Curvature Values Research Articles

Investigations on the multistability of series-connected unsymmetric laminates

Multistable composite shells have received great attention in shape-changing morphing applications due to their ability to attain more than one stable shape when cooled down from curing to room temperature. However, an individual bistable shell may not completely fulfil all the requirements of a morphing structure as they may require more than two stable states during the morphing action. Also, on several occasions, cylindrical bistable shapes can be found to be limiting for morphing applications. Therefore, studies on highly multistable non-cylindrical shapes are a subject of interest. In this study, we explore how unsymmetric laminates connected in series can result in an increased number of stable shapes. To analyze series-connected laminates, a semi-analytical model is developed using the Rayleigh-Ritz approach. The shapes predicted by the semi-analytical model have been validated using the results from a full geometrically non-linear finite element model and corresponding experimental results. A further enhancement in the design space of series-connected laminates is proposed by replacing the conventional cross-ply laminate with curvilinear fiber variable stiffness (VS) laminates as they allow the designer to tailor stiffness properties. Although VS laminates can be used to generate the similar stable configurations as that of conventional cross-ply laminates, they may result in different curvature values leading to tailored snap-through requirements. The developed finite element model is extended to account for unsymmetric variable stiffness laminates, where effect of curvilinear fiber alignment on the multistable design space is investigated.

Abdominal Adiposity Increases Lordosis and Doubles the Risk of Low Back Pain

Vertebral disorders have significant health and economic impacts, and due to aging and current lifestyle habits, there is a trend toward their increase. Obesity and the alignment of vertebral curvatures can be associated with back pain. Objective: This study aims to analyze whether general and abdominal obesity are associated with cervical, dorsal, and lumbar vertebral pain as well as increased or decreased values of cervical, dorsal, and lumbar vertebral curvatures. Methodology: Body composition, degree of vertebral curvature, and the perception of cervical, dorsal, and lumbar pain were evaluated in a study population of 301 people (>18 years old). Linear and logistic regression analyses were performed to evaluate the influence of several variables of body composition on vertebral angles and cervical, dorsal, and lumbar pain. Results: Lumbar pain was the most prevalent (66.1%), mainly affecting women (70.9%). They were also shown to have greater lumbar angles (p < 0.001). The degrees of lumbar curvature increased, as did the BMI, waist circumference, and waist-to-height ratio. Cervical and dorsal curvatures were increased by all the variables of adiposity and abdominal adiposity. It was found that people with abdominal obesity carried twice the risk of lower back pain than those without abdominal obesity (OR = 2.172, p < 0.05). In addition, an increased lumbar angle was related to an increased risk of low back pain (OR = 1.031, p < 0.05). Cervical pain, on the other hand, was associated with the waist-height index (OR = 0.948, p <0.01). Conclusions: This study shows that increased lumbar curvature and abdominal obesity may be risk factors for lower back pain. In addition, it shows an association between the amount of body and abdominal fat in relation to the degree of curvature of the spine in the sagittal plane. Investigating the effect of obesity on vertebral morphology and musculoskeletal disorders makes it possible to prescribe interventions and therapeutic strategies.

Evaluation of ocular biometry in the Japanese population using a multicenter approach: Prospective observational study.

This prospective observational study aimed to evaluate the ocular biometry of Japanese people through a multicenter approach. The uncorrected and corrected distance visual acuity (UDVA and CDVA, respectively) in the log minimum angle of resolution (logMAR), subjective and objective spherical equivalent values (SE) of ocular refraction, anterior and posterior corneal curvature (ACC and PCC, respectively), anterior and posterior corneal asphericity (ACA and PCA, respectively), central corneal thickness (CCT), anterior chamber depth (ACD), and ocular axial length (AL) were measured in the eyes of 250 participants (mean age = 46.5 ± 18.0 years, range: 20–90 years) across five institutions in Japan. The mean UDVA, CDVA, subjective SE, objective SE, ACC, PCC, ACA, PCA, CCT, ACD, and AL were 0.68, −0.08, −2.42 D, −2.66 D, 7.77 mm, 6.33 mm, −0.31, −0.39, 0.55 mm, 2.92 mm, and 24.78 mm, respectively. Age-related changes and sex-based differences were noted in the visual acuity, refraction, corneal shape, ACD, and AL. Our results serve as basis for future studies aiming to develop refractive correction methods and various vision-related fields.

