Morse taper implants at different bone levels: a finite element analysis of stress distribution

AIM: To explore the biomechanical effects of the different implantation bone levels of Morse taper implants, employing a finite element analysis (FEA). METHODS: Dental implants (TitamaxCM) with 4x13 mm and 4x11 mm, and their respective abutments with 3.5 mm height, simulating a screwed premolar metal-ceramic crown, had their design performed using the software AnsysWorkbench 10.0. They were positioned in bone blocks, covered by 2.5 mm thickness of mucosa. The cortical bone was designed with 1.5 mm thickness and the trabecular bone completed the bone block. Four groups were formed: group 11CBL (11 mm implant length on cortical bone level), group 11TBL (11 mm implant length on trabecular bone level), group 13CBL (13mm implant length on cortical bone level) and group 13TBL (13 mm implant length on trabecular bone level). Oblique 200 N loads were applied. Von Mises equivalent stresses in cortical and trabecular bones were evaluated with the same design program. RESULTS: The results were shown qualitatively and quantitatively by standard scales for each type of bone. By the results obtained, it can be suggested that positioning the implant completely in trabecular bone brings harm with respect to the generated stresses. Its implantation in the cortical bone has advantages with respect to better anchoring and locking, reflecting a better dissipation of the stresses along the implant/bone interfaces. In addition, the search for anchoring the implant in its apical region in cortical bone is of great value to improve stabilization and consequently better stress distribution. CONCLUSIONS: The implant position slightly below the bone in relation to the bone crest brings advantages as the best long-term predictability with respect to the expected neck bone loss.

Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

Asymptotically exact probability distribution for the Sinai model with finite drift

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, similar to v(mu n), where mu <1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrodinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasicontinuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.

An experimental and finite element investigation of the biomechanics of vertebral compression fractures

Osteoporosis is a disease characterized by low bone mass and micro-architectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture. Osteoporosis affects over 200 million people worldwide, with an estimated 1.5 million fractures annually in the United States alone, and with attendant costs exceeding $10 billion dollars per annum. Osteoporosis reduces bone density through a series of structural changes to the honeycomb-like trabecular bone structure (micro-structure). The reduced bone density, coupled with the microstructural changes, results in significant loss of bone strength and increased fracture risk. Vertebral compression fractures are the most common type of osteoporotic fracture and are associated with pain, increased thoracic curvature, reduced mobility, and difficulty with self care. Surgical interventions, such as kyphoplasty or vertebroplasty, are used to treat osteoporotic vertebral fractures by restoring vertebral stability and alleviating pain. These minimally invasive procedures involve injecting bone cement into the fractured vertebrae. The techniques are still relatively new and while initial results are promising, with the procedures relieving pain in 70-95% of cases, medium-term investigations are now indicating an increased risk of adjacent level fracture following the procedure. With the aging population, understanding and treatment of osteoporosis is an increasingly important public health issue in developed Western countries. The aim of this study was to investigate the biomechanics of spinal osteoporosis and osteoporotic vertebral compression fractures by developing multi-scale computational, Finite Element (FE) models of both healthy and osteoporotic vertebral bodies. The multi-scale approach included the overall vertebral body anatomy, as well as a detailed representation of the internal trabecular microstructure. This novel, multi-scale approach overcame limitations of previous investigations by allowing simultaneous investigation of the mechanics of the trabecular micro-structure as well as overall vertebral body mechanics. The models were used to simulate the progression of osteoporosis, the effect of different loading conditions on vertebral strength and stiffness, and the effects of vertebroplasty on vertebral and trabecular mechanics. The model development process began with the development of an individual trabecular strut model using 3D beam elements, which was used as the building block for lattice-type, structural trabecular bone models, which were in turn incorporated into the vertebral body models. At each stage of model development, model predictions were compared to analytical solutions and in-vitro data from existing literature. The incremental process provided confidence in the predictions of each model before incorporation into the overall vertebral body model. The trabecular bone model, vertebral body model and vertebroplasty models were validated against in-vitro data from a series of compression tests performed using human cadaveric vertebral bodies. Firstly, trabecular bone samples were acquired and morphological parameters for each sample were measured using high resolution micro-computed tomography (CT). Apparent mechanical properties for each sample were then determined using uni-axial compression tests. Bone tissue properties were inversely determined using voxel-based FE models based on the micro-CT data. Specimen specific trabecular bone models were developed and the predicted apparent stiffness and strength were compared to the experimentally measured apparent stiffness and strength of the corresponding specimen. Following the trabecular specimen tests, a series of 12 whole cadaveric vertebrae were then divided into treated and non-treated groups and vertebroplasty performed on the specimens of the treated group. The vertebrae in both groups underwent clinical-CT scanning and destructive uniaxial compression testing. Specimen specific FE vertebral body models were developed and the predicted mechanical response compared to the experimentally measured responses. The validation process demonstrated that the multi-scale FE models comprising a lattice network of beam elements were able to accurately capture the failure mechanics of trabecular bone; and a trabecular core represented with beam elements enclosed in a layer of shell elements to represent the cortical shell was able to adequately represent the failure mechanics of intact vertebral bodies with varying degrees of osteoporosis. Following model development and validation, the models were used to investigate the effects of progressive osteoporosis on vertebral body mechanics and trabecular bone mechanics. These simulations showed that overall failure of the osteoporotic vertebral body is initiated by failure of the trabecular core, and the failure mechanism of the trabeculae varies with the progression of osteoporosis; from tissue yield in healthy trabecular bone, to failure due to instability (buckling) in osteoporotic bone with its thinner trabecular struts. The mechanical response of the vertebral body under load is highly dependent on the ability of the endplates to deform to transmit the load to the underlying trabecular bone. The ability of the endplate to evenly transfer the load through the core diminishes with osteoporosis. Investigation into the effect of different loading conditions on the vertebral body found that, because the trabecular bone structural changes which occur in osteoporosis result in a structure that is highly aligned with the loading direction, the vertebral body is consequently less able to withstand non-uniform loading states such as occurs in forward flexion. Changes in vertebral body loading due to disc degeneration were simulated, but proved to have little effect on osteoporotic vertebra mechanics. Conversely, differences in vertebral body loading between simulated invivo (uniform endplate pressure) and in-vitro conditions (where the vertebral endplates are rigidly cemented) had a dramatic effect on the predicted vertebral mechanics. This investigation suggested that in-vitro loading using bone cement potting of both endplates has major limitations in its ability to represent vertebral body mechanics in-vivo. And lastly, FE investigation into the biomechanical effect of vertebroplasty was performed. The results of this investigation demonstrated that the effect of vertebroplasty on overall vertebra mechanics is strongly governed by the cement distribution achieved within the trabecular core. In agreement with a recent study, the models predicted that vertebroplasty cement distributions which do not form one continuous mass which contacts both endplates have little effect on vertebral body stiffness or strength. In summary, this work presents the development of a novel, multi-scale Finite Element model of the osteoporotic vertebral body, which provides a powerful new tool for investigating the mechanics of osteoporotic vertebral compression fractures at the trabecular bone micro-structural level, and at the vertebral body level.

