Applications of Meshfree Particle Method in Structural Engineering

Abstract

In the history of Structural Engineering, the methods available for numerical simulation include Finite Element Method (FEM), Finite Difference method (FDM) and Finite Volume method (FVM). In these numerical methods the process of grid formation for irregular geometry requires tedious mathematical transformation; and the treatment of deformation in meshing requires rezoning which is tedious & time consuming. Hence the grid based methods cannot be used to solve problems with large discontinuities and deformations. So meshfree particle method is chosen to overcome this limitation. Mesh free particle method is a particle based mesh free approach where the computational frames in MPM are moving particles in space. There is no necessity of predefined connectivity between the particles. This particle method based on the concepts of Lagrangian theory, whereas the approximation of any desired function in MPM method is carried out in two stages namely kernel and particle approximation. The resulting function from the particle approximation is numerically simulated to obtain the required functional output. Hence MPM serves as a versatile method to handle problems with highly irregular and even dynamic geometry with large deformations. Owing to these advantages, this method has been largely applied to solve different problems in Structural engineering. Typical examples include issues with free surface, deformable frame, moving interface and large deformation. This paper presents an overview on the concepts and benefits of MPM method, its recent developments and the future scope for meshfree particle methods in Structural Engineering applications.