Akhilendra Singh

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.

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.

Springback analysis in torsion of rectangular strips

Abstract A theoretical analysis of the springback of narrow rectangular strips under torsional loading is presented. The theoretical analysis is supported by experimental results for different materials, different thicknesses and different lengths, keeping the width of the strips constant. Finally an analytical generalized expression relating angle of twist and twisting moment and residual angle of twist per unit length for rectangular bars under plastic torsion is obtained in non-dimensionalized form.

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.

Thermo-elastic failure simulation of 3-D orthotropic composites by XFEM

Orthotropic composite materials exhibits higher specific strength and stiffness; hence extensively used in various industrial and engineering applications such as aerospace, armored and automobile etc. During their service life, these critical engineering components are subjected to thermo-elastic loads. These loading conditions generate local thermal stress concentration near the crack/voids present in the structures, which leads to sudden failure of engineering components. Therefore, the study of crack tip stress field under thermo-elastic loading becomes very important to understand the effect of lamina orientation on the strength of orthotropic composite components. The presented work deals with XFEM formulation and implementation to simulate 3-D orthotropic fracture problems under thermo-elastic loading environment. In XFEM based formulation, meshed topology does not exhibit any geometrical discontinuity. All desired discontinuity can be captured by enriching primary variable approximations by additional mathematical functions (Heaviside and crack front enrichment functions). These enrichment functions are derived from theoretical background of the problem under consideration. The crack surface element enriched by Heaviside function whereas, crack front elements treated by orthotropic crack front asymptotic functions. Mixed mode stress intensity factors are computed by domain based interaction integral approach. Few example of 3-D orthotropic thermo-elastic crack problem is presented to illustrate the effectiveness and robustness of proposed method.

Composite Patch Repair of Structural Member by Coupled FE-EFG Approach

This paper presents a simple and efficient coupled finite element-element free Galekrin (FE-EFG) approach to simulate three-dimensional composite patch repair problem. In coupled FE-EFG approach, extended element free Galerkin (XEFG) is used near the crack surface as it can accurately model the discontinuities while the rest of domain is approximated by standard finite element (FE) method. The transition between FE and XEFG was modelled by a ramp function. The geometric discontinuities like crack and material interface are modeled by adding enrichment functions in EFG displacement approximation through partition of unity (PU). The location of geometrical discontinuity is traced by vector level set method. A domain based J-integral approach is used for the evaluation of stress intensity factors.

Recent Advances in Computational Mechanics

Computational mechanics deals with the use of computational methods in engineering to study physical phenomena governed by the principles of mechanics. It has got huge potential for the future growth and applications by incorporating new models of physical and biological systems based on quantum, molecular, biomechanics, and so on. The computational mechanics spans to several areas of mechanics, mathematics, computer science, and many others. Over the years, it has made a significant contribution in the design and development of new process and products due to the availability of effective computational resources. Nowadays, the computationalmethods are applied in all areas of engineering and sciences. This special issue covers the papers from various topics including thermal, fluid, solid mechanics, vibration, and vehicle dynamics. In totality, these papers provide the reader with an overall picture of the computational mechanics along with engineering and industrial applications. In this special issue, the editors received 38 manuscripts on various topics of computational mechanics. After peer review and based on the comments from reviewers, only 16 manuscripts have been accepted for publication.