Revisiting borehole stresses in anisotropic elastic media : comparison of analytical versus numerical solutions

We present a rigorous validation of the analyticalAmadei solution for the stress concentration around arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients β11 and β55 are not equal. It is shown from theoretical considerations and published experimental data that the β11 and β55 are not equal for realistic rocks. Second, we develop a 3D finite-element elastic model within a hybrid analyticalnumerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic and transverse isotropic symmetries. It is concluded that the analytical Amadei solution is valid with no restrictions on the borehole orientation or elastic anisotropy symmetry.

Generalized element load method for first- and second-order element solutions with element load effect

The finite element method in principle adaptively divides the continuous domain with complex geometry into discrete simple subdomain by using an approximate element function, and the continuous element loads are also converted into the nodal load by means of the traditional lumping and consistent load methods, which can standardise a plethora of element loads into a typical numerical procedure, but element load effect is restricted to the nodal solution. It in turn means the accurate continuous element solutions with the element load effects are merely restricted to element nodes discretely, and further limited to either displacement or force field depending on which type of approximate function is derived. On the other hand, the analytical stability functions can give the accurate continuous element solutions due to element loads. Unfortunately, the expressions of stability functions are very diverse and distinct when subjected to different element loads that deter the numerical routine for practical applications. To this end, this paper presents a displacement-based finite element function (generalised element load method) with a plethora of element load effects in the similar fashion that never be achieved by the stability function, as well as it can generate the continuous first- and second-order elastic displacement and force solutions along an element without loss of accuracy considerably as the analytical approach that never be achieved by neither the lumping nor consistent load methods. Hence, the salient and unique features of this paper (generalised element load method) embody its robustness, versatility and accuracy in continuous element solutions when subjected to the great diversity of transverse element loads.

Response of segmented bored transit tunnels to surface blast

Increasing threat of terrorism highlights the importance of enhancing the resilience of underground tunnels to all hazards. This paper develops, applies and compares the Arbitrary Lagrangian Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH) techniques to treat the response of buried tunnels to surface explosions. The results and outcomes of the two techniques were compared, along with results from existing test data. The comparison shows that the ALE technique is a better method for describing the tunnel response for above ground explosion with regards to modeling accuracy and computational efficiency. The ALE technique was then applied to treat the blast response of different types of segmented bored tunnels buried in dry sand. Results indicate that the most used modern ring type segmented tunnels were more flexible for in-plane response, however, they suffered permanent drifts between the rings. Hexagonal segmented tunnels responded with negligible drifts in the longitudinal direction, but the magnitudes of in-plane drifts were large and hence hazardous for the tunnel. Interlocking segmented tunnels suffered from permanent drifts in both the longitudinal and transverse directions. Multi-surface radial joints in both the hexagonal and interlocking segments affected the flexibility of the tunnel in the transverse direction. The findings offer significant new information in the behavior of segmented bored tunnels to guide their future implementation in civil engineering applications.

Blast response of segmented bored tunnel using coupled SPH–FE method

Underground transport tunnels are vulnerable to blast events. This paper develops and applies a fully coupled technique involving the Smooth Particle Hydrodynamics and Finite Element techniques to investigate the blast response of segmented bored tunnels. Findings indicate that several bolts failed in the longitudinal direction due to redistribution of blast loading to adjacent tunnel rings. The tunnel segments respond as arch mechanisms in the transverse direction and suffered damage mainly due to high bending stresses. The novel information from the present study will enable safer designs of buried tunnels and provide a benchmark reference for future developments in this area.

Web crippling tests of cold-formed steel channels under two flange load cases

Cold-formed steel members have many advantages over hot-rolled steel members. However, they are susceptible to various buckling modes at stresses below the yield stress of the member because of their relatively high width-to-thickness ratio. Web crippling is a form of localized failure mode that can occur when the members are subjected to transverse high concentrated loadings and/or reactions. The four common loading conditions are the end-one-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF) loadings. Recently a test method has been proposed by AISI to obtain the web crippling capacities under these four loading conditions. Using this test method 42 tests were conducted in this research to investigate the web crippling behaviour and strengths of unlipped channels with stocky webs under ETF and ITF cases. DuraGal sections having a nominal yield stress of 450 MPa were tested with different web slenderness and bearing lengths. The flanges of these channel sections were not fastened to the supports. In this research the suitability of the currently available design rules for unlipped channels subject to web crippling was investigated, and suitable modifications were proposed where necessary. In addition to this, a new design rule was proposed based on the direct strength method to predict the web crippling capacities of tested beams. This paper presents the details of this experimental study and the results.