Controlled synthesis of biomimetic materials with protruding structures by in situ growth of silica nanorods via hydroxyl-localized droplet template method

Inspired by the Lotus-Effect in nature, biomimetic materials with a protruding structure have been prepared through a hydroxyl-localized droplet templating method, in which the droplets are formed by polyvinylpyrrolidone as a surfactant and sodium citrate as a stabilizer. Silica nanorods grow uniformly and densely unidirectionally on the surface of high silica fibers. With the adjustment of reaction conditions and reagent concentration, the aspect ratio of the nanorods is adjustable between 1.73 and 17.58, where the length and diameter are controllable in the range of 180–368 nm and 194–1489 nm, respectively. Meanwhile, the structure also undergoes changes from straight rod-like to curved linear shapes with curvature values up to 1.50. It is found that the hydroxyl group on the fiber surface, which adsorbs the attachment of emulsified droplets and participates in the condensation reaction of tetraethyl orthosilicate, serves as the key to the in-situ growth of silica nanorods. In addition, silica nanorods are also successfully grown on mullite fibers and basalt fibers yielding biomimetic materials with protruding structures. The mean lengths of silica nanorods on mullite and basalt fibers are 833 nm and 1361 nm, correspondingly, along with respective mean diameters of 379 nm and 271 nm.

The return process of physiological umbilical herniation in human fetuses: The possible role of the vascular tree and umbilical ring.

The human intestine elongates during the early fetal period, herniates into the extraembryonic coelom (EC), and subsequently returns to the abdominal cavity (AC). The process by which the intestinal loop returns to the abdomen remains unclear. This study aimed to document positional changes in the intestinal tract with the superior mesenteric artery (SMA) and branches in 3D to elucidate the intestinal loop return process (transition phase). Serial histological cross-sections from human fetuses (crown-rump length [CRL] range: 30-50 mm) in the herniation (n=1), transition (n=7), and return (n=2) phases were selected from the Blechschmidt Collection. The distribution of the SMA trunk and all intestinal and sister branches entering the intestines was visualized so that positional changes in branches were continuous from the herniation to return phases. Positional changes in SMA branches proceeded in an orderly and structured manner; this is essential for continuous blood supply via the SMA to the intestine during transition and for safe intestinal return. Changes in the SMA distribution proceeded prior to the detection of initiation of intestinal tract return, which might start earlier and last much longer than our consensus (i.e., that the return of the herniated intestine begins when the CRL is approximately 40 mm and ends within a short time). In the cross-section of the umbilical ring in the herniation and transition phases, one proximal limb and one distal limb were observed with SMA intestinal branches, which were fully packed in the umbilical ring. The SMA branches were aligned from inferior to superior along the SMA main trunk. In the herniation phase, the distribution of 3rd-13th branches aligned from proximal inferior medial to distal superior left with a slight spiral in the EC, the tips of which suggested an orderly running course of the small intestine. In the transition phase, SMA branches running across the umbilical ring that fed the small intestine were observed, suggesting that the intestine was uncoiled and ran across the umbilical ring almost vertically. The estimated curvature value supported the phenomenon of uncoiling at the umbilical ring; the value at the umbilical ring was lesser than that in the AC and EC. During the transition phase, the proximal and distal limbs transversely ran side by side in the AC, umbilical ring, limbs on the cranial side, and mesentery on the caudal side. The SMA trunk and its branches ran in parallel, cranially to caudally aligned in the mesentery. This layout of the umbilical ring was maintained during the transition phase. In the return phase, the SMA trunk was gently curved from the upper left to the lower right of the AC; around 12 branches spread with a winding staircase appearance. The intestinal tract reached its definitive position immediately after all tissues crossed the umbilical ring and released any restriction. Each SMA branch and the corresponding region of the intestinal tract form a unit and change their position, though the conformation may change within each unit when running across the umbilical ring. We suggest that the slide-stack model requires revision.

Travel-Time Estimation by Cubic Hermite Curve

Travel time is a measure of time taken to travel from one place to another. Global Positioning System (GPS) navigation applications such as Waze and Google Maps are easily accessible presently and allow users to plan a route based on travel time from one place to another. However, these applications can only estimate general travel time based on a vehicle’s total distance and average safe speed without considering route curvature. A parametric cubic curve has shown a potential result in travel-time estimation through geometric properties. In this paper, travel time has been estimated using the curvature value obtained from the Hermite Interpolation curve fitted to each section of the selected road. Design speed is determined from the curvature value, and thus an algorithm for travel-time estimation incorporating initial driving information is developed. The proposed method’s accuracy was compared to the existing method’s accuracy using a real-life driving test. This comparison demonstrated that the proposed method estimates travel time more accurately than Google Maps and Waze. Future study can further improve the estimation by embedding traffic data into the algorithm.