Mixed convection over a horizontal plate with streamwise non-uniform surface temperature distribution

Numerical investigation on mixed convection of a two-dimensional incompressible laminar flow over a horizontal flat plate with streamwise sinusoidal distribution of surface temperature has been performed for different values of Rayleigh number, Reynolds number and frequency of periodic temperature for constant Prandtl number and amplitude of periodic temperature. Finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm basis numerical scheme has been employed. The investigating parameters are the Rayleigh number, the Reynolds number and frequency of periodic temperature. The effect of variation of individual investigating parameters on mixed convection flow characteristics has been studied to observe the hydrodynamic and thermal behavior for while keeping the other parameters constant. The fluid considered in this study is air with Prandtl number 0.72. The results are obtained for the Rayleigh number range of 102 to 104, Reynolds number ranging from 1 to 100 and the frequency of periodic temperature from 1 to 5. Isotherms, streamlines, average and local Nusselt numbers are presented to show the effect of the different values of aforementioned investigating parameters on fluid flow and heat transfer.

Saturated core high-temperature superconducting fault current limiters as an alternative to conventional series reactors in a distribution grid

Series reactors are used in distribution grids to reduce the short-circuit fault level. Some of the disadvantages of the application of these devices are the voltage drop produced across the reactor and the steep front rise of the transient recovery voltage (TRV), which generally exceeds the rating of the associated circuit breaker. Simulations were performed to compare the characteristics of a saturated core High-Temperature Superconducting Fault Current Limiter (HTS FCL) and a series reactor. The design of the HTS FCL was optimized using the evolutionary algorithm. The resulting Pareto frontier curve of optimum solution is presented in this paper. The results show that the steady-state impedance of an HTS FCL is significantly lower than that of a series reactor for the same level of fault current limiting. Tests performed on a prototype 11 kV HTS FCL confirm the theoretical results. The respective transient recovery voltages (TRV) of the HTS FCL and an air core reactor of comparable fault current limiting capability are also determined. The results show that the saturated core HTS FCL has a significantly lower effect on the rate of rise of the circuit breaker TRV as compared to the air core reactor. The simulations results are validated with shortcircuit test results.

Stress distribution of CFRP strengthened steel hollow sections under tension

Carbon fibre reinforced polymer (CFRP) sheets have many outstanding properties such as high strength, high elastic modulus, light weight and good durability which are made them a suitable alternative for steel in strengthening work. This paper describe the ultimate load carrying capacity of steel hollow sections at effective bond length in terms of its cross sectional area and the stress distribution within bond region for different layers CFRP. It was found that depending on their size and orientation of uni- directional CFRP layers, the ultimate tensile load was different. Along with these tests, non linear finite element analysis was also performed to validate the ultimate load carrying capacity depending on their cross sections. The predicted ultimate loads from FE analysis are found very close to the laboratory test results. The validated model has been used to determine the stress distribution at bond joint for different orientation of CFRP. This research shows the effect of stress distribution and suitable wrapping layer to be used for the strengthening of steel hollow sections in tension.

