Designing Volumetric Truss Structures

We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself

Quad Meshing

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing

HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid- based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques

Development of combustion models for RANS and LES applications in SI engines

Prediction of flow and combustion in IC engines remains a challenging task. Traditional Reynolds Averaged Navier Stokes (RANS) methods and emerging Large Eddy Simulation (LES) techniques are being used as reliable mathematical tools for such predictions. However, RANS models have to be further refined to make them more predictive by eliminating or reducing the requirement for application based fine tuning. LES holds a great potential for more accurate predictions in engine related unsteady combustion and associated cycle-tocycle variations. Accordingly, in the present work, new advanced CFD based flow models were developed and validated for RANS and LES modelling of turbulent premixed combustion in SI engines. In the research undertaken for RANS modelling, theoretical and experimental based modifications have been investigated, such that the Bray-Moss-Libby (BML) model can be applied to wall-bounded combustion modelling, eliminating its inherent wall flame acceleration problem. Estimation of integral length scale of turbulence has been made dynamic providing allowances for spatial inhomogeneity of turbulence. A new dynamic formulation has been proposed to evaluate the mean flame wrinkling scale based on the Kolmogorov Pertovsky Piskunow (KPP) analysis and fractal geometry. In addition, a novel empirical correlation to quantify the quenching rates in the influenced zone of the quenching region near solid boundaries has been derived based on experimentally estimated flame image data. Moreover, to model the spark ignition and early stage of flame kernel formation, an improved version of the Discrete Particle Ignition Kernel (DPIK) model was developed, accounting for local bulk flow convection effects. These models were first verified against published benchmark test cases. Subsequently, full cycle combustion in a Ricardo E6 engine for different operating conditions was simulated. An experimental programme was conducted to obtain engine data and operating conditions of the Ricardo E6 engine and the formulated model was validated using the obtained experimental data. Results show that, the present improvements have been successful in eliminating the wall flame acceleration problem, while accurately predicting the in-cylinder pressure rise and flame propagation characteristics throughout the combustion period. In the LES work carried out in this research, the KIVA-4 RANS code was modified to incorporate the LES capability. Various turbulence models were implemented and validated in engine applications. The flame surface density approach was implemented to model the combustion process. A new ignition and flame kernel formation model was also developed to simulate the early stage of flame propagation in the context of LES. A dynamic procedure was formulated, where all model coefficients were locally evaluated using the resolved and test filtered flow properties during the fully turbulent phase of combustion. A test filtering technique was adopted to use in wall bounded systems. The developed methodology was then applied to simulate the combustion and associated unsteady effects in Ricardo E6 spark ignition engine at different operating conditions. Results show that, present LES model has been able to resolve the evolution of a large number of in-cylinder flow structures, which are more influential for engine performance. Predicted heat release rates, flame propagation characteristics, in-cylinder pressure rise and their cyclic variations are also in good agreement with measurements

Simulation of fracture strength improvements of a human proximal femur using finite element analysis.