Pore-scale processes in tertiary low salinity waterflooding in a carbonate rock: Micro-dispersions, water film growth, and wettability change

HypothesisThe wettability change from oil-wet towards more water-wet conditions by injecting diluted brine can improve oil recovery from reservoir rocks, known as low salinity waterflooding. We investigated the underlying pore-scale mechanisms of this process to determine if improved recovery was associated with a change in local contact angle, and if additional displacement was facilitated by the formation of micro-dispersions of water in oil and water film swelling. ExperimentsX-ray imaging and high-pressure and temperature flow apparatus were used to investigate and compare high and low salinity waterflooding in a carbonate rock sample. The sample was placed in contact with crude oil to obtain an initial wetting state found in hydrocarbon reservoirs. High salinity brine was then injected at increasing flow rates followed by low salinity brine injection using the same procedure. FindingsDevelopment of water micro-droplets within the oil phase and detachment of oil layers from the rock surface were observed after low salinity waterflooding. During high salinity waterflooding, contact angles showed insignificant changes from the initial value of 115°, while the mean curvature and local capillary pressure values remained negative, consistent with oil-wet conditions. However, with low salinity, the decrease in contact angle to 102° and the shift in the mean curvature and capillary pressure to positive values indicate a wettability change. Overall, our analysis captured the in situ mechanisms and processes associated with the low salinity effect and ultimate increase in oil recovery.

A Dynamical Approach to Position Vector of Timelike Curve by Vectorial Momentum, Torque and Tangential Dual Curve

In this study, the position vector of a timelike curve wp is stated by a linear combination of its Serret Frenet frame with differentiable functions. The definition of tangential dual curve of the curve wp is stated by using these differentiable functions. Moreover, tangential torque curve of timelike curve wp is defined and investigated. New dynamically and physical results are stated depending on the torque of the timelike curve wp and the direction of the tangent vector component of the curve. Then, the position vector of a timelike W curve is again stated by differentiable functions. Therefore, solutions of differential equation of the position vector of timelike W curve with two different types depending on the values of curvature and torsion of timelike curve are obtained. By using the differentiable functions obtained as a result of these solutions, tangential dual and torque curve of the timelike W curve are obtained. Depending on the tangential dual and torque curve of the timelike W curve, results are given for two different cases separately.

Scattering of plane waves by an open arc with different boundary conditions on its sides

The paper considers an approach to numerical modelling of the problem of electromagnetic plane waves scattering by an open arc with different boundary conditions on its sides. The corresponding mixed boundary value problem is reduced to a system of two singular and hypersingular integral equations. The method of collocation for numerical solutions to the equations obtained is proposed and analyzed. Numerical results of the radar cross-section for different values of arc curvatures are presented.

Impact of pulse dynamic loading direction and surface curvature on the stress-strain state of a three-layered spherical shell

On two size types of the semispherical three-layered structures, impact of the surface curvature and impact of the pulse dynamic loading on the stress-strain state (SSS) of these structures has been investigated. The layered hemispheres have been analyzed with the clamped footing and diameters (D1=0.30 m, D2=0.60 m), which had similar bearing layers’ thickness (h1=h3=0.010 m), polymeric filler with h2=0.020 m thickness, reinforced with the 5 discrete stiffening rings rigidly bound to the bearing layers.
 Values of normal stresses and vertical displacements of the structures’ bearing layers and distribution of these indicators along the spatial coordinate have been determined. Distribution of displacements’ and stresses’ magnitudes along the spatial coordinate α was determined by the software complex Nastran through the direct transient dynamic process algorithm within the time interval 0 ≤ t ≤ 10T. The time interval step duration was 0.25*10-6 s and the total number of steps was 200. The detailed and accurate calculation results have determined the choice of the solid finite element type.
 Value of the Gaussian curvature of the layered shell structures impacts their stress-strain state. Increase of the surface curvature of spherical structures under the impact of the dynamic pulse load increases the displacement and stress of their bearing layers.
 In addition to the vertical displacements and normal stresses of the bearing layers of the analyzed semispherical three-layered structures, their first natural frequency (f1) was also calculated.

