Composite materials are becoming popular in almost all industries. Carbon-fiber and glass-fiber composites are used in aircraft, sports equipment, boats, prosthetics, and wind turbine blades. In all these applications, the composites are subjected to different loads. Loads can take the form of impact or cyclic/fatigue loading, both of which decrease the strength of composites as micro-cracks grow through the composite. Composite laminates are made up of fiber plies (thin layers of fiber) and the fibers are surrounded by a resin like epoxy. It is common for laminates to fail because of delamination growth (plies peeling apart). Small delaminations do not fail a composite, but as delaminations grow, the composite weakens and eventually fails. Composites behave differently than metals do, and failure analysis is more complicated because of the various directions of fibers. Numerical methods (specifically Finite Element Analysis) exist for predicting when failure will occur, but improvements are needed to make these numerical methods more accurate and efficient. The method created, for this thesis, is computationally efficient because it doesn’t require the analyst or computer to adjust the simulation based on where the delamination is (or what kind of shape it is). Energy values are extracted directly from the delamination front and not averaged from nearby locations.

While Lisfranc injuries in the mid foot are less common than other ankle and mid foot injuries, they pose challenges in both properly identifying them and treating them. When Lisfranc injuries are ligamentous and do not include obvious fractures, they are very challenging for clinicians to identify unless weight bearing radiographs are used. The result is that 20%-40% of Lisfranc injuries are missed in the initial evaluation. Even when injuries are correctly identified the outcomes of surgical procedures remain poor. Existing literature has compared the different surgical procedures but has not had a standard approach or procedures across studies. This study uses a computational biomechanical model validated on a cadaveric study to evaluate factors that impact injury presentation and to compare the different procedures ability to stabilize the Lisfranc joint after an injury. Using SolidWorks® a rigid body kinematic model of a healthy human foot was created whereby the 3D bony anatomy, articular contacts, and soft tissue restraints guided biomechanical function under the action of external perturbations and muscle forces. The model was validated on a cadaveric study to ensure it matched the behavior of a healthy Lisfranc joint and one with a ligamentous injury. The validated model was then extended to incorporate muscle forces and different foot orientations when simulating a weight bearing radiograph. The last section of work was to compare the stability of four different surgical repairs for Lisfranc injuries. These procedures were three open reduction and internal fixation (ORIF) procedures with different hardware (screws, screws and dorsal plates, and endobuttons) and primary arthrodesis with screws. They required use of finite element analysis which was performed in Ansys Workbench. For the presentation of injuries, both muscle forces and standing with inversion or eversion could reduce the diastasis (separation) observed for weight bearing radiographs and thus confuse the diagnosis. When comparing the different surgical procedures, the ORIF with screws and primary arthrodesis with screws showed the most stable post-operative Lisfranc joint. However, the use of cannulated screws for fixation showed regions of high stress that may be susceptible to breakage. A challenge in the literature has been the use of different experimental designs and metrics when comparing two of the possible procedures for a Lisfranc injury head to head. This study has been able to benchmark four procedures using the same model and set of metrics. Since none of the existing procedures showed consistently good to excellent patient outcomes, more procedures could be proposed in the future. If this were to occur, this study offers a standard procedure for benchmarking the new procedure’s post-operative mechanical stability versus those procedures currently in use.

BACKGROUND: Finite element models of lung motion can aid in understanding mechanically driven lung deformation. Current finite element models consider each lung half as a continuum, lacking the ability to capture the displacement discontinuity at fissures caused by lobe sliding. OBJECTIVE: The objective of this work was to develop and evaluate finite element models for simulating lung motion that incorporate the role of sliding at the lobe boundaries. METHODS: Finite element models were developed from 4DCT of tidal breathing from five cancer subjects. To allow sliding, the lobes were modeled as independent bodies within a pleural cavity shell. Pleural cavity deformation was obtained from deformable image registration of the lung segmentations. Contact between the pleural cavity and lobes prevented penetration and allowed sliding at all interfaces. Lung parenchyma was modeled as a homogeneous, 2-parameter, Neo-Hookean finite elastic model. The parameters of the Neo-Hookean model, C1 and D1, were optimized by perturbation within realistic reported ranges; defined by the equivalent infinitesimal elasticity parameters: Young's modulus (from 0.7 kPa to 70 kPa) and ν (from 0.2 to 0.49). The frictional coefficient at fissures was perturbed between 0 (free sliding) and 1.5 (no sliding). 1,960 finite element analyses were performed across the five subjects. The optimal parameter ranges were evaluated by average landmark error and percentage of converged solutions. The developed finite element method, using optimized material and friction parameters, was further evaluated in a data set of six healthy subjects with image pairs spanning functional residual capacity (FRC) to total lung capacity (TLC). The finite element predicted displacement field for lobe sliding finite element models and continuum-based finite element models were compared using average landmark error and correlation with the lobe-by-lobe deformable image registration results. RESULTS AND DISCUSSION: The optimal parameters for Young's modulus were 49 kPa to 70 kPa and Poisson's ratio were 0.2 to 0.4. Variation of inter-lobar frictional coefficients did change displacement field accuracy assessed by landmark error or correlation to lobe-by-lobe deformable image registration. Characteristics of sliding predicted by the lobe sliding finite element models were consistent with characteristics in sliding observed in deformable image registration results. Also, variations in regional ventilation, quantified at the lobe level, were predicted by the finite element models and were shown to be influenced by the amount of lobe sliding allowed by the models.

