I.V. Singh

HEAT TRANSFER ANALYSIS OF TWO-DIMENSIONAL FINS USING MESHLESS ELEMENT FREE GALERKIN METHOD

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 least-square approximants are used to approximate the unknown function of temperature T h (x) with Th (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.

Numerical Solution of Temperature-Dependent Thermal Conductivity Problems Using a Meshless Method

In this article, the meshless element-free Galerkin (EFG) method is extended to obtain numerical solution of nonlinear heat conduction problems with temperature-dependent thermal conductivity. The thermal conductivity of the material is assumed to vary linearly with temperature. A quasi-linearization scheme is adopted to avoid the iteration for nonlinear solution, and time integration is performed by the backward difference method. The essential boundary conditions are enforced by Lagrange multiplier technique. Meshless formulations are presented for one- and two-dimensional nonlinear heat conduction problems. MATLAB codes have been developed to obtain the EFG results. The results obtained by the EFG method are compared with those obtained by finite-element and analytical methods.

THE ELEMENT FREE GALERKIN METHOD IN THREE DIMENSIONAL STEADY STATE HEAT CONDUCTION

This paper deals with the solution of three dimensional steady state heat conduction problems using a meshless Element Free Galerkin Method. The unknown function T(x, y, z) is approximated by using moving least square approximants. These approximants are constructed using a weight function, a monomial basis and a set of non-constant coefficients. The governing equations are developed using a variational technique and essential boundary conditions are imposed by using Lagrange multiplier method. A hyperbolic weight function has been proposed. The results are obtained for a three dimensional model by taking different types of weight functions. the Element Free Galerkin Method has been validated by comparing the results with those obtained by finite element and analytical methods.

A simple and efficient XFEM approach for 3-D cracks simulations

In this work, a simple and efficient XFEM approach has been presented to solve 3-D crack problems in linear elastic materials. In XFEM, displacement approximation is enriched by additional functions using the concept of partition of unity. In the proposed approach, a crack front is divided into a number of piecewise curve segments to avoid an iterative solution. A nearest point on the crack front from an arbitrary (Gauss) point is obtained for each crack segment. In crack front elements, the level set functions are approximated by higher order shape functions which assure the accurate modeling of the crack front. The values of stress intensity factors are obtained from XFEM solution by domain based interaction integral approach. Many benchmark crack problems are solved by the proposed XFEM approach. A convergence study has been conducted for few test problems. The results obtained by proposed XFEM approach are compared with the analytical/reference solutions.

Mechanical and Wear Characterization of GF Reinforced Vinyl Ester Resin Composites with Different Co-Monomers

This article reports the mechanical characterization and sliding wear behavior of glass fiber-reinforced vinyl ester resins of varying acid values, based on epoxy-novalocs in the presence of three different comonomers (styrene, methyl acrylate and butyl acrylate) as reactive diluents. It presents a special account of the optimization of fabrication techniques of glass fiber-reinforced vinyl ester resin composites. It outlines optimum reaction conditions such as temperature, time, monomer type and initiator concentration. The experimental plan consisted of preparation of vinyl ester resin followed by the composite samples. Mechanical characterization was done and a comparison was made between the different samples. It was found that these composites have fairly good tensile and flexural properties. The composites with styrene and butyl acrylate as co-monomers had similar tensile strength which was higher than that of the composite with methyl acrylate. Hardness values of the three composites were almost the same without any significant effect of the comonomer type. Volumetric wear rate was estimated for these samples under various test conditions. A steady wear rate regime after certain amount of sliding was observed all the three cases.

Fatigue crack growth simulations of bi-material interfacial cracks under thermo-elastic loading by extended finite element method

In this paper, fatigue crack growth simulations of bi-material interfacial cracks have been performed using extended finite element method (XFEM) under thermo-elastic loading. The material discontinuity (interface) has been modelled by a signed distance function whereas a strong discontinuity (crack) has been modelled by two functions i.e. Heaviside and asymptotic crack tip enrichment functions. The values of stress intensity factors are extracted from the XFEM solution by domain based interaction integral approach. Standard Paris fatigue crack growth law is used for the life estimation of various model problems. The results obtained by XFEM for an interfacial edge and centre cracks are compared with those obtained by finite element method based on a remeshing approach.

Evaluation of elastic properties of interpenetrating phase composites by mesh-free method:

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.

Numerical simulations of cracked plate using XIGA under different loads and boundary conditions

ABSTRACT This article deals with the numerical simulation of cracked plate using extended isogeometric analysis (XIGA) under different loads and boundary conditions. The plate formulation is done using first-order shear deformation theory. The crack faces are modeled by the Heaviside function, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. The stress intensity factors for the cracked plate are numerically computed using a domain-based interaction integral. The results obtained by XIGA for the center and edge crack plate are compared with extended finite element method and/or literature results for different types of loads and boundary conditions.

Evaluation of effective thermal conductivity of CNT‐based nano‐composites by element free Galerkin method

Purpose – The purpose of this paper is to evaluate the thermal properties of carbon nanotube composites via meshless element free Galerkin (EFG) method.Design/methodology/approach – The EFG method is based on moving least square approximation, which is constructed by three components: a weight function associated with each node, a basis function and a set of non‐constant coefficients. In principle, EFG method is almost identical to finite element method. The EFG method does not require elements for the interpolation (or approximation) of field variable, but only requires a set of nodes for the construction of approximation function.Findings – The equivalent thermal conductivity of the composite has been calculated, and plotted against nanotube length, nanotube radius, RVE length, and RVE radius. Temperature distribution has been obtained and plotted with RVE length. An approximate numerical formula is proposed to calculate the equivalent thermal conductivity of CNT‐composites. Present computations show th...

A Numerical Study of Weight Functions, Scaling, and Penalty Parameters for Heat Transfer Applications

ABSTRACT This article describes a numerical study of weight functions, scaling, and penalty parameters for heat transfer problems. The numerical analysis is carried out using a meshless element-free Galerkin (EFG) method, which utilizes moving least-square (MLS) approximants to approximate the unknown function of temperature. These MLS approximants are constructed by using a weight function, a basis function, and a set of coefficients that depend on position. Lagrange multiplier and penalty methods are used to enforce the essential boundary conditions. MATLAB software is developed to obtain the EFG results. A new rational weight function is proposed. Comparisons are made among the results obtained using cubic spline, quartic spline, Gaussian, quadratic, hyperbolic, rational, exponential and, cosine weight functions in one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) heat transfer problems. The L2 error norm and rate of convergence are evaluated for different EFG weight functions and the finite-element method (FEM). The effect of scaling and penalty parameters on EFG results is discussed in detail. The results obtained by the EFG method are compared with those obtained by finite-element and analytical methods.