate, is obtained. It is observed that the temperature can be brought to (60°C)-(-30°C) at a faster freezing rate on the infusion of different nanoparticles. Besides increasing the freezing rate, the volume of the nanoparticle can also control the size and growth of ice crystals formed during the freezing process. The study is also made to find the time required to achieve the desired temperature. The problem is further extended for multi tumors of different shapes and sizes. The irregular shape of the frozen domain and the direction of ice growth are very sensitive issues, posing a challenge for simulation. The Meshfree method has been one of the accurate methods in such problems as a domain is naturally irregular. The discretization is done using the nodes only. MLS approximation is taken in order to generate the shape functions. Sufficiently accurate results are obtained.

Keywords: cryosurgery, EFGM, hybrid, nanoparticles

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