Though the literature contains many computational models studying RSA, very few utilize finite element analysis to study stresses in the implant and the surrounding bone. The introductions section shows that many parameters (center of rotation lateralization, center of rotation superior or inferior position, tilt of the cut glenoid surface, glenosphere shape design, glenosphere size, humeral design, notch severity, etc.) have been studied independently utilizing many different methods (finite element modeling and non-FE computational modeling). However, the introduction section also detailed the current limitations in modern modeling as well as many examples of the heights to which finite element modeling can be taken to study RSA. Using these limitations as guidelines, the goal of this project is to create a robust FE model of RSA to study the effect of lateralization on scapular notching and shoulder function. In the following chapters, the development of the model is detailed. In addition, results produced by the incrementally advanced models are shown. In Chapter 2, the initial finite element model encompassing scapular and RSA hardware geometry is described. Chapter 3 contains description of incremental changes to the model including humeral geometry and muscle element incorporation. An anatomically realistic configuration of the finite element model with increased functionality is detailed in Chapter 4. Finally, Chapter 5 discusses the assets and limitations of the current model as a platform for future research. In addition, a proposed validation protocol is presented.

Post-traumatic osteoarthritis (PTOA) is a debilitating joint disease in which cartilage degenerates following joint trauma, including intra-articular fracture or ligament rupture. Acute damage and chronically altered joint loading have both been implicated in the development of PTOA, but the precise pathway leading from injury to cartilage degeneration is not yet known. A series of computational analyses were performed to gain insight into the initiation and progression of cartilage degeneration. Finite element models of in vitro drop-tower impacts were created to evaluate the local stress and strain distributions that cartilage experiences during such experiments. These distributions were compared with confocal imaging of cell viability and histologically apparent matrix damage. Shear strain and tensile strain both appear to correlate with the non-uniform percentage of cell death seen in the impact region. In order to objectively evaluate structural damage to the cartilage matrix, an automated image processing program was written to quantify morphologic characteristics of cartilage cracks, as seen in histology slides. This algorithm was used to compare the damage caused by different rabbit models of PTOA and to investigate the progression of matrix damage over time. Osteochondral defect insults resulted in more numerous and more severe cracks than ACL transection. Interestingly, no progression of structural damage was identified between 8 weeks and 16 weeks in these rabbit PTOA models. A finite element based optimization algorithm was developed to determine cartilage material properties based on the relaxation behavior of an indentation test. This was then used to evaluate the spatial and temporal progression of cartilage degeneration after impact. Impacting cartilage with 2.18 J/cm2 through a metal impactor caused an immediate increase in permeability and decrease in modulus, both of which recover to nearly pre-impact levels within two weeks. Biologic testing suggests that the modulus changes were due to collagen fibril damage that is then repaired. Impacting with higher energy caused material softening that did not return to normal, suggesting an impact injury threshold below which cartilage had some ability to repair itself. To evaluate the effects of cartilage cracks on local stress and strain environments, finite element models of cracked cartilage were created. A physiologically-relevant, depth-dependent cartilage material model was developed and used to ensure accurate strains throughout the cartilage depth. The presence of a single crack was highly disruptive to the strain fields, but the particular shape or size of that crack had little effect. The most detrimental perturbations included two cracks within close proximity. When two cracks were within 0.5 mm of one another, the strain field between them increased in an additive fashion, suggesting a threshold for the amount of structural damage cartilage can withstand without being severely overloaded. The finite element models of cracked cartilage were also incorporated into an iterative degeneration simulation to evaluate the ability of mechanical loading to cause localized cartilage damage to spread to full-joint osteoarthritis.

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This thesis provides a contribution towards a general procedure for solving robustly and efficiently limit and shakedown analyses of engineering structures within the static approach which has been chosen for its simplicity of implementation. Throughout the thesis, attempts at improving the robustness and efficiency of the computations are presented. Beginning with efforts to prevent volumetric locking, which is a severe shortcoming of traditional low order h-type displacement elements, the investigation proposes the use of the high order p-version of the finite element method. It is shown theoretically and confirmed numerically that this p-method is not only robust in preventing locking, but also provides very accurate results. However, the use of uniformly distributed high order p-elements may be computationally demanding when the size of the problem becomes large. This difficulty is tackled by two main approaches: use of a p-adaptive procedure at the elastic computation stage and use of approximate piecewise linear yield functions. The p-adaptive scheme produces a non-uniform p-distribution and helps to greatly reduce the number of degrees of freedom needed while still guaranteeing the required level of accuracy. The overall gain is that the sizes of the models are reduced significantly and hence also the computational effort. The adoption of piecewise linear yield surfaces helps to further increase the efficiency at the expense of possibly slightly less accurate, but still very acceptable, results. State-of-the-art linear programming solvers based on the very efficient interior point methodology are used. Significant gains in efficiency are achieved. A heuristic, semi-adaptive scheme to piecewise linearize the yield surfaces is then developed to further reduce the size of the underlying optimization problems. The results show additional gains in efficiency. Finally, major conclusions are summarized, and various aspects suitable for further research are highlighted.