Influence of leading edge point on aerodynamic performance of asymmetric leading edge compressor airfoils

Abstract Leading edge (LE) plays a prominent role in compressor flow. The asymmetric leading edge (ASYLE) has shown superiorities to symmetric LE in blade aerodynamic performance. However, the influencing rules of ASYLE design parameters are still ambiguous. In this work, numerical calculations were conducted to investigate the influencing effects of LE point curvature and position. The results show that the operating range of ASYLE blades expand with the decrease of LE point curvature, which helps to moderate LE flow acceleration, while the LE point position mainly affects the operating range. It is also revealed that the SSLE curvature peak is supposed to be close to LE point, and the maximum value of PSLE curvature should be restricted.

Continuous Extraction and Continuous Backfill Mining Method Using Carbon Dioxide Mineralized Filling Body to Preserve Shallow Water in Northwest China

The exploitation and utilization of coal resources are not only prone to causing water table lowering, but also produce a large amount of CO2 and coal-based solid waste. A scientific concept that employs the CO2 and solid wastes to develop filling bodies and inject them into the mined-out area, to sequestrate CO2 and mitigate the overburden migration and thus preserve the overlying aquifer, is proposed. Continuous extraction and continuous backfill (CECB) mining was selected as the mining method to meet the aforementioned objectives. Additionally, carbon dioxide mineralized filling body (CMFB) under ambient temperature and pressure was developed, with fly ash as aggregate, and CO2 gas, silicate additives and cement as accessories. The uniaxial compressive strength (UCS) and tensile strength of CMFB with various curing times and fly ash contents were tested indoors. A physical analogue simulation and FLAC3D numerical calculation were then successively implemented on the premise of determining a similar material ratio of CMFB in analogue simulation and calibrating the parameters of the CMFB in numerical simulation. The deformation of aquifuge and water level lowering while using CECB and CMFB with various proportion of fly ash were obtained. When using the CMFB with 75% fly ash content and 28 d curing time, the maximum values of vertical displacement, horizontal displacement, inclination, horizontal deformation and curvature of aquiclude were 26 mm, 6.5 mm, 0.12 mm/m, 0.08 mm/m and 0.0015 mm/m2, respectively, and the water table decreased 0.47 m. The results show that the CMFB with 75% fly ash is the most appropriate ratio to realize water preservation mining, CO2 sequestration and harmless treatment of solid wastes, contributing to the green and sustainable development of coal areas.

Assessment of changes in the sagittal plane of the spine in girls with adolescent idiopathic scoliosis using the moire method.

The gold standard in the clinical assessment of the extent of scoliosis is the Cobb method but the analysis also covers the changes that occur within the spine and trunk in relation to the transverse and sagittal planes. The study aimed to estimate changes in the sagittal plane of the spine in girls with right-sided thoracic adolescent idiopathic scoliosis. The study involved 29 girls with scoliosis (13.6 ± 0.6 years) and 36 healthy girls as the comparison group. The tests included an interview, clinical examination (with the use of Adam's test and the Cobb angle), and examination of shape of the spine surface with the use of the photogrammetric method and the projection moire effect. Lower values of the thoracic kyphosis parameters were found in the scoliosis group. Significant differences were noted for the parameters of the lumbosacral section α (p= 0.02), thoracolumbar section β (p< 0.001), the upper thoracic section γ (p< 0.001), thoracolumbar and upper thoracic section β+γ (p< 0.001) and the total size of α+β+γ (p< 0.001) curvatures. The study showed that with an increase in the angular value of the thoracic curvature, the thoracic kyphosis decreased.

Length effect on the plastic deformation of SiO2 microcantilevers

SiO2 films are of much interest for the realization of suspended micromechanical structures such as microcantilevers and micro-bridges owing to their superior characteristics when compared to conventional c-Si. However, presence of residual stress induced bending and structural plastic deformation in these devices especially at elevated temperatures hinder their potential for real-time field applications. Moreover, the impact of micro-scale dimensional effects on the magnitude of deformation in these devices is not well understood. In this work, we have investigated the effect of post-release high temperature annealing on the bending and resonance frequency characteristics of SiO2 microcantilevers (MCs) with a specific focus on the length effect. For this purpose, SiO2 MCs of various lengths (Length: 50–190 μm, Width: 37 μm and thickness: 0.98 μm) were fabricated using direct laser writer and wet chemical etching methods and were subjected to high temperature annealing under N2 and O2 environments. We demonstrate through our experiments that the curvature of SiO2 MCs increases with both annealing temperature and length square of MCs. Our experiments revealed that, apart from onset of plastic deformation, stress accumulation at the fixed end of SiO2 MCs is also responsible for the observed curvature increase. From the measured curvature, mean (σ0) and gradient (σ1) residual stress values were estimated and found to increase with annealing temperature. Interestingly, there exists a critical length of MCs (90 μm) below which both σ0 and σ1 were found to increase further with reducing MC length and is shown to be due to the existence of large transverse curvature at these dimensions. High temperature annealing was also found to increase the resonance frequency of MCs and the increase was maximum ∼ 8% for 130 μm long MC. Various possible reasons for the frequency shift is discussed in detail.