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.

Bending and torsion of hollow flange channel beams

The LiteSteel beam (LSB) is a cold-formed high strength steel channel section made of two torsionally rigid closed flanges and a slender web. Due to its mono-symmetric characteristics, its centroid and shear centre do not coincide. The LSBs can be used in floor systems as joists or bearers and in these applications they are often subjected to transverse loads that are applied away from the shear centre. Hence they are often subjected to combined bending and torsion actions. Previous researches on LSBs have concentrated on their bending or shear behaviour and strengths, and only limited research has been undertaken on their combined bending and torsion behaviour. Therefore in this research a series of nine experiments was first conducted on LSBs subject to combined bending and torsion. Three LSB sections were tested to failure under eccentric loading at mid-span, and appropriate results were obtained from seven tests. A special test rig was used to simulate two different eccentricities and to provide accurate simple boundary conditions at the supports. Finite element models of tested LSBs were developed using ANSYS, and the ultimate strengths, failure modes, and load–displacement curves were obtained and compared with corresponding test results. Finite element analyses agreed well with test results and hence the developed models were used in a parametric study to investigate the effects of load locations, eccentricities, and spans on the combined bending and torsion behaviour of LSBs. The interaction between the ultimate bending and torsional moment capacities was studied and a simple design rule was proposed. This paper presents the details of the tests, finite element analyses, and parametric study of LSBs subject to combined bending and torsion, and the results.

The vertebral venous system in healthy and scoliotic adolescent spines - a 3D MRI investigation

Introduction. The venous drainage system within vertebral bodies (VBs) has been well documented previously in cadaveric specimens. Advances in 3D imaging and image processing now allow for in vivo quantification of larger venous vessels, such as the basivertebral vein. Differences between healthy and scoliotic VB veins can therefore be investigated. Methods. 20 healthy adolescent controls and 21 AIS patients were recruited (with ethics approval) to undergo 3D MRI, using a 3 Tesla, T1-weighted 3D gradient echo sequence, resulting in 512 slices across the thoraco-lumbar spine, with a voxel size of 0.5x0.5x0.5mm. Using Amira Filament Editor, five transverse slices through the VB were examined simultaneously and the resulting observable vascular network traced. Each VB was assessed, and a vascular network recorded when observable. A local coordinate system was created in the centre of each VB and the vascular networks aligned to this. The length of the vascular network on the left and right sides (with a small central region) of the VB was calculated, and the spatial patterning of the networks assessed level-by-level within each subject. Results. An average of 6 (range 4-10) vascular networks, consistent with descriptions of the basivertebral vein, were identifiable within each subject, most commonly between T10-L1. Differences were seen in the left/right distribution of vessels in the control and AIS subjects. Healthy controls saw a percentage distribution of 29:18:53 across the left:centre:right regions respectively, whereas the AIS subjects had a slightly shifted distribution of 33:25:42. The control group showed consistent spatial patterning of the vascular networks across most levels, but this was not seen in the AIS group. Conclusion. Observation and quantification of the basivertebral vein in vivo is possible using 3D MRI. The AIS group lacked the spatial pattern repetition seen in the control group and minor differences were seen in the left/right distribution of vessels.

Agreement between physiotherapists rating scapular posture in multiple planes in patients with neck pain: Reliability study

Objective Evaluation of scapular posture is an integral component of the clinical assessment of painful neck disorders. The aim of this study was to evaluate agreement between therapist judgements of scapula posture in multiple biomechanical planes in individuals with neck pain. Design Inter-therapist reliability study. Setting Research laboratory. Participants Fifteen participants with chronic neck pain. Main outcome measures Four physiotherapists recorded ratings of scapular orientation (relative to the thorax) in five different scapula postural planes (plane of scapula, sagittal plane, transverse plane, horizontal plane, and vertical plane) under four test conditions (at rest, and during three isometric shoulder conditions) in all participants. Inter-therapist reliability was expressed using both generalized and paired kappa coefficient. Results Following adjustment for expected agreement and the high prevalence of neutral ratings (81%), on average both the generalised kappa (0.37) as well as Cohen's Kappa for the two therapist pairs (0.45 and 0.42) demonstrated only slight to moderate inter-therapist reliability. Conclusions The findings suggest that ratings of scapular posture in individuals with neck pain by visual inspection has only slight to moderate reliability and should only be used in conjunction with other clinical tests when judging scapula function in these patients.

