Vibration characteristics of plate elements subjected in-plane loads (axial loads)

Axial deformations resulting from in-plane loads (axial forces) of plate elements impact significantly on their vibration characteristics. Although, numerous methods have been developed to quantify axial forces and hence deformations of individual plate elements with different boundary conditions based on their natural frequencies, these methods are unable to apply to the plate elements in a structural system. This is because the natural frequency is a global parameter for the entire structure. Thus, this paper proposes a comprehensive vibration based procedure to quantify axial deformations of plate elements in a structural framing system. Unique capabilities of the proposed method present through illustrative examples. Keywords- Plate Elements, Dynamic Stiffness Matrix, Finite Element Method, Vibration Characteristics, Axial Deformation

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Numerical modelling of light gauge cold-formed steel compression members subjected to distortional buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing loss of properties and lives during fires. However, fire performance of light gauge cold-formed steel structures is not well understood despite its increased usage in buildings. Cold-formed steel compression members are susceptible to various buckling modes such as local and distortional buckling and their ultimate strength behaviour is governed by these buckling modes. Therefore a research project based on experimental and numerical studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. Lipped channel sections with and without additional lips were selected with three thicknesses of 0.6, 0.8, and 0.95 mm and both low and high strength steels (G250 and G550 steels). More than 150 compression tests were undertaken first at ambient and elevated temperatures. Finite element models of the tested compression members were then developed by including the degradation of mechanical properties with increasing temperatures. Comparison of finite element analysis and experimental results showed that the developed finite element models were capable of simulating the distortional buckling and strength behaviour at ambient and elevated temperatures up to 800 °C. The validated model was used to determine the effects of mechanical properties, geometric imperfections and residual stresses on the distortional buckling behaviour and strength of cold-formed steel columns. This paper presents the details of the numerical study and the results. It demonstrated the importance of using accurate mechanical properties at elevated temperatures in order to obtain reliable strength characteristics of cold-formed steel columns under fire conditions.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Quantifying in-plane deformation of plate elements using vibration characteristics

Plate elements are used in many engineering applications. In-plane loads and deformations have significant influence on the vibration characteristics of plate elements. Numerous methods have been developed to quantify the effects of in-plane loads and deformations of individual plate elements with different boundary conditions based on their natural frequencies. However, these developments cannot be applied to the plate elements in a structural system as the natural frequency is a global parameter for the entire structure. This highlights the need for a method to quantify in-plane deformations of plate elements in structural framing systems. Motivated by this gap in knowledge, this research has developed a comprehensive vibration based procedure to quantify in-plane deformation of plate elements in a structural framing system. This procedure with its unique capabilities to capture the influence of load migration, boundary conditions and different tributary areas is presented herein and illustrated through examples.

Numerical modelling of non-load bearing light gauge cold-formed steel frame walls under fire conditions

Recently an innovative composite panel system was developed, where a thin insulation layer was used externally between two plasterboards to improve the fire performance of light gauge cold-formed steel frame walls. In this research, finite-element thermal models of both the traditional light gauge cold-formed steel frame wall panels with cavity insulation and the new light gauge cold-formed steel frame composite wall panels were developed to simulate their thermal behaviour under standard and realistic fire conditions. Suitable apparent thermal properties of gypsum plasterboard, insulation materials and steel were proposed and used. The developed models were then validated by comparing their results with available fire test results. This article presents the details of the developed finite-element models of small-scale non-load-bearing light gauge cold-formed steel frame wall panels and the results of the thermal analysis. It has been shown that accurate finite-element models can be used to simulate the thermal behaviour of small-scale light gauge cold-formed steel frame walls with varying configurations of insulations and plasterboards. The numerical results show that the use of cavity insulation was detrimental to the fire rating of light gauge cold-formed steel frame walls, while the use of external insulation offered superior thermal protection to them. The effects of real fire conditions are also presented.

Footwear modifies coronal plane forefoot and sagittal plane hallux kinematics during stance phase of walking gait

Footwear is designed to reduce injury, and enhance performance. However, the effect footwear has on foot and ankle kinematics currently remains unknown. Acknowledging the need for improved understanding, multi-segment models of the foot-shoe complex need to be established to both describe and quantify the effect footwear has on the foot and ankle during stance phase of gait. The purpose of this study was to quantify how footwear alters the kinematics of the foot inside the shoe during stance phase of walking gait.

