Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 58

Search results for: torsion

58 Experimental Options for the Role of Dynamic Torsion in General Relativity

Authors: Ivan Ravlich, Ivan Linscott, Sigrid Close


The experimental search for spin coupling in General Relativity via torsion has been inconclusive. In this work, further experimental avenues to test dynamic torsion are proposed and evaluated. In the extended theory, by relaxing the torsion free condition on the metric connection, general relativity is reformulated to relate the spin density of particles to a new quantity, the torsion tensor. In torsion theories, the spin tensor and torsion tensor are related in much the same way as the stress-energy tensor is related to the metric connection. Similarly, as the metric is the field associated with the metric connection, fields can be associated with the torsion tensor resulting in a field that is either propagating or static. Experimental searches for static torsion have thus far been inconclusive, and currently, there have been no experimental tests for propagating torsion. Experimental tests of propagating theories of torsion are proposed utilizing various spin densities of matter, such as interfaces in superconducting materials and plasmas. The experimental feasibility and observable bounds are estimated, and the most viable candidates are selected to pursue in detail in a future work.

Keywords: general relativity, gravitation, propagating torsion, spin density

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57 Torsional Design Method of Asymmetric and Irregular Building under Horizontal Earthquake Action

Authors: Radhwane Boudjelthia


Based upon elaborate analysis on torsional design methods of asymmetric and irregular structure under horizontal earthquake action, it points out that the main design principles of an asymmetric building subjected to horizontal earthquake are: the torsion of vertical members induced by the torsion angle of the floor (rigid diaphragm) cannot exceed the allowable value, the inter-story displacement at outermost frame or shear wall should be less than that required by design code, stresses in plane of the slab should be controlled within acceptable extent under different intensity earthquakes. That current seismic design code only utilizes the torsion displacement ratio to control the floor torsion, which seems not reasonable enough since its connotation is the multiple of the floor torsion angle and the distance of floor mass center to the edge frame or shear wall.

Keywords: earthquake, building, seismic forces, displacement, resonance, response

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56 Statistical Analysis of Parameters Effects on Maximum Strain and Torsion Angle of FRP Honeycomb Sandwich Panels Subjected to Torsion

Authors: Mehdi Modabberifar, Milad Roodi, Ehsan Souri


In recent years, honeycomb fiber reinforced plastic (FRP) sandwich panels have been increasingly used in various industries. Low weight, low price, and high mechanical strength are the benefits of these structures. However, their mechanical properties and behavior have not been fully explored. The objective of this study is to conduct a combined numerical-statistical investigation of honeycomb FRP sandwich beams subject to torsion load. In this paper, the effect of geometric parameters of the sandwich panel on the maximum shear strain in both face and core and angle of torsion in a honeycomb FRP sandwich structures in torsion is investigated. The effect of Parameters including core thickness, face skin thickness, cell shape, cell size, and cell thickness on mechanical behavior of the structure were numerically investigated. Main effects of factors were considered in this paper and regression equations were derived. Taguchi method was employed as experimental design and an optimum parameter combination for the maximum structure stiffness has been obtained. The results showed that cell size and face skin thickness have the most significant impacts on torsion angle, maximum shear strain in face and core.

Keywords: finite element, honeycomb FRP sandwich panel, torsion, civil engineering

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55 Investigating the Capacity of Cracking Torsion of Rectangular and Cylindrical RC Beams with Spiral and Normal Stirrups

Authors: Hadi Barghlame, M. A. Lotfollahi-Yaghin, Mehdi Mohammad Rezaei, Saeed Eskanderzadeh


In this paper, the capacity of cracking torsion on rectangular and cylindrical beams with spiral and normal stirrups in similar properties are investigated. Also, in the beams with spiral stirrups, stirrups are not wrapping and spiral stirrups similar to normal stirrups in ACI code. Therefore, models of above-mentioned beams have been numerically analyzed under various loads using ANSYS software. In this research, the behavior of rectangular reinforced concrete beams is compared with the cylindrical reinforced concrete beams. The capacity of cracking torsion of rectangular and cylindrical RC beams with spiral and normal stirrups are same. In the other words, the behavior of rectangular RC beams is similar to cylindrical beams.

Keywords: cracking torsion, RC beams, spiral stirrups, normal stirrups

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54 Protective Effects of Vitamin C and Vitamin E on Experimentally Induced Testicular Torsion and Detorsion in Rat Model

Authors: Anu Vinod Ranade


Aim: To evaluate and compare the effects of Vitamin C and Vitamin E on experimentally induced testicular torsion and detorsion in rats. Methods: Forty Male Wistar Albino rats were divided into five groups. Animals in the Group I underwent Sham operation, Group II consisted of animals that were subjected to torsion for three hours followed by detorsion for 24 hours without any treatment. While Group III, IV and V were orally pretreated with Vitamin C (40mg/, vitamin E (100mg/ and a combination of Vitamin C and vitamin E respectively for a period of 30 days. The testes of the experimental groups were manually rotated to 720° clockwise for three hours and counter rotated for 24 hours to induce ischemia and reperfusion. Sequential biopsies were performed and the testes were collected at the end of 24 hours of detrosion for morphological evaluation. Result: There was a significant decrease in the standard tubular diameter and the epithelial height of the seminiferous tubules in the untreated group when compared to Sham controls. The standard tubular diameter and seminiferous epithelial height showed near normal values when animals were pretreated with Vitamin C and Vitamin E individually or in combination. Conclusion: The results showed that pretreatment of with antioxidants vitamin E and vitamin C when administered prior to testicular torsion in rats significantly reduced the torsion and detorsion induced histopathlogical injury.