Fiber Bragg grating accelerometer based on a transversely rotating stick

Fiber Bragg Grating (FBG) accelerometers using transverse forces with an inertial object placed at the middle of the FBG have a high sensitivity but low resonant frequency. The resonant frequency 26 Hz and sensitivity at 6 Hz 1.29 nm/g were reported based on a 50mm-long FBG accelerometer. We demonstrate that the first FBG accelerometer based on a transversely rotating stick, which can, at the same or even larger size, keep the high sensitivity and significantly increase the low resonant frequency. In our experiments, a 77.5mm-long FBG accelerometer has achieved a similar sensitivity but 65% higher resonant frequency. This novel structure not only significantly widens the potential applications of FBG accelerometers by increasing their resonant frequencies but also provides a new route to design other accelerometers, e.g. micro accelerometers.

Altered nociceptive, endocrine, and dorsal horn neuron responses in rats following a neonatal immune challenge

Summary The neonatal period is characterized by significant plasticity where the immune, endocrine, and nociceptive systems undergo fine-tuning and maturation. Painful experiences during this period can result in long-term alterations in the neurocircuitry underlying nociception, including increased sensitivity to mechanical or thermal stimuli. Less is known about the impact of neonatal exposure to mild inflammatory stimuli, such as lipopolysaccharide (LPS), on subsequent inflammatory pain responses. Here we examine the impact of neonatal LPS exposure on inflammatory pain sensitivity and HPA axis activity during the first three postnatal weeks. Wistar rats were injected with LPS (0.05 mg/kg IP, Salmonella enteritidis) or saline on postnatal days (PNDs) 3 and 5 and later subjected to the formalin test at PNDs 7, 13, and 22. One hour after formalin injection, blood was collected to assess corticosterone responses. Transverse spinal cord slices were also prepared for whole-cell patch clamp recording from lumbar superficial dorsal horn neurons (SDH). Brains were obtained at PND 22 and the hypothalamus was isolated to measure glucocorticoid (GR) and mineralocorticoid receptor (MR) transcript expression using qRT-PCR. Behavioural analyses indicate that at PND 7, no significant differences were observed between saline- or LPS-challenged rats. At PND 13, LPS-challenged rats exhibited enhanced licking (p < .01), and at PND 22, increased flinching in response to formalin injection (p < .05). LPS-challenged rats also displayed increased plasma corticosterone at PND 7 and PND 22 (p < .001) but not at PND 13 following formalin administration. Furthermore, at PND 22 neonatal LPS exposure induced decreased levels of GR mRNA and increased levels of MR mRNA in the hypothalamus. The intrinsic properties of SDH neurons were similar at PND 7 and PND 13. However, at PND 22, ipsilateral SDH neurons in LPS-challenged rats had a lower input resistance compared to their saline-challenged counterparts (p < .05). These data suggest neonatal LPS exposure produces developmentally regulated changes in formalin-induced behavioural responses, corticosterone levels, and dorsal horn neuron properties following noxious stimulation later in life. These findings highlight the importance of immune activation during the neonatal period in shaping pain sensitivity later in life. This programming involves both spinal cord neurons and the HPA axis.

Scattering of electromagnetic waves from chirally coated cylinders

The problem of electromagnetic scattering from an isotropic homogeneous chirally coated conducting cylinder is analysed. The cylinder is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Mie's analysis is used to evaluate the scattering characteristics. The computed results include the evaluation of the normalized scattering width and the absorption efficiency. The results show that there is a significant reduction in the normalized scattering width as compared to a RAM coated cylinder. This reduction has been attributed to increased absorption.

Static analysis of infinite laminated cylindrical shell panel

This paper presents an approximate three-dimensional elasticity solution for an infinitely long, cross-ply laminated circular cylindrical shell panel with simply supported boundary conditions, subjected to an arbitrary discontinuous transverse loading. The solution is based on the principal assumption that the ratio of the thickness of the lamina to its middle surface radius is negligible compared to unity. The validity of this assumption and the range of application of this approximate solution have been established through a comparison with an exact solution. Results of classical and first-order shear deformation shell theories have been compared with the results of the present solution to bring out the accuracy of these theories. It is also shown that for very shallow shell panels the definition of a thin shell should be based on the ratio of thickness to chord width rather than the ratio of thickness to mean radius.

Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.