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.

Segmental torso masses and coronal plane joint torques in the adolescent scoliotic spine

Introduction. Calculating segmental (vertebral level-by-level) torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be determined. This study used CT scans of AIS patients to measure segmental torso masses and explores how joint moments in the coronal plane are affected by changes in the position of the intervertebral joint’s axis of rotation; particularly at the apex of a scoliotic major curve. Methods. Existing low dose CT data from the Paediatric Spine Research Group was used to calculate vertebral level-by-level torso masses and joint torques occurring in the spine for a group of 20 female AIS patients (mean age 15.0 ± 2.7 years, mean Cobb angle 53 ± 7.1°). Image processing software, ImageJ (v1.45 NIH USA) was used to threshold the T1 to L5 CT images and calculate the segmental torso volume and mass corresponding to each vertebral level. Body segment masses for the head, neck and arms were taken from published anthropometric data. Intervertebral (IV) joint torques at each vertebral level were found using principles of static equilibrium together with the segmental body mass data. Summing the torque contributions for each level above the required joint, allowed the cumulative joint torque at a particular level to be found. Since there is some uncertainty in the position of the coronal plane Instantaneous Axis of Rotation (IAR) for scoliosis patients, it was assumed the IAR was located in the centre of the IV disc. A sensitivity analysis was performed to see what effect the IAR had on the joint torques by moving it laterally 10mm in both directions. Results. The magnitude of the torso masses from T1-L5 increased inferiorly, with a 150% increase in mean segmental torso mass from 0.6kg at T1 to 1.5kg at L5. The magnitudes of the calculated coronal plane joint torques during relaxed standing were typically 5-7 Nm at the apex of the curve, with the highest apex joint torque of 7Nm being found in patient 13. Shifting the assumed IAR by 10mm towards the convexity of the spine, increased the joint torque at that level by a mean 9.0%, showing that calculated joint torques were moderately sensitive to the assumed IAR location. When the IAR midline position was moved 10mm away from the convexity of the spine, the joint torque reduced by a mean 8.9%. Conclusion. Coronal plane joint torques as high as 7Nm can occur during relaxed standing in scoliosis patients, which may help to explain the mechanics of AIS progression. This study provides new anthropometric reference data on vertebral level-by-level torso mass in AIS patients which will be useful for biomechanical models of scoliosis progression and treatment. However, the CT scans were performed in supine (no gravitational load on spine) and curve magnitudes are known to be smaller than those measured in standing.