The most common hip fracture in the elderly occurs as a result of a fall to the side with impact over the greater trochanter resulting in a fracture of the proximal femur. The fracture usually involves the femoral neck or the intertrochanteric region. It has recently been determined that the fracture crack of a hip fracture typically initiates on the superior-lateral cortex of the femoral neck and then propagates across the femoral neck, resulting in a complete fracture. The strength of the superior-lateral cortex of the femoral neck is likely determined by the combined properties of the generally thin cortex (outer layer) and the underlying trabecular bone in this region. The objective of this study was to determine the relative effects of increasing or decreasing the thickness of these bone tissues on the overall failure strength of the proximal femur. The clinical significance of this work relates to hip fracture risk with various potential treatment options to improve either cortical or trabecular bone quality. A human femur obtained from a 68 year old female donor was scanned using computed tomography at 60-micron voxel resolution and a series of high-resolution finite element models were generated. The models were constructed with a base-element dimension of 120 microns and models included a basic model with cortical and trabecular thicknesses representative of the cadaver specimen from the original scan. Other models used a standardized algorithm to either dilate or erode the trabecular and cortical bone compartments of the femoral neck so that a total of nine models were created including the basic model. Each model was used to simulate a fall-to-the-side loading condition with appropriate boundary and loading conditions as used in previous models and experiments. An experimental test of the cadaver femur was also performed with three strain gauges placed on the proximal femur: on the superior-lateral cortex, on the inferior-medial cortex, and on the medial cortex positioned distal to the lesser trochanter. This femur was loaded at a rate of 100 mm/s until fracture of the femoral neck using a standard fall-to-the-side setup and the applied load and gauge strains were recorded. The femur neck fractured at a load of 2140 N. To validate the basic finite element model, the strain gauge strains at the load levels of 1000 N and 2000 N were compared to the calculated strains from the basic model at the same loads and same location as the gauge on the cadaver femur. After the basic model was validated, a failure criterion was determined as the volume percentage of the elements in the model that had exceeded 7000 µε at the failure load corresponding to the load at which the cadaver femur failed. Subsequently, this failure criterion was applied to the other eight models as a parametric analysis to estimate the increase or decrease in failure strength caused by the changes in cortical and trabecular thickness. The validation test results showed that the basic finite element model calculated strain on the superolateral cortex was within 2.1% of the experimentally measured strain at 1000 N loading. The validated basic model was then used to determine that the percentage of finite elements (by volume of the model) in excess of 7000 µε at the failure load was 4.2%. This failure criterion was then used to estimate the failure load for the other eight models with different combinations of either thicker (+120 µm) or thinner (-120 µm) cortex and trabeculae in the femoral neck. The calculated failure loads ranged from 324 N for the model with thinned cortex and thinned trabeculae to 3336 N for the model with thickened cortex and thickened trabeculae. The model with normal cortex and thickened trabeculae had a failure load of 3242 N, which is only 2.8% less than the strongest case. The largest single parameter effect on proximal femoral strength is realized by an increase in trabecular thickness. This is somewhat surprising considering that cortical bone is typically stronger than cancellous bone. However, the spatial arrangement of trabecular bone and the buttress support it provides to the thin cortex apparently plays an important role in the ability of a global increase in thickness to have a significant beneficial effect

Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches designed to minimize the number of cells used to augment/stabilize the least-squares stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cellaverage gradients is described. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet engine flowpath is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the preferred gradient method for a realistic 3-D geometry on a non-hex-dominant grid

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 numerical assessment of architectural parameters for anisotropic behavior in idealised trabecular structures