Dielectrowetting on curved surfaces

Programmable fluidic systems on curved and flexible substrates are of increasing interest. One approach to achieving programmability is the controlled sequential wetting and dewetting on a surface using voltage actuation. In particular, liquid dielectrophoresis techniques have recently been shown to provide the ability to form a spread liquid film on a normally liquid repellent, but rigid, substrate via applying a spatially periodic electrical potential underneath an initial sessile droplet. In this work, we demonstrate the creation of thin, rectangular shaped, films of electrically insulating liquid on the side of a curved and flexible liquid repellant substrate using dielectrophoresis forces. We find that the experimental threshold voltage VT(κs) for film formation has a monotonic dependence on the value of the substrate curvature κs in the range −0.4 mm−1 &amp;lt; κs &amp;lt; 0.26 mm−1. By considering the balance of stresses acting on the films, including the Laplace pressure and the Maxwell stress, we develop an analytical theoretical expression that is in excellent quantitative agreement with our curvature dependent experimental threshold voltage measurements. The resulting physical insights and the demonstration of programmable wettability on curved and flexible substrates with both positive and negative curvature provide the foundations for applications in imaging, displays, and biochemical analysis.

Laser In Situ Keratomileusis (LASIK) Combined with Prophylactic Corneal Cross-Linking for Correction of Myopia: Regional Analysis of Corneal Morphology.

IntroductionThis study evaluated the outcomes of laser in situ keratomileusis (LASIK) combined with prophylactic corneal collagen cross-linking (CXL) in correcting myopia in cases with increased estimated risk of postoperative corneal ectasia, detected by regional analysis of corneal morphology.MethodsThe retrospective study included 180 eyes of 99 patients. Group 1 (94 eyes of 49 patients) with increased risk of postoperative corneal ectasia, as detected by “Ectasia Risk Factor Score System for LASIK”, underwent femtosecond laser-assisted LASIK (FS-LASIK) combined with prophylactic CXL, using short riboflavin soaking time and low UV energy. Group 2 (86 eyes of 50 patients) with normal corneal topography, who underwent FS-LASIK alone, were used as controls. Refractive and visual outcomes and Scheimpflug topo/tomography were analyzed preoperatively and 1 week, 1 month, and 12 months postoperatively. Mean regional corneal curvature (M) values for three subregions (the central 3.0 mm region, the paracentral 3.0–6.0 mm region, and the peripheral 6.0–9.0 mm region) of both anterior and posterior surfaces were calculated.ResultsAn increase in flattening of the peripheral anterior region and more steepening of the posterior paracentral region were shown at 12 months compared to 1 month postoperatively in group 1. The findings were significantly more pronounced than in group 2 (P < 0.001 and P = 0.035, respectively). The refractive and visual outcomes were comparable in the two groups.ConclusionsProphylactic CXL seems to influence corneal regional reshaping after surgery, while not affecting the 1-year visual and refractive results.

On Weyl tensor of ACR-manifolds of class $C_{12}$ with applications

In this paper, we determine the components of the Weyl tensor of almost contact metric (ACR-) manifold of class $C_{12}$ on associated G-structure (AG-structure) space. As an application, we prove that the conformally flat ACR-manifold of class $C_{12}$ with $n&gt;2$ is an $\eta$-Einstein manifold and conclude that it is an Einstein manifold such that the scalar curvature $r$ has provided. Also, the case when $n=2$ is discussed explicitly. Moreover, the relationships among conformally flat, conformally symmetric, $\xi$-conformally flat and $\Phi$-invariant Ricci tensor have been widely considered here and consequently we determine the value of scalar curvature $r$ explicitly with other applications. Finally, we define new classes with identities analogously to Gray identities and discuss their connections with class $C_{12}$ of ACR-manifold.

