Advantages of Mesh Free Methods for Structural and Fluid Analysis 2019-01-0939

An introduction to a set of numerical methods that have been designed to solve problems where traditional meshing methods fail or are computationally difficult to run. The methods discussed will be external approximations for structural simulation and Moving Particle Simulation (MPS) for incompressible fluid simulation. External approximations is a generalized finite element method in the sense that it allows for elements of arbitrary size and shape. An entire part is represented by a single element, and basis functions approximating areas of interest can be of arbitrary class and independent of element shape making it very efficient for large assemblies. MPS discretizes the volume in question using free-moving particles whose interaction with all surrounding particles are evaluated at every time step, avoiding the issue of high aspect ratio elements entirely. Boundaries are represented by functions that are generated in the pre-processing phase rather than discretized at a user selected resolution. These properties make it very efficient for transient problems with moving boundaries such as oil flow in gearboxes. Both methods have an advantage over traditional techniques because they do not rely on a traditional mesh and have low sensitivity to complex geometry, decreasing time spent preparing models, generating meshes, and running the simulation.