Cerclage, evolution and potential of a Cinderella Technology : an overview with reference to periprosthetic fractures

Periprosthetic fractures are increasingly frequent. The fracture may be located over the shaft of the prosthesis, at its tip or below (21). The treatment of explosion fractures is difficult because the shaft blocks the application of implants, like screws, which need to penetrate the medullary cavity. The cerclage, as a simple periosteal loop, made of wire or more recently cable, does not only avoid the medullary cavity. Its centripetal mode of action is well suited for reducing and maintaining radially displaced fractures. Furthermore, the cerclage lends itself well for minimally invasive internal fixation. New insight challenges the disrepute of which the cerclage technology suffered for decades. The outcome of cerclage fixation benefits from an improved understanding of its technology, mechano-biology and periosteal blood supply. Preconceived and generally accepted opinions like "strangulation of blood supply" need to be re-examined. Recent mechanical evaluations (22) demonstrate that the wire application may be improved but cable is superior in hand- ling, maintenance of tension and strength. Beside the classical concepts of absolute and relative stability a defined stability condition needs consideration. It is typical for cerclage. Called "loose-lock stability" it specifies the situation where a loosened implant allows first unimpeded displacement changing abruptly into a locked fixation preventing further dislocation.

Perspectives on practical experiences in professional education : an editorial and introduction

How important are the practical experiences through which our neophyte professionals are prepared for the real world of work? P. E. P. E. (Practical Experiences in Professional Education) Inc has generated this book with, not only, the aim of disseminating knowledge through networks within the professional silos of distinctive disciplines but to generate a space and platform for generic concepts and practices that can be examined and incorporated across many disciplines. Mentoring, ethics and transitioning into the profession are explored in the book but each chapter illustrates how PEPE Inc has within its community a culture of engagement, experimentation and deep thinking that connects all aspects of learning in the field. Ken Zeichner’s research clearly shows that field experiences are important occasions for professional learning rather than merely times for pre-service candidates to demonstrate or apply things previously learned. Susan Groundwater-Smith acknowledges PEPE Inc on being a leader in supporting the evolution of a developmental practicum curriculum in the initial education of professionals, mainly in the field of education, but also with respect to the preparation of health and allied professionals, those preparing to become social workers and even in professional practices such as engineering and architecture.

Ocular aberrations in the peripheral visual field

We modified a commercial Hartmann-Shack aberrometer and used it to measure ocular aberrations across the central 42º horizontal x 32º vertical visual fields of five young emmetropic subjects. Some Zernike aberration coefficients show coefficient field distributions that were similar to the field dependence predicted by Seidel theory (astigmatism, oblique astigmatism, horizontal coma, vertical coma), but defocus did not demonstrate such similarity.

Performance load testing and structural adequacy evaluation of road bridge decks

Many ageing road bridges, particularly timber bridges, require urgent improvement due to the demand imposed by the recent version of the Australian bridge loading code, AS 5100. As traffic volume plays a key role in the decision of budget allocations for bridge refurbishment/ replacement, many bridges in low volume traffic network remain in poor condition with axle load and/ or speed restrictions, thus disadvantaging many rural communities. This thesis examines an economical and environmentally sensible option of incorporating disused flat rail wagons (FRW) in the construction of bridges in low volume, high axle load road network. The constructability, economy and structural adequacy of the FRW road bridge is reported in the thesis with particular focus of a demonstration bridge commissioned in regional Queensland. The demonstration bridge comprises of a reinforced concrete slab (RCS) pavement resting on two FRWs with custom designed connection brackets at regular intervals along the span of the bridge. The FRW-RC bridge deck assembly is supported on elastomeric rubber pads resting on the abutment. As this type of bridge replacement technology is new and its structural design is not covered in the design standards, the in-service structural performance of the FRW bridge subjected to the high axle loadings prescribed in AS 5100 is examined through performance load testing. Both the static and the moving load tests are carried out using a fully laden commonly available three-axle tandem truck. The bridge deck is extensively strain gauged and displacement at several key locations is measured using linear variable displacement transducers (LVDTs). A high speed camera is used in the performance test and the digital image data are analysed using proprietary software to capture the locations of the wheel positions on the bridge span accurately. The wheel location is thus synchronised with the displacement and strain time series to infer the structural response of the FRW bridge. Field test data are used to calibrate a grillage model, developed for further analysis of the FRW bridge to various sets of high axle loads stipulated in the bridge design standard. Bridge behaviour predicted by the grillage model has exemplified that the live load stresses of the FRW bridge is significantly lower than the yield strength of steel and the deflections are well below the serviceability limit state set out in AS 5100. Based on the results reported in this thesis, it is concluded that the disused FRWs are competent to resist high axle loading prescribed in AS 5100 and are a viable alternative structural solution of bridge deck in the context of the low volume road networks.

Deformation behaviours of coarse-grained and nanocrystalline Mg-5wt% Al alloys

Magnesium alloys have been of growing interest to various engineering applications, such as the automobile, aerospace, communication and computer industries due to their low density, high specific strength, good machineability and availability as compared with other structural materials. However, most Mg alloys suffer from poor plasticity due to their Hexagonal Close Packed structure. Grain refinement has been proved to be an effective method to enhance the strength and alter the ductility of the materials. Several methods have been proposed to produce materials with nanocrystalline grain structures. So far, most of the research work on nanocrystalline materials has been carried out on Face-Centered Cubic and Body-Centered Cubic metals. However, there has been little investigation of nanocrystalline Mg alloys. In this study, bulk coarse-grained and nanocrystalline Mg alloys were fabricated by a mechanical alloying method. The mixed powder of Mg chips and Al powder was mechanically milled under argon atmosphere for different durations of 0 hours (MA0), 10 hours (MA10), 20 hours (MA20), 30 hours (MA30) and 40 hours (MA40), followed by compaction and sintering. Then the sintered billets were hot-extruded into metallic rods with a 7 mm diameter. The obtained Mg alloys have a nominal composition of Mg–5wt% Al, with grain sizes ranging from 13 μm down to 50 nm, depending on the milling durations. The microstructure characterization and evolution after deformation were carried out by means of Optical microscopy, X-Ray Diffraction, Scanning Electron Microscopy, Transmission Electron Microscopy, Scanning Probe Microscopy and Neutron Diffraction techniques. Nanoindentaion, compression and micro-compression tests on micro-pillars were used to study the size effects on the mechanical behaviour of the Mg alloys. Two kinds of size effects on the mechanical behaviours and deformation mechanisms were investigated: grain size effect and sample size effect. The nanoindentation tests were composed of constant strain rate, constant loading rate and indentation creep tests. The normally reported indentation size effect in single crystal and coarse-grained crystals was observed in both the coarse-grained and nanocrystalline Mg alloys. Since the indentation size effect is correlated to the Geometrically Necessary Dislocations under the indenter to accommodate the plastic deformation, the good agreement between the experimental results and the Indentation Size Effect model indicated that, in the current nanocrystalline MA20 and MA30, the dislocation plasticity was still the dominant deformation mechanism. Significant hardness enhancement with decreasing grain size, down to 58 nm, was found in the nanocrystalline Mg alloys. Further reduction of grain size would lead to a drop in the hardness values. The failure of grain refinement strengthening with the relatively high strain rate sensitivity of nanocrystalline Mg alloys suggested a change in the deformation mechanism. Indentation creep tests showed that the stress exponent was dependent on the loading rate during the loading section of the indentation, which was related to the dislocation structures before the creep starts. The influence of grain size on the mechanical behaviour and strength of extruded coarse-grained and nanocrystalline Mg alloys were investigated using uniaxial compression tests. The macroscopic response of the Mg alloys transited from strain hardening to strain softening behaviour, with grain size reduced from 13 ìm to 50 nm. The strain hardening was related to the twinning induced hardening and dislocation hardening effect, while the strain softening was attributed to the localized deformation in the nanocrystalline grains. The tension–compression yield asymmetry was noticed in the nanocrystalline region, demonstrating the twinning effect in the ultra-fine-grained and nanocrystalline region. The relationship k tensions < k compression failed in the nanocrystalline Mg alloys; this was attributed to the twofold effect of grain size on twinning. The nanocrystalline Mg alloys were found to exhibit increased strain rate sensitivity with decreasing grain size, with strain rate ranging from 0.0001/s to 0.01/s. Strain rate sensitivity of coarse-grained MA0 was increased by more than 10 times in MA40. The Hall-Petch relationship broke down at a critical grain size in the nanocrystalline region. The breakdown of the Hall-Petch relationship and the increased strain rate sensitivity were due to the localized dislocation activities (generalization and annihilation at grain boundaries) and the more significant contribution from grain boundary mediated mechanisms. In the micro-compression tests, the sample size effects on the mechanical behaviours were studied on MA0, MA20 and MA40 micro-pillars. In contrast to the bulk samples under compression, the stress-strain curves of MA0 and MA20 micro-pillars were characterized with a number of discrete strain burst events separated by nearly elastic strain segments. Unlike MA0 and MA20, the stress-strain curves of MA40 micro-pillars were smooth, without obvious strain bursts. The deformation mechanisms of the MA0 and MA20 micro-pillars under micro-compression tests were considered to be initially dominated by deformation twinning, followed by dislocation mechanisms. For MA40 pillars, the deformation mechanisms were believed to be localized dislocation activities and grain boundary related mechanisms. The strain hardening behaviours of the micro-pillars suggested that the grain boundaries in the nanocrystalline micro-pillars would reduce the source (nucleation sources for twins/dislocations) starvation hardening effect. The power law relationship of the yield strength on pillar dimensions in MA0, MA20 supported the fact that the twinning mechanism was correlated to the pre-existing defects, which can promote the nucleation of the twins. Then, we provided a latitudinal comparison of the results and conclusions derived from the different techniques used for testing the coarse-grained and nanocrystalline Mg alloy; this helps to better understand the deformation mechanisms of the Mg alloys as a whole. At the end, we summarized the thesis and highlighted the conclusions, contributions, innovations and outcomes of the research. Finally, it outlined recommendations for future work.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury

Towards a controlled growth of self-assembled nanostructures: shaping, ordering and localization in Ge/Si heteroepitaxy.

The strain-induced self-assembly of suitable semiconductor pairs is an attractive natural route to nanofabrication. To bring to fruition their full potential for actual applications, individual nanostructures need to be combined into ordered patterns in which the location of each single unit is coupled with others and the surrounding environment. Within the Ge/Si model system, we analyze a number of examples of bottom-up strategies in which the shape, positioning, and actual growth mode of epitaxial nanostructures are tailored by manipulating the intrinsic physical processes of heteroepitaxy. The possibility of controlling elastic interactions and, hence, the configuration of self-assembled quantum dots by modulating surface orientation with the miscut angle is discussed. We focus on the use of atomic steps and step bunching as natural templates for nanodot clustering. Then, we consider several different patterning techniques which allow one to harness the natural self-organization dynamics of the system, such as: scanning tunneling nanolithography, focused ion beam and nanoindentation patterning. By analyzing the evolution of the dot assembly by scanning probe microscopy, we follow the pathway which leads to lateral ordering, discussing the thermodynamic and kinetic effects involved in selective nucleation on patterned substrates.

Iron biogeochemistry and associated greenhouse gas evolution in a forested subtropical Australian coastal catchment : Poona Creek, Southeast Queensland

Iron (Fe) is the fourth most abundant element in the Earth’s crust. Excess Fe mobilization from terrestrial into aquatic systems is of concern for deterioration of water quality via biofouling and nuisance algal blooms in coastal and marine systems. Substantial Fe dissolution and transport involve alternate Fe(II) oxidation followed by Fe(III) reduction, with a diversity of Bacteria and Archaea acting as the key catalyst. Microbially-mediated Fe cycling is of global significance with regard to cycles of carbon (C), sulfur (S) and manganese (Mn). However, knowledge regarding microbial Fe cycling in circumneutral-pH habitats that prevail on Earth has been lacking until recently. In particular, little is known regarding microbial function in Fe cycling and associated Fe mobilization and greenhouse (CO2 and CH4, GHG) evolution in subtropical Australian coastal systems where microbial response to ambient variations such as seasonal flooding and land use changes is of concern. Using the plantation-forested Poona Creek catchment on the Fraser Coast of Southeast Queensland (SEQ), this research aimed to 1) study Fe cycling-associated bacterial populations in diverse terrestrial and aquatic habitats of a representative subtropical coastal circumneutral-pH (4–7) ecosystem; and 2) assess potential impacts of Pinus plantation forestry practices on microbially-mediated Fe mobilization, organic C mineralization and associated GHG evolution in coastal SEQ. A combination of wet-chemical extraction, undisturbed core microcosm, laboratory bacterial cultivation, microscopy and 16S rRNA-based molecular phylogenetic techniques were employed. The study area consisted primarily of loamy sands, with low organic C and dissolved nutrients. Total reactive Fe was abundant and evenly distributed within soil 0–30 cm profiles. Organic complexation primarily controlled Fe bioavailability and forms in well-drained plantation soils and water-logged, native riparian soils, whereas tidal flushing exerted a strong “seawater effect” in estuarine locations and formed a large proportion of inorganic Fe(III) complexes. There was a lack of Fe(II) sources across the catchment terrestrial system. Mature, first-rotation plantation clear-felling and second-rotation replanting significantly decreased organic matter and poorly crystalline Fe in well-drained soils, although variations in labile soil organic C fractions (dissolved organic C, DOC; and microbial biomass C, MBC) were minor. Both well-drained plantation soils and water-logged, native-vegetation soils were inhabited by a variety of cultivable, chemotrophic bacterial populations capable of C, Fe, S and Mn metabolism via lithotrophic or heterotrophic, (micro)aerobic or anaerobic pathways. Neutrophilic Fe(III)-reducing bacteria (FeRB) were most abundant, followed by aerobic, heterotrophic bacteria (heterotrophic plate count, HPC). Despite an abundance of FeRB, cultivable Fe(II)-oxidizing bacteria (FeOB) were absent in associated soils. A lack of links between cultivable Fe, S or Mn bacterial densities and relevant chemical measurements (except for HPC correlated with DOC) was likely due to complex biogeochemical interactions. Neither did variations in cultivable bacterial densities correlate with plantation forestry practices, despite total cultivable bacterial densities being significantly lower in estuarine soils when compared with well-drained plantation soils and water-logged, riparian native-vegetation soils. Given that bacterial Fe(III) reduction is the primary mechanism of Fe oxide dissolution in soils upon saturation, associated Fe mobilization involved several abiotic and biological processes. Abiotic oxidation of dissolved Fe(II) by Mn appeared to control Fe transport and inhibit Fe dissolution from mature, first-rotation plantation soils post-saturation. Such an effect was not observed in clear-felled and replanted soils associated with low SOM and potentially low Mn reactivity. Associated GHG evolution post-saturation mainly involved variable CO2 emissions, with low, but consistently increasing CH4 effluxes in mature, first-rotation plantation soil only. In comparison, water-logged soils in the riparian native-vegetation buffer zone functioned as an important GHG source, with high potentials for Fe mobilization and GHG, particularly CH4 emissions in riparian loam soils associated with high clay and crystalline Fe fractions. Active Fe–C cycling was unlikely to occur in lower-catchment estuarine soils associated with low cultivable bacterial densities and GHG effluxes. As a key component of bacterial Fe cycling, neutrophilic FeOB widely occurred in diverse aquatic, but not terrestrial, habitats of the catchment study area. Stalked and sheathed FeOB resembling Gallionella and Leptothrix were limited to microbial mat material deposited in surface fresh waters associated with a circumneutral-pH seep, and clay-rich soil within riparian buffer zones. Unicellular, Sideroxydans-related FeOB (96% sequence identity) were ubiquitous in surface and subsurface freshwater environments, with highest abundance in estuary-adjacent shallow coastal groundwater water associated with redox transition. The abundance of dissolved C and Fe in the groundwater-dependent system was associated with high numbers of cultivable anaerobic, heterotrophic FeRB, microaerophilic, putatively lithotrophic FeOB and aerobic, heterotrophic bacteria. This research represents the first study of microbial Fe cycling in diverse circumneutral-pH environments (terrestrial–aquatic, freshwater–estuarine, surface–subsurface) of a subtropical coastal ecosystem. It also represents the first study of its kind in the southern hemisphere. This work highlights the significance of bacterial Fe(III) reduction in terrestrial, and bacterial Fe(II) oxidation in aquatic catchment Fe cycling. Results indicate the risk of promotion of Fe mobilization due to plantation clear-felling and replanting, and GHG emissions associated with seasonal water-logging. Additional significant outcomes were also achieved. The first direct evidence for multiple biomineralization patterns of neutrophilic, microaerophilic, unicellular FeOB was presented. A putatively pure culture, which represents the first cultivable neutrophilic FeOB from the southern hemisphere, was obtained as representative FeOB ubiquitous in diverse catchment aquatic habitats.

Sky high and back again : the evolution of simulation-based design from aerospace to construction

Emerging from the challenge to reduce energy consumption in buildings is a need for research and development into the more effective use of simulation as a decision-support tool. Despite significant research, persistent limitations in process and software inhibit the integration of energy simulation in early architectural design. This paper presents a green star case study to highlight the obstacles commonly encountered with current integration strategies. It then examines simulation-based design in the aerospace industry, which has overcome similar limitations. Finally, it proposes a design system based on this contrasting approach, coupling parametric modelling and energy simulation software for rapid and iterative performance assessment of early design options.

Hamstring strain injuries : factors that lead to injury and re-injury

Hamstring strain injuries (HSIs) are common in a number of sports and incidence rates have not declined in recent times. Additionally, the high rate of recurrent injuries suggests that our current understanding of HSI and re-injury risk is incomplete. Whilst the multifactoral nature of HSIs is agreed upon by many, often individual risk factors and/or causes of injury are examined in isolation. This review aims to bring together the causes, risk factors and interventions associated with HSIs to better understand why HSIs are so prevalent. Running is often identified as the primary activity type for HSIs and given the high eccentric forces and moderate muscle strain placed on the hamstrings during running these factors are considered to be part of the aetiology of HSIs. However, the exact causes of HSIs remain unknown and whilst eccentric contraction and muscle strain purportedly play a role, accumulated muscle damage and/or a single injurious event may also contribute. Potentially, all of these factors interact to varying degrees depending on the injurious activity type (i.e. running, kicking). Furthermore, anatomical factors, such as the biarticular organization, the dual innervations of biceps femoris (BF), fibre type distribution, muscle architecture and the degree of anterior pelvic tilt, have all been implicated. Each of these variables impact upon HSI risk via a number of different mechanisms that include increasing hamstring muscle strain and altering the susceptibility of the hamstrings to muscle damage. Reported risk factors for HSIs include age, previous injury, ethnicity, strength imbalances, flexibility and fatigue. Of these, little is known, definitively, about why previous injury increases the risk of future HSIs. Nevertheless, interventions put in place to reduce the incidence of HSIs by addressing modifiable risk factors have focused primarily on increasing eccentric strength, correcting strength imbalances and improving flexibility. The response to these intervention programmes has been mixed with varied levels of success reported. A conceptual framework is presented suggesting that neuromuscular inhibition following HSIs may impede the rehabilitation process and subsequently lead to maladaptation of hamstring muscle structure and function, including preferentially eccentric weakness, atrophy of the previously injured muscles and alterations in the angle of peak knee flexor torque. This remains an area for future research and practitioners need to remain aware of the multifactoral nature of HSIs if injury rates are to decline.

Evaluating the learning outcomes of an international field trip in postgraduate lighting design courses

Lighting industry professionals work in an international marketplace and encounter a range of social, geographical and cultural challenges associated with this. Education in lighting should introduce students to aspects of these challenges. To achieve this, an international field trip was recently undertaken that sought to provide an authentic learning experience for students. Twelve Masters of Lighting students from two Australian universities took part in a field trip to Shanghai, China and surrounding areas. The goal was to offer students insight into practical issues in the lighting industry at an international level and to do so in a unique and authentic context. To evaluate the outcomes of the trip, each participant was surveyed afterwards. Benefits were identified in terms of: increased knowledge and insight into manufacturing issues in lighting, experiential learning in lighting design practice not available locally (e.g, master planning), increased understanding of cultural influences in design and enhancing professional contacts within the lighting industry. Field trips may also act as an inverted curriculum experience for new students to engage them and promote learning within a professional context.

Cultural chaos : Journalism, News and Power in a Globalised World

With examples drawn from media coverage of the War on Terror, the 2003 invasion of Iraq, Hurricane Katrina and the London underground bombings, Cultural Chaos explores the changing relationship between journalism and power in an increasingly globalised news culture. In this new text, Brian McNair examines the processes of cultural, geographic and political dissolution in the post-Cold War era and the rapid evolution of information and communication technologies. He investigates the impact of these trends on domestic and international journalism and on political processes in democratic and authoritarian societies across the world. Written in a lively and accessible style, Cultural Chaos provides students with an overview of the evolution of the sociology of journalism, a critical review of current thinking within media studies and an argument for a revision and renewal of the paradigms that have dominated the field since the early twentieth century. Separate chapters are devoted to new developments such as the rise of the blogosphere and satellite television news and their impact on journalism more generally. Cultural Chaos will be essential reading for all those interested in the emerging globalised news culture of the twenty-first century.

Complexity, evolution, and the structure of demand

This chapter argues that evolutionary economics should be founded upon complex systems theory rather than neo-Darwinian analogies concerning natural selection, which focus on supply side considerations and competition amongst firms and technologies. It suggests that conceptions such as production and consumption functions should be replaced by network representations, in which the preferences or, more correctly, the aspirations of consumers are fundamental and, as such, the primary drivers of economic growth. Technological innovation is viewed as a process that is intermediate between these aspirational networks, and the organizational networks in which goods and services are produced. Consumer knowledge becomes at least as important as producer knowledge in determining how economic value is generated. It becomes clear that the stability afforded by connective systems of rules is essential for economic flexibility to exist, but that too many rules result in inert and structurally unstable states. In contrast, too few rules result in a more stable state, but at a low level of ordered complexity. Economic evolution from this perspective is explored using random and scale free network representations of complex systems.

Tracking the defining moments of crisis process and practice

Crisis holds the potential for profound change in organizations and industries. The past 50 years of crisis management highlight key shifts in crisis practice, creating opportunities for multiple theories and research tracks. Defining crises such as Tylenol, Exxon Valdez, and September 11 terrorist attacks have influenced or challenged the principles of best practice of crisis communication in public relations. This study traces the development of crisis process and practice by identifying shifts in crisis research and models and mapping these against key management theories and practices. The findings define three crisis domains: crisis planning, building and testing predictive models, and mapping and measuring external environmental influences. These crisis domains mirror but lag the evolution of management theory, suggesting challenges for researchers to reshape the research agenda to close the gap and lead the next stage of development in the field of crisis communication for effective organizational outcomes.

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).