There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Soil Chemical Analysis

Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Polymer nanocomposites based on functionalized carbon nanotubes

The numerical simulation of fatigue crack growth using extended finite element method

Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions

An adaptive multiscale phase field method for brittle fracture

An investigation of fatigue crack growth of interfacial cracks in bi-layered materials using the extended finite element method is presented. The bi-material consists of two layers of dissimilar materials. The bottom layer is made of aluminium alloy while the upper one is made of functionally graded material (FGM). The FGM layer consists of 100 % aluminium alloy on the left side and 100 % ceramic (alumina) on the right side. The gradation in material property of the FGM layer is assumed to be exponential from the alloy side to the ceramic side. The domain based interaction integral approach is extended to obtain the stress intensity factors for an interfacial crack under thermo-mechanical load. The edge and centre cracks are taken at the interface of bi-layered material. The fatigue life of the interface crack plate is obtained using the Paris law of fatigue crack growth under cyclic mode-I, mixed-mode and thermal loads. This study reveals that the crack propagates into the FGM layer under all types of loads.

Indra Vir Singh

Papers

The numerical simulation of fatigue crack growth using extended finite element method

Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions

An adaptive multiscale phase field method for brittle fracture

Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems