Unstructured and semi-structured hexahedral mesh generation methods

Discretization techniques such as the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in ap- plied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to gener- ate. However, in many applications such as boundary layers in computational fluid dy- namics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.Peer ReviewedPostprint (published version

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Analysis of a Nuclear Reactor Boilure Closure Unit Through Development of a 3D Parallel Finite Element Code

Three dimensional (3D) finite element analysis (FEA) allows the mechanical integrity of complex structures to be estimated with some confidence. This research is concerned with extending an existing parallel FEA code. This code has been run on up to 16 processors on Durham University’s high performance computing (HPC) cluster and two different parallel linear solvers have been compared. A key feature of the work has been to develop tools for structural analyses. An automatic mesh refinement program has been written, the Zienkiewicz and Zhu error estimator has been coded for 3D hexahedral meshes and post processing techniques have been used to calculate and visualise principal stress data and peak stress criteria. This project also reports on three peak stress envelopes used to assess the condition of a concrete sub-structure. The development of this parallel code has enabled the deformation behaviour of a key component of a nuclear rector vessel to be determined. The BCU is a prestressed cylindrical concrete vessel (depth of 1.73m and diameter of 3.37m) sealing the top of a boilers housed within the walls of the reactor. In recent years possible problems have been identified at the Hartlepool and Heysham I Advance Gas-Cooled nuclear reactors (AGR) with respect to the structural condition of the BCU (in particular the condition of the prestressed circumferential wires designed to maintain the BCU in a state of compression). This problem provides an interesting case study for this project. Four different BCU meshes have been used containing either 40201 or 321608 elements (the elements are either 8 or 20-noded hexahedral elements). Three different load cases have been used to model the BCU. The results of the analyses confirm that the circumferential pre-stressing is vital in order to keep the BCU is a state of compression and operating under safe working conditions. These results have been confirmed using principal stress plots and three different peak stress envelopes. The results show that when the pre-stressing is released approximately one quarter of the elements contain stresses at Gauss points which exceed the peak strength of the concrete. This suggests that under these extreme conditions the BCU’s structural integrity has been severely compromised, concrete rupture is possible and the nuclear reactor is no-longer safe to operate

A collocated C0 finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics

We demonstrate the potential of collocation methods for efficient higher-order analysis on standard nodal finite element meshes. We focus on a collocation method that is variationally consistent and geometrically flexible, converges optimally, embraces concepts of reduced quadrature, and leads to symmetric stiffness and diagonal consistent mass matrices. At the same time, it minimizes the evaluation cost per quadrature point, thus reducing formation and assembly effort significantly with respect to standard Galerkin finite element methods. We provide a detailed review of all components of the technology in the context of elastodynamics, that is, weighted residual formulation, nodal basis functions on Gauss–Lobatto quadrature points, and symmetrization by averaging with the ultra-weak formulation. We quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings. Our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort, such as higher-order elastostatic analysis. Furthermore, we illustrate the potential of collocation for efficient higher-order explicit dynamics. Throughout this work, we advocate a straightforward implementation based on simple modifications of standard finite element codes. We also point out the close connection to spectral element methods, where many of the key ideas are already established

Multi-angle valve seat machining: experimental analysis and numerical modelling

Modern automotive manufacturers operate in highly competitive markets, heavily influenced by Government regulation and ever more environmentally conscious consumers. Modern high-temperature, high-pressure engines that use high hardness multi-angle valve seats are an attractive environmental option, but one that manufacturers find requires more advanced materials and tighter geometric tolerances to maintain engine performance.Tool manufacturers meet these increasingly tougher demands by using, higher hardness cutting materials such as polycrystalline cubic boron nitride (pcBN), that on paper, promise to wear at a lower rate, require less coolant and deliver tighter tolerances than their carbide counterparts.The low brittle fracture toughness of pcBN makes tools that use it vulnerable to minute chipping. A review of literature for this work pointed to no clear answer to this problem, although suggestions range from manufacturing defects, dynamic and flexibility problems with the production line machinery and fixtures, and radial imbalances in the cutting loads.This work set about experimentally investigating those potential explanations, coming to the conclusion that the high radial imbalance of the cutting loads is responsible for pcBN cutting insert failure during multi-angle valve seat machining, and that by simply relocating the cutting inserts around the multi angle cutting tool, the imbalance can be reduced, thus extending the life of the cutting inserts.It is not always easy to predict the imbalance due to the multiple flexibilities in the system, and simulating such a system in 3D with all its associated cutting phenomena such as friction, thermal expansion, chip flow and shearing, would call upon extraordinary computational power and extremely precise experimental inputs to reduce cumulative error.This thesis proves that such a 3D simulation can be made, that runs in exceptionally short durations compared to traditional methods, by making a number of simplifications.MSC Marc was used to host the simulation, with a parametric script written in Python responsible for generating the model geometry and cutter layout. A Fortran program was developed that is called upon by Marc to calculate the required cutting load outputs and generate new workpiece meshes as material is removed.</div