Fiber Bragg grating strain modulation based on nonlinear string transverse force amplifier

The only effective method of Fiber Bragg Grating (FBG) strain modulation has been by changing the distance between its two fixed ends. We demonstrate an alternative being more sensitive to force based on the nonlinear amplification relationship between a transverse force applied to a stretched string and its induced axial force. It may improve the sensitivity and size of an FBG force sensor, reduce the number of FBGs needed for multi-axial force monitoring, and control the resonant frequency of an FBG accelerometer.

A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Effect of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions

The objective of this research was to investigate the effects of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions of a tri-axle semi-trailer. A novel nonlinear model of a multi-axle semi-trailer with longitudinal-connected air suspension was formulated based on fluid mechanics and thermodynamics and was validated through test results. The effects of driving conditions and suspension parameters on dynamic load-sharing and road-friendliness of the semi-trailer were analyzed. Simulation results indicate that the road-friendliness metric-DLC (dynamic load coefficient) is not always in accordance with the load-sharing metric-DLSC (dynamic load-sharing coefficient). The effect of employing larger air lines and connectors on the DLSC optimization ratio gives varying results as road roughness increases and as driving speed increases. When the vehicle load reduces, or the static pressure increases, the DLSC optimization ratio declines monotonically. The results also indicate that if the air line diameter is always assumed to be larger than the connector diameter, the influence of air line diameter on load-sharing is more significant than that of the connector.

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Steps toward the validation of the Trendelenburg Test : the effect of experimentally reduced hip abductor muscle function on frontal plane mechanics

Objective: To investigate the validity of the Trendelenburg test (TT) using an ultrasound-guided nerve block (UNB) of the superior gluteal nerve and determine whether the reduction in hip abductor muscle (HABD) strength would result in the theorized mechanical compensatory strategies measured during the TT. Design: Quasi-experimental. Setting: Hospital. Participants: Convenience sample of 9 healthy men. Only participants with no current or previous injury to the lumbar spine, pelvis, or lower extremities, and no previous surgeries were included. Interventions: Ultrasound-guided nerve block. Main Outcome Measures: Hip abductor muscle strength (percent body weight [%BW]), contralateral pelvic drop (cPD), change in contralateral pelvic drop (Delta cPD), ipsilateral hip adduction, and ipsilateral trunk sway (TRUNK) measured in degrees. Results: The median age and weight of the participants were 31 years (interquartile range [IQR], 22-32 years) and 73 kg (IQR, 67-81 kg), respectively. An average 52% reduction of HABD strength (z = 2.36, P = 0.02) resulted after the UNB. No differences were found in cPD or Delta cPD (z = 0.01, P = 0.99, z = 20.67, P = 0.49, respectively). Individual changes in biomechanics showed no consistency between participants and nonsystematic changes across the group. One participant demonstrated the mechanical compensations described by Trendelenburg. Conclusions: The TT should not be used as a screening measure for HABD strength in populations demonstrating strength greater than 30% BW but should be reserved for use with populations with marked HABD weakness. Clinical Relevance: This study presents data regarding a critical level of HABD strength required to support the pelvis during the TT.

Steps towards the validation of the Trendelenburg test : The effect of experimentally reduced hip abductor muscle function on frontal plane mechanics

Introduction: The Trendelenburg Test (TT) is used to assess the functional strength of the hip abductor muscles (HABD), their ability to control frontal plane motion of the pelvis, and the ability of the lumbopelvic complex to transfer load into single leg stance. Rationale: Although a standard method to perform the test has been described for use within clinical populations, no study has directly investigated Trendelenburg’s hypotheses. Purpose: To investigate the validity of the TT using an ultrasound guided nerve block (UNB) of the superior gluteal nerve and determine whether the reduction in HABD strength would result in the theorized mechanical compensatory strategies measured during the TT. Methods: Quasi-experimental design using a convenience sample of nine healthy males. Only subjects with no current or previous injury to the lumbar spine, pelvis, or lower extremities, and no previous surgeries were included. Force dynamometry was used to evaluation HABD strength (%BW). 2D mechanics were used to evaluate contralateral pelvic drop (cMPD), change in contralateral pelvic drop (∆cMPD), ipsilateral hip adduction (iHADD) and ipsilateral trunk sway (TRUNK) measured in degrees (°). All measures were collected prior to and following a UNB on the superior gluteal nerve performed by an interventional radiologist. Results: Subjects’ age was median 31yrs (IQR:22-32yrs); and weight was median 73kg (IQR:67-81kg). An average 52% reduction of HABD strength (z=2.36,p=0.02) resulted following the UNB. No differences were found in cMPD or ∆cMPD (z=0.01,p= 0.99, z=-0.67,p=0.49). Individual changes in biomechanics show no consistency between subjects and non-systematic changes across the group. One subject demonstrated the mechanical compensations described by Trendelenburg. Discussion: The TT should not be used as screening measure for HABD strength in populations demonstrating strength greater than 30%BW but reserved for use with populations with marked HABD weakness. Importance: This study presents data regarding a critical level of HABD strength required to support the pelvis during the TT.

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Young men utilise limited neuromuscular prepartion to regulate post-impact knee mechanics during step landing

Purpose The neuromuscular mechanisms determining the mechanical behaviour of the knee during landing impact remain poorly understood. It was hypothesised that neuromuscular preparation is subject-specific and ranges along a continuum from passive to active. Methods A group of healthy men (N = 12) stepped-down from a knee-high platform for 60 consecutive trials. Surface EMG of the quadriceps and hamstrings was used to determine pre-impact onset timing, activation amplitude and cocontraction for each trial. Partial least squares regression was used to associate pre-impact preparation with post-impact knee stiffness and coordination. Results The group analysis revealed few significant changes in pre-impact preparation across trial blocks. Single-subject analyses revealed changes in muscle activity that varied in size and direction between individuals. Further, the association between pre-impact preparation and post-impact knee mechanics was subject-specific and ranged along a continuum of strategies. Conclusion The findings suggest that neuromuscular preparation during step landing is subject-specific and its association to post-impact knee mechanics occurs along a continuum, ranging from passive to active control strategies. Further work should examine the implications of these strategies on the distribution of knee forces in-vivo.

Nonlinear actuator fault detection for small-scale UAS

This paper presents a recursive strategy for online detection of actuator faults on a unmanned aerial system (UAS) subjected to accidental actuator faults. The proposed detection algorithm aims to provide a UAS with the capability of identifying and determining characteristics of actuator faults, offering necessary flight information for the design of fault-tolerant mechanism to compensate for the resultant side-effect when faults occur. The proposed fault detection strategy consists of a bank of unscented Kalman filters (UKFs) with each one detecting a specific type of actuator faults and estimating corresponding velocity and attitude information. Performance of the proposed method is evaluated using a typical nonlinear UAS model and it is demonstrated in simulations that our method is able to detect representative faults with a sufficient accuracy and acceptable time delay, and can be applied to the design of fault-tolerant flight control systems of UASs.