Numerical Simulation Of Some Problems in Mechanics Using Advanced FE Techniques

Abstract:  Differential Equations (DEs) form the basis of most of the mathematical models of physical, chemical and biological phenomena. Computational modelling of these problems is challenging due to the presence of nonlinearity in them. Numerical methods are essential for the effective simulation of the mathematical model as the underlying DEs usually need to be approximated. Numerical techniques can be broadly classified into two categories: Grid based methods and grid free (Meshfree) methods. The grid based methods discretize the domain using a mesh whereas in Meshfree methods, the domain is represented using a set of nodes (or particles) without using a mesh that describes the connectivity. The grid based methods are widely used to simulate various engineering applications. These methods are inefficient for problems with free surface, deformable boundary, moving interface, large deformation, complex mesh generation, mesh adaptivity, and multi-scale resolution. Meshfree methods are expected to be superior to the conventional grid-based methods for many such applications. The difficulty with implementing Meshfree Methods is that they are time consuming and thus, have a high cost of computation. The talk will focus on numerical study of some problems of both fluid and solid mechanics using advanced FE techniques.