This PhD thesis presents research aims to improving the dynamic modelling of coupled plate structures across a wide frequency range by using analytical, statistical and experimental methods. The analytical waveguide method is used to model the flexural displacement of coupled plate structures which are simply supported along two parallel edges. A method of quickly predicting the average energy level in a plate from details of the waveguide model is described, and used for comparison with SEA models. The Poynting and Impedance methods of predicting the energy flow in coupled plate structures are investigated. Transmission coefficients for coupled plate structures are evaluated using the analytical waveguide method for both semi-infinite and finite coupled plate structures. Finite transmission coefficients have traditionally been more difficult to evaluate due to the presence of a reverberant field, but in this work a novel method of separating the reverberant field using a scattering matrix method is presented. The transmission coefficients for semi-infinite and finite structures are then compared for L-shaped plates. A modal transmission coefficient is also defined and for the cases considered, and is used to develop an alternative method of deriving the transmission coefficient in a finite structure. Frequency averaged transmission coefficients are also considered, and the transmission coefficients derived for finite and semi-infinite structures are found to be very similar after frequency averaging. Statistical Energy Analysis models of coupled plates are evaluated using transmission coefficients derived from waveguide models. The results of the SEA models are compared to those predicted by the analytical waveguide method. A modal transmission coefficient based SEA model is also investigated. In an attempt to validate the numerical work presented in this thesis, experiments have been conducted. Using a wave extraction technique, both the wave amplitudes and plate properties have been evaluated from experimental data, and are subsequently used to experimentally measure the transmission coefficient for two plates coupled at different angles.

The ongoing drive for lighter and more efficient structural components by the commercial engineering industry has resulted in the rapid adoption of the finite element method (FE) for design analysis. Satisfied with the success of finite elements in reducing prototyping costs and overall production times, the industry has begun to look at other areas where the finite element method can save time, and in particular, improve designs. First, the mathematical methods of optimisation, on which the methods of structural design improvement are based, are presented. This includes the methods of: topology, influence functions, basis vectors, geometric splines and direct sensitivity methods. Each method is demonstrated with the solution of a sample structural improvement problem for various objectives (frequency, stress and weight reduction, for example). The practical application of the individual methods has been tested by solving three structural engineering problems sourced from the automotive engineering industry: the redesign of two different front suspension control arms, and the cost-reduction of an automatic brake tubing system. All three problems were solved successfully, resulting in improved designs. Each method has been evaluated with respect the practical application, popularity of the method and also any problems using the method. The solutions presented in each section were all solved using the FE design improvement software ReSHAPE from Advea Engineering Pty. Ltd.

This thesis presents numerical techniques which have been developed to analyse three dimensional problems in offshore engineering. In particular, the three dimensional liquefaction analysis of offshore foundations on granular soils is the main subject of the thesis. The subject matter is broadly divided into four sections: 1)Development of an efficient method for the three dimensional elasto?plastic finite element analysis of consolidating soil through the use of a discrete Fourier representation of field quantities. 2)Validation of the three dimensional method through analyses of shallow offshore foundations subjected to three dimensional loading and investigation of the yield locus for foundations on purely cohesive soils. 3)Formulation of governing equations suitable for three dimensional liquefaction analyses of offshore foundations founded on granular soil, presentation of a method for liquefaction analyses, and application of the method in modified elastic liquefaction analyses of offshore foundations. 4)Application of a conventional elasto?plastic soil model in the liquefaction analyses of offshore foundations using the three dimensional finite element method. The finite element method developed in this thesis provides a rigorous and efficient numerical tool for the analysis of geotechnical problems subjected to three dimensional loading. The efficiency of the numerical tool makes it possible to tackle some of the problems in geotechnical engineering which would otherwise need enormous computing time and thus would be impractical. The accuracy of the numerical scheme is demonstrated by solving the bearing capacity problem of shallow foundations subjected to three dimensional loading. The generalized governing equations and the numerical method for liquefaction analyses presented in this thesis provide a solid base for the analysis of offshore foundations subjected to cyclic wave loading where they are founded on potentially liquefiable soil. The practicability of the numerical scheme is also demonstrated by a modified elastic liquefaction analysis of offshore foundations. The liquefaction phenomenon is redefined in the context of the conventional Mohr?Coulomb model, so that a relatively simple and practical model for elasto?plastic liquefaction analysis is presented. The three dimensional finite element method together with the numerical scheme for liquefaction analysis and the elasto?plastic soil model provide a suitable practical engineering tool for exploring the responses of offshore foundations subjected to cyclic wave loading.