Error Estimates for Finite Element Simulations Using Neural Networks

In this work residual error estimates are constructed using Neural Networks for Finite Element Method. These can be used to do adaptive mesh refinement. Two neural networks are developed the Multilayer Perceptron and the Transformer model. The error estimates are made for 1d poisson equations but the idea will generalise to higher dimensions as...

Finite Element Method for two dimensional Westervelt Equation

This essay shows a two dimensional implementation of the finite element method for the Westervelt equation. To do this the finite element method is first applied to the linear wave equation, then to non-linear diffusion and finally to the Westervelt equation. Both an element by element and a faster vectorized implementation are given for the...

Design and simulation of an invisibility cloak device in Julia

Mankind has always adapted materials to fullfil a need. Recent developments in nano-science allows us to construct objects with varying permittivity and permeability. One possible structure is an invisibility cloak device. This device is put around an object. Any plane wave that enters the cloak should go around this object. The wave exits the...

Modelling Magnetic Phase Transitions: with Density Functional Theory and the Finite Element Method

The present thesis discusses two modelling endeavours that serve to provide insights into both the magnetic and structural dynamics associated with a first order magnetic phase transition. <br/>Firstly, density functional theory has been used to model the lithiation of a supercell of 2x2x2 the conventional unit cell of the ferromagnet Fe2P....

An elastic model for meshfitting for the Level-set Method

The numerical errors involving the application of the level-set method to a problem can be minimized by fitting a mesh (usually a triangular mesh in two dimensions) to the zero level-set curve defined by the level-set function. These numerical errors depend on two things: the size and skewness of the triangles in the mesh. To fit the mesh, Timo...

Meshfitting for the Level-set Method

In applying the level-set method in the context of a finite-element method, errors can be minimized by adjusting the mesh to the shape of the level-set curve. The size of the different types of errors that occur depend on the goodness of fit to the zero levelset curve, the skewness of the triangles and the size of the triangles of the mesh. To...

Modelling FRP open-hole tensile tests in Abaqus

The use of fibre reinforced polymers (FRP) are stimulated in the construction industry for their remarkable corrosion resistance, good thermo-mechanical properties, high strength-to-weight ratio and high stiffness-to-weight ratio. The open-hole strength of FRP is an important parameter in a composite design because it can be representative in...

Permanent Magnet Motor Simulation: For the Nuon Solar Team

This thesis is about the simulation of the permanent magnet motors of the Nuna Solar Car in order to find their fundamental motor parameters. These parameters can then be used in a Field-Oriented control algorithm to be used in a new motorcontroller for the team. A finite element analysis is done on the two current motors of the Nuna solar car,...

On the accuracy and convergence of the finite element method for truss and frame structures

During applied mechanics courses for undergraduates, the words `finite element' will be mentioned if a structural problem is so complex that it cannot be solved analytically or simply because it would require too much time to solve it by hand. The lecturer refers to a software package and explains how to work with it. Unfortunately, during these...

Design and Structural Analysis of the Propellant Tank for a Water Resistojet

The purpose of this Thesis is to develop the design process of the pressurised propellant tank for a water resistojet, applicable to nanosatellite missions. The motivation of this system is its use on the CubeSat mission DelFFi, from the Technical University of Delft. The need for a small-sized pressure vessel is covered by the Detail Design...

Finite Element Method Applied to the One-dimensional Westervelt Equation

In this thesis we researched the applicability, properties and efficiency of the finite element method to solve the one-dimensional Westervelt equation, which describes nonlinear plane wave propagation. The goal was to investigate whether this lesser-known solution method has advantages or disadvantages compared to more commonly used solution...

Numerical modelling on super-diffusion of carbon-dioxide in coal

Case II (super)-diffusion is characterized by a diffusion like process that goes faster than the square root of time. Superdiffusion can occur in polymeric structures if a stress gradient enhances the diffusion process. In such a case the part of the polymer invaded by the penetrant, e.g. CO2, undergoes a transition in structure from the glass...