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This article presents a numerical solution of three-dimensional cracks using coupled EFGM and FEM. The FEM adequately handles problems without discontinuities but faces severe limitations in solving crack growth problems, while EFGM does fairly well in handling such problems. Hence, EFGM has been used in a region near the crack whereas FEM has been utilized in the rest of the region. In the interface/transition region, a coupling scheme known as mixed-mode interpolation is used to obtain the shape functions. These simulations show that the results obtained by the coupled scheme are found to be in good agreement with analytical solutions. [ABSTRACT FROM AUTHOR]

The present work deals with the fatigue crack growth simulation of alloy/ceramic functionally graded materials (FGMs) using extended finite element method (XFEM). Various cases of FGM containing multiple inhomogeneities/discontinuities along with either a major edge or a center crack are taken for the purpose of simulation. The fatigue life of the FGM plate is calculated using Paris law of fatigue crack growth under cyclic loading. The effect of multiple inhomogeneities/discontinuities (minor cracks, holes/voids, and inclusions) on the fatigue life of cracked FGM plate is studied in detail. These simulations show that the presence of inhomogeneities/discontinuities in the domain significantly influences the fatigue life of the components. [ABSTRACT FROM AUTHOR]

Interpenetrating phase composites can be defined as multiphase materials in which each phase is three-dimensionally interconnected throughout the structure. The unique geometry of the reinforcement offers improved combination of mechanical and physical properties. Over the years, a lot of efforts have been put to study these composites experimentally. However, due to the complexity in microstructure and randomness in behaviour of interpenetrating phase composite, the modelling of these composites has not been sufficiently studied so far. Therefore, in this study, two models, namely, unit cell and self-consistent models have been presented to find the elastic properties of interpenetrating phase composites. All influencing parameters such as volume fraction and random geometry are duly incorporated in these models. These models are analysed by a mesh-free method known as element-free Galerkin method. The effective properties of these composites are calculated by an effective medium approximation approach. The real microstructure of interpenetrating phase composites is partially interpenetrating and partially particulate in nature; hence, a control parameter has been included in the model to simulate this behaviour. The main feature of the proposed unit cell model is that it is easy to implement and less time consuming as compared to three-dimensional existing model and characterises all the governing features of interpenetrating phase composite microstructure. [ABSTRACT FROM AUTHOR]

This paper deals with three dimensional heat transfer analysis of composite slabs using meshless element free Galerkin method. The element free Galerkin method (EFG) method utilizes moving least square (MLS) approximants to approximate the unknown function of temperature Tx). These approximants are constructed by using a weight function, a basis function and a set of coefficients that depends on position. Penalty and Lagrange multiplier techniques have been used to enforce the essential boundary conditions. MATLAB codes have been developed to obtain the EFG results. Two new basis functions namely trigonometric and polynomial have been proposed. A comparison has been made among the results obtained using existing (linear) and proposed (trigonometric and polynomial) basis functions for three dimensional heat transfer in composite slabs. The effect of penalty parameter on EFG results has also been discussed. The results obtained by EFG method are compared with those obtained by finite element method [ABSTRACT FROM AUTHOR]

This article deals with the parallel computing solution of fluid flow problems using a meshless element-free Galerkin (EFG) method. The EFG method utilizes moving least-square (MLS) approximants to approximate the unknown field variables. The MLS approximant consists of three components: a weight function, a basis function, and a set of nonconstant coefficients. A new parallel algorithm is proposed for the EFG method. The code has been written in FORTRAN language using MPI message passing library and implemented on a MIMD (multiple-instruction multiple-data)-type PARAM 10000 supercomputer. The code has been validated by solving three model fluid flow problems. A comparison is made among the results (velocities values) obtained by the EFG method with those obtained by the finite-element method (FEM) at a few typical locations. For 8 processors, speedup and efficiency have been obtained as 2.73 and 34.22% for N = 1,552 in 1-D (Example I), 7.20 and 90.00% for N = 1,462 in 2-D (Example II), and 7.30 and 91.27% for N = 1,346 in 2-D (Example III), respectively. [ABSTRACT FROM AUTHOR]

The parallel implementation of the element free Galerkin (EFG) method for heat transfer and fluid flow problems on MIMD type parallel computer is treated. A new parallel algorithm has been proposed in which parallelization is performed by row-wise data distribution among the processors. The codes have been developed in FORTRAN language using MPI message passing library. Two model (one each in heat transfer and fluid flow) problems have been solved to validate the proposed algorithm. The total time, communication time, user time, speedup and efficiency have been estimated for heat transfer and fluid flow problems. For eight processors, the speedup and efficiency are obtained to be 7.11 and 88.87% respectively in heat transfer problems for a data size ofN=2,116 whereas 7.20 and 90.04% respectively in fluid flow problems for a data size ofN=2,378. [ABSTRACT FROM AUTHOR]

This article deals with the transient and steady-state solution of two-dimensional heat transfer through the fins using a meshless element free Galerkin method. Moving leastsquare approximants are used to approximate the unknown function of temperature T(x) with T[sup h](x). These approximants are constructed by using a linear basis, a weight function, and a set of nonconstant coefficients. The variational method has been used for the development of discrete equations. Essential boundary conditions are enforced by using Lagrange multipliers. A hyperbolic weight function has been proposed. The results are obtained for a two-dimensional model and compared with the results of the finite-element method. [ABSTRACT FROM AUTHOR]