Phantom Scatter and the A-SI EPID

Introduction: The use of amorphous-silicon electronic portal imaging devices (a-Si EPIDs) for dosimetry is complicated by the effects of scattered radiation. In photon radiotherapy, primary signal at the detector can be accompanied by photons scattered from linear accelerator components, detector materials, intervening air, treatment room surfaces (floor, walls, etc) and from the patient/phantom being irradiated. Consequently, EPID measurements which presume to take scatter into account are highly sensitive to the identification of these contributions. One example of this susceptibility is the process of calibrating an EPID for use as a gauge of (radiological) thickness, where specific allowance must be made for the effect of phantom-scatter on the intensity of radiation measured through different thicknesses of phantom. This is usually done via a theoretical calculation which assumes that phantom scatter is linearly related to thickness and field-size. We have, however, undertaken a more detailed study of the scattering effects of fields of different dimensions when applied to phantoms of various thicknesses in order to derive scattered-primary ratios (SPRs) directly from simulation results. This allows us to make a more-accurate calibration of the EPID, and to qualify the appositeness of the theoretical SPR calculations. Methods: This study uses a full MC model of the entire linac-phantom-detector system simulated using EGSnrc/BEAMnrc codes. The Elekta linac and EPID are modelled according to specifications from the manufacturer and the intervening phantoms are modelled as rectilinear blocks of water or plastic, with their densities set to a range of physically realistic and unrealistic values. Transmissions through these various phantoms are calculated using the dose detected in the model EPID and used in an evaluation of the field-size-dependence of SPR, in different media, applying a method suggested for experimental systems by Swindell and Evans [1]. These results are compared firstly with SPRs calculated using the theoretical, linear relationship between SPR and irradiated volume, and secondly with SPRs evaluated from our own experimental data. An alternate evaluation of the SPR in each simulated system is also made by modifying the BEAMnrc user code READPHSP, to identify and count those particles in a given plane of the system that have undergone a scattering event. In addition to these simulations, which are designed to closely replicate the experimental setup, we also used MC models to examine the effects of varying the setup in experimentally challenging ways (changing the size of the air gap between the phantom and the EPID, changing the longitudinal position of the EPID itself). Experimental measurements used in this study were made using an Elekta Precise linear accelerator, operating at 6MV, with an Elekta iView GT a-Si EPID. Results and Discussion: 1. Comparison with theory: With the Elekta iView EPID fixed at 160 cm from the photon source, the phantoms, when positioned isocentrically, are located 41 to 55 cm from the surface of the panel. At this geometry, a close but imperfect agreement (differing by up to 5%) can be identified between the results of the simulations and the theoretical calculations. However, this agreement can be totally disrupted by shifting the phantom out of the isocentric position. Evidently, the allowance made for source-phantom-detector geometry by the theoretical expression for SPR is inadequate to describe the effect that phantom proximity can have on measurements made using an (infamously low-energy sensitive) a-Si EPID. 2. Comparison with experiment: For various square field sizes and across the range of phantom thicknesses, there is good agreement between simulation data and experimental measurements of the transmissions and the derived values of the primary intensities. However, the values of SPR obtained through these simulations and measurements seem to be much more sensitive to slight differences between the simulated and real systems, leading to difficulties in producing a simulated system which adequately replicates the experimental data. (For instance, small changes to simulated phantom density make large differences to resulting SPR.) 3. Comparison with direct calculation: By developing a method for directly counting the number scattered particles reaching the detector after passing through the various isocentric phantom thicknesses, we show that the experimental method discussed above is providing a good measure of the actual degree of scattering produced by the phantom. This calculation also permits the analysis of the scattering sources/sinks within the linac and EPID, as well as the phantom and intervening air. Conclusions: This work challenges the assumption that scatter to and within an EPID can be accounted for using a simple, linear model. Simulations discussed here are intended to contribute to a fuller understanding of the contribution of scattered radiation to the EPID images that are used in dosimetry calculations. Acknowledgements: This work is funded by the NHMRC, through a project grant, and supported by the Queensland University of Technology (QUT) and the Royal Brisbane and Women's Hospital, Brisbane, Australia. The authors are also grateful to Elekta for the provision of manufacturing specifications which permitted the detailed simulation of their linear accelerators and amorphous-silicon electronic portal imaging devices. Computational resources and services used in this work were provided by the HPC and Research Support Group, QUT, Brisbane, Australia.

Segmental torso masses and gravity-induced coronal plane joint moments in adolescent idiopathic scoliosis

Introduction: Calculating segmental (vertebral level-by-level) torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. This study used supine CT scans of AIS patients to measure segmental torso masses and explored the joint moments in the coronal plane, particularly at the apex of a scoliotic major curve. Methods: Existing low dose CT data from the Paediatric Spine Research Group was used to calculate vertebral level-by-level torso masses and joint moments occurring in the spine for a group of 20 female AIS patients with right sided thoracic curves. The mean age was 15.0 ± 2.7 years and all curves were classified Lenke Type 1 with a mean Cobb angle 52 ± 5.9°. Image processing software, ImageJ (v1.45 NIH USA) was used to create reformatted coronal plane images, reconstruct vertebral level-by-level torso segments and subsequently measure the torso volume corresponding to each vertebral level. Segment mass was then determined by assuming a tissue density of 1.04x103 kg/m3. Body segment masses for the head, neck and arms were taken from published anthropometric data (Winter 2009). Intervertebral joint moments in the coronal plane at each vertebral level were found from the position of the centroid of the segment masses relative to the joint centres with the segmental body mass data. Results and Discussion: The magnitude of the torso masses from T1-L5 increased inferiorly, with a 150% increase in mean segmental torso mass from 0.6kg at T1 to 1.5kg at L5. The magnitudes of the calculated coronal plane joint moments during relaxed standing were typically 5-7 Nm at the apex of the curve, with the highest apex joint torque of 7Nm. The CT scans were performed in the supine position and curve magnitudes are known to be 7-10° smaller than those measured in standing, due to the absence of gravity acting on the spine. Hence, it can be expected that the moments produced by gravity in the standing individual will be greater than those calculated here.