Inelastic finite element analysis of composite beams on the basis of the plastic hinge approach

This paper emphasizes material nonlinear effects on composite beams with recourse to the plastic hinge method. Numerous combinations of steel and concrete sections form arbitrary composite sections. Secondly, the material properties of composite beams vary remarkably across its section from ductile steel to brittle concrete. Thirdly, concrete is weak in tension, so composite section changes are dependent on load distribution. To this end, the plastic zone approach is convenient for inelastic analysis of composite sections that can evaluate member resistance, including material nonlinearities, by routine numerical integration with respect to every fiber across the composite section. As a result, many researchers usually adopt the plastic zone approach for numerical inelastic analyses of composite structures. On the other hand, the plastic hinge method describes nonlinear material behaviour of an overall composite section integrally. Consequently, proper section properties for use in plastic hinge spring stiffness are required to represent the material behaviour across the arbitrary whole composite section. In view of numerical efficiency and convergence, the plastic hinge method is superior to the plastic zone method. Therefore, based on the plastic hinge approach, how to incorporate the material nonlinearities of the arbitrary composite section into the plastic hinge stiffness formulation becomes a prime objective of the present paper. The partial shear connection in this paper is by virtue of the effective flexural rigidity as AISC 1993 [American Institute of Steel Construction (AISC). Load and resistance factor design specifications. 2nd ed., Chicago; 1993]. Nonlinear behaviour of different kinds of composite beam is investigated in this paper, including two simply supported composite beams, a cantilever and a two span continuous composite beam.

Fast re-parameterisation of Gaussian mixture models for robotics applications

Autonomous navigation and picture compilation tasks require robust feature descriptions or models. Given the non Gaussian nature of sensor observations, it will be shown that Gaussian mixture models provide a general probabilistic representation allowing analytical solutions to the update and prediction operations in the general Bayesian filtering problem. Each operation in the Bayesian filter for Gaussian mixture models multiplicatively increases the number of parameters in the representation leading to the need for a re-parameterisation step. A computationally efficient re-parameterisation step will be demonstrated resulting in a compact and accurate estimate of the true distribution.

Finite element analysis of CFRP strengthened steel hollow sections under tension

This paper presents a nonlinear finite element (FE) model for the analysis of very high strength (VHS) steel hollow sections wrapped by high modulus carbon fibre rein forced polymer (CFRP) sheets. The bond strength of CFRP wrapped VHS circular steel hollow section under tension is investigated using the FE model. The three dimensional FE model by Nonlinear static analysis has been carried out by Strand 7 finite element software. The model is validated by the experimental data obtained from Fawzia et al [1]. A detail parametric study has been performed to examine the effect of number of CFRP layers, different diameters of VHS steel tube and different bond lengths of CFRP sheet. The analytical model developed by Fawzia et al. [1] has been used to determine the load carrying capacity of different diameters of CFRP strengthened VHS steel tube by using the capacity from each layer of CFRP sheet. The results from FE model have found in reasonable agreement with the analytical model developed by Fawzia et al [1]. This validation was necessary because the analytical model by Fawzia et al [1] was developed by using only one diameter of VHS steel tube and fixed (five) number of CFRP layers. It can be concluded that the developed analytical model is valid for CFRP strengthened VHS steel tubes with diameter range of 38mm to 100mm and CFRP layer range of 3 to 5 layers. Based on the results it can also be concluded that the effective bond length is consistent for different diameters of steel tubes and different layers of CFRP. Three layers of CFRP is considered most effective wrapping scheme due to the cost effectiveness. Finally the distribution of longitudinal and hoop stress has been determined by the finite element model for different diameters of CFRP strengthened VHS steel tube.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Numerical simulation of railway track supporting system using finite-infinite and thin layer elements under impulsive loads

The present study deals with two dimensional, numerical simulation of railway track supporting system subjected to dynamic excitation force. Under plane strain condition, the coupled finite-infinite elements to represent the near and far field stress distribution and thin layer interface element was employed to model the interfacial behavior between sleepers and ballast. To account for the relative debonding, slipping and crushing that could take place in the contact area between the sleepers and ballast, modified Mohr-Coulomb criterion was adopted. Furthermore an attempt has been made to consider the elasto-plastic material non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and supporting materials. Based on the proposed physical and constitutive modeling a code has been developed for dynamic loads. The applicability of the developed F.E code has been demonstrated by analyzing a real railway supporting structure.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

A novel measure of fractional anisotropy based on the tensor distribution function

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.