A new speed planning method based on predictive curvature calculation for autonomous driving

As the number of vehicles in traffic is increasing day by day, the accident rates and driving effort are significantly raising. For this reason, ensuring safety and driving comfort is becoming more and more important. Driver assistance systems are the most common systems that are adopted for this purpose. With the development of technology, lane tracking support and adaptive cruise control systems are now being sold as standard equipment. More advanced research is being done for fully autonomous driving. One of the most critical parts of autonomous driving is speed profile planning. In this paper, a curvature-based predictive speed planner is designed using a fuzzy logic strategy. In addition to the predictive curvature value, lateral error to the planned path is considered for the final decision. With the help of the proposed predictive nature, which is not included in classical curvature-based planners, the vehicle is able to reduce the speed before cornering. Similarly, it starts increasing the speed when it is still in a curve but very near to the straight part of the road. In order to illustrate the efficiency of the proposed method and compare it with other approaches, the simulations are performed using realistic vehicle dynamics models of CarMaker software. After the comparative analysis, the designed planner is utilized on a real 1/10 scaled autonomous vehicle platform to show its real-world performance. The results show that the proposed speed planner is an effective and promising algorithm for both the comfort and path tracking performance.

The effect of the combination of acupuncture and kinesiotherapy on upper cross syndrome based on mechanical balance principle – A randomized clinical trial: 浅析基于力学平衡原理针刺结合运动疗法治疗上交叉综合征疗效观察 -- 随机对照试验

ObjectiveTo observe the clinical effect of combined acupuncture and kinesiotherapy on upper cross syndrome (UCS) by a parallel randomized clinical trial. MethodsA total of 45 patients with UCS were recruited from the outpatients of Acupuncture-Moxibustion, Tuina and Rehabilitation Department of the First Affiliated Hospital of Hunan University of Chinese Medicine, the students of Hunan University of Chinese Medicine and the patients from the nearby communities in accordance with the inclusion criteria. Using the random number table method, they were divided into a combined treatment group (acupuncture plus kinesiotherapy, 23 cases) and a simple kinesiotherapy group (22 patients). Treatment for 4 weeks was one course, and two consecutive courses were required. The visual analog scale (VAS) score, the score of the assessment scale for cervical spondylosis, the value of surface electromyography (root mean square, RMS), and the cervical curvature value were used in the evaluation. The allocation scheme was concealed from the outcome assessors. ResultsThe data from 23 cases of the combined treatment group and 22 cases of the simple kinesiotherapy group were analyzed. Before treatment, the differences were not statistically significant in the general conditions, VAS score, assessment score of cervical spondylosis, cervical curvature value, and RMS in UCS patients between the two groups (all P > 0.05). After treatment, the VAS score was reduced compared with that before treatment in both groups (all P < 0.05). In two courses of treatment, the VAS score decreased as compared with that in one course of treatment in both groups (both P < 0.05), and the VAS score in the combined treatment group decreased more obviously after each course of treatment (both P < 0.05). The RMS decreased compared with that before treatment in each group (both P < 0.05), and the decrease in the combined treatment group was more obvious (P < 0.05). After treatment of each course, the assessment score was all increased as compared with that before treatment in two groups (all P < 0.05). In two courses of treatment, the assessment score was increased as compared with that in one course of treatment in both groups (both P < 0.05), and the score in the combined treatment group was increased more obviously in the two courses of treatment (P < 0.05). Regarding either the intra-group comparison or the inter-group comparison before and after treatment, the differences were not statistically significant (all P > 0.05), suggesting no obvious improvement of cervical curvature in the two courses of treatment in patients with UCS. However, cervical curvature tended to improve in the combined treatment group. The total effective rate was significantly different between the two groups (P < 0.05), indicating that the total effective rate in the combined treatment group was better than that in the simple kinesiotherapy group.No any adverse reactions occurred. ConclusionCombined treatment with acupuncture, kinesiotherapy, and kinesiotherapy alleviated pain, relieved the symptoms and physical signs, and improved the daily movement of the patients. However, the combined treatment of acupuncture and kinesiotherapy had a much better effect on UCS.

Curved beams with circular cross‐sections under pure in‐plane bending

AbstractThis paper deals with the phenomenon of flattening or inflation of cross‐sections caused by pure bending on beams of hollow circular cross‐section with or without initial curvature. Both initially straight and initially bent tubes are analyzed under in plane bending. Results over a wide range of initial curvature values are presented. Finally, the area of validity of the expressions used is studied, as well as the deformations and stresses that occur in practice.