Bones macroscopically consist of two major constituents; namely cortical and trabecular (also known as cancellous) bone. Cortical bone is the hard and dense outer layer of bone, which holds majority of the load bearing capacity. Trabecular bone is the porous internal bone, which distributes loads at joints by allowing for a larger bearing surface and acts as an energy absorber. Trabecular bone has a complex, heterogeneous, anisotropic open cell lattice structure with a large variation in mechanical properties across anatomic site, species, sex, age, normal loading direction and disease state. A common attempt to account for this variation is to correlate the structure of the trabecular bone sample to the mechanical response, which requires a means of quantifying the structure. Microstructural indices such as bone volume vs. total volume (BV/TV), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), structural modal index (SMI) and mean intercept length (MIL) have been widely used to find correlations between structure and properties. Early studies only considered densitometric indices, which accounted for much of the variation however cross study correlations did not agree, leading to an interest in capturing non-scalar valued indices to account for features such as the anisotropy of the bone. The structural anisotropy varies from fully equiaxed to highly directional based on where the trabecular bone is located and what the function would be. The mean intercept length has been proposed as a measure of the structural anisotropy, specifically the interfacial anisotropy of the sample, which is commonly used to account for the mechanical anisotropy. This research falls within a longer term goal of investigating and understanding the mechanical anisotropy of trabecular bone. To that end, the anisotropy of regular lattice structures was investigated, with the particular goal that the investigated lattices were simple analogues for the more complex structures seen in trabecular bone. A framework for assessing the structure-property relations of trabecular bone is created, with focus on anisotropy. The mechanical anisotropy of idealised trabecular structures is quantified using well known microstructural indices, which are compared to the numerically determined mechanical response. The modelling methodology initially investigated 2D lattices that have very well known responses, such that the modelled approach could be verified. Three 2D lattices were used to do this, with the aim that the 3D lattices would be their analogues. Specifically a 2D square, hexagonal and triangular lattice were investigated. The square lattice is highly anisotropic as is the cubic lattice. The hexagonal lattice is isotropic with a large constraint effect as is the Kelvin cell, and the triangular lattice is isotropic with a small constraint effect. The octet-truss was the closest analogue to the triangular lattice, having a small constraint effect and being less anisotropic than the cubic lattice. The three 3D lattices were chosen to represent highly directional trabecular bone (using a cubic lattice) and more equiaxed trabecular bone, with the fully isotropic Kelvin cell lattice (also known as a tetrakaidecahedron) and the octet-truss lattice which has a lower degree of anisotropy than the cubic. Two confinement arrangements were also investigated as analogues for the trabecular bone at the free surface and at the cortical surface. To assess the mean intercept length analysis as a measure of mechanical anisotropy, this research performed the analysis on three 3D periodic lattice structures and compared the results to mechanical properties which were numerically determined using finite element analysis. The mean intercept analysis was performed by generating 3D images for the lattices, similar to the output of (mu)CT images, using a combination of open-source software and custom code, and performing the analysis in BoneJ, an open-source software package. The mechanical response was determined using two methods, namely discrete and continuum modelling approaches. The discrete approach characterised the lattice with each strut modelled as a Timoshenko beam element solved in LS-DYNA. To capture the anisotropy, the lattice had to be loaded at arbitrary angles, which was achieved by a rotating the whole lattice and cropping it to a specified test region using custom code. The continuum modelling approach used a homogenisation approach by treating the lattice as a solid material with effective properties, this was solved in a custom implicit solver written in MATLAB using solid elements. The anisotropy was modelled by transforming the elasticity tensor to arbitrary coordinate systems to load the model in arbitrary directions. The discrete modelling approach suffered from high computational costs and difficulty in removing the boundary effects, all of which would be worsened for models of real trabecular bone. However the discrete approach did accurately captured the mechanical behaviour of the lattices tested. The continuum approach accurately captured some of the responses but failed to capture all behaviour caused by confinement. The continuum model could not capture the switch in predominant deformation mode of the 2D hexagonal lattice caused by lateral confinement, and failed to accurately capture the symmetry of the highly anisotropic 3D cubic lattice. The mean intercept length analysis failed to capture the anisotropic response of simple periodic lattices, showing no significant difference between the octet-truss and cubic lattices, despite them having a very large difference in mechanical anisotropy. It also showed that the Kelvin cell lattice had the highest degree of geometric anisotropy, which is compared to having the lowest mechanical anisotropy being the only fully isotropic 3D lattice investigated. The mechanical investigation showed that the lateral confinement has a large effect, significantly scaling the response of isotropic lattices whilst distinctly changing the anisotropic behaviour of the cubic and octet-truss lattice. The mean intercept length analysis cannot capture the mechanical confinement effect from geometry alone, and thus fails to capture the mechanical response due to confinement Overall, the continuum modelling approach showed difficulty in capturing the confinement effect in all lattices and thus a more robust method is required. The mean intercept analysis proved unsuccessful in capturing the mechanical response of three periodic idealised trabecular structures. A new microstructural index that can capture the mechanical anisotropy is required, with the ability to consider the effects of confinement on the structure