Keywords: vitamin C, vitamin E, standard tubular diameter, standard epithelial height, testicular torsion

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53 Relationship between Trauma and Acute Scrotum: Test Torsion and Epididymal Appendix Torsion

Authors: Saimir Heta, Kastriot Haxhirexha, Virtut Velmishi, Nevila Alliu, Ilma Robo


Background: Testicular rotation can occur at any age. The possibility to save the testicle is the fastest possible surgical intervention which is indicated by the presence of acute pain even at rest. The time element is more important to diagnose and proceed further with surgical intervention. Testicular damage is a consequence which mainly depends on the moment of onset of symptoms, at the time when the symptoms are diagnosed, the earliest action to be performed is surgical intervention. Sometimes medical tests are needed to confirm a diagnosis, or to help identify another cause for symptoms; for example, the urine test, that is used to check for infection, associated with the scrotal ultrasound test. Control of blood flow to the longitudinal supply vessels of the testicles is indicated. The sign that indicates testicular rotation is a reduction in blood flow. This is the element which is distinguished from ultrasound examination. Surgery may be needed to determine if the patient’s symptoms are caused by the rotation of the testis or any other condition. Discussion: As a surgical intervention of the emergency, the torsion of the test depends very much on the duration of the torsion, as the success in the life of the testicle depends on the fastest surgical intervention. From the previous clinic, it is noted that in any case presented to the pediatric patient diagnosed with testicular rotation, there is always a link with personal history that the patient refers to the presence of a previous episode of testicular trauma. Literature supports this fact very logically. Conclusions: Salvation without testicular atrophy depends closely on establishing the diagnosis of testicular rotation as soon as possible. Following the logic above, it can be said that the diagnosis for rotation should be performed as soon as possible, to avoid consequences that will not be favorable for the patient.

Keywords: acute scrotum, test torsion, newborns, clinical presentation

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52 Evaluation of the End Effect Impact on the Torsion Test for Determining the Shear Modulus of a Timber Beam through a Photogrammetry Approach

Authors: Niaz Gharavi, Hexin Zhang, Yanjun Xie


The timber beam end effect in the torsion test is evaluated using binocular stereo vision system. It is recommended by BS EN 408:2010+A1:2012 to exclude a distance of two to three times of cross-sectional thickness (b) from ends to avoid the end effect; whereas, this study indicates that this distance is not sufficiently far enough to remove this effect in slender cross-sections. The shear modulus of six timber beams with different aspect ratios is determined at the various angles and cross-sections. The result of this experiment shows that the end affected span of each specimen varies depending on their aspect ratios. It is concluded that by increasing the aspect ratio this span will increase. However, by increasing the distance from the ends to the values greater than 6b, the shear modulus trend becomes constant and end effect will be negligible. Moreover, it is concluded that end affected span is preferred to be depth-dependent rather than thickness-dependant.

Keywords: end clamp effect, full-size timber test, shear properties, torsion test, wood engineering

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51 The Microwave and Far Infrared Spectra of Acetaldehyde-d1 in vt=2

Authors: A. Larrousi, M. Elkeurti, K. Amara, M. Zemouli, L. H. Coudert, I. R. Medvedev, F. C. De Lucia, Atsuko Maeda, R. W. C. McKellar, D. Appadoo


Experimental and theoretical investigations of the microwave and far infrared spectra of CH3COD are reported. Two hundred twelve lines were identified in the far infrared spectrum recorded using the Canadian synchrotron radiation light source. Two thousand one hundred and sixty-eight lines in vt=0,1 and 216 in vt=2 have been measured in the microwave spectrum obtained using the fast scan submillimeter spectroscopic technique. A global analysis of the new data and of already available microwave lines has been carried out and yielded values for rotation–torsion parameters. The unitless weighted standard deviation of the fit is 1.6. 46 parameters and 216 lines were identified.

Keywords: CH3COD, torsion, the microwave spectra, far infrared spectra high resolution

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50 Influence of Chemical Treatment on Elastic Properties of the Band Cotton Crepe 100%

Authors: Bachir Chemani, Rachid Halfaoui, Madani Maalem


The manufacturing technology of band cotton is very delicate and depends to choice of certain parameters such as torsion of warp yarn. The fabric elasticity is achieved without the use of any elastic material, chemical expansion, artificial or synthetic and it’s capable of creating pressures useful for therapeutic treatments.Before use, the band is subjected to treatments of specific preparation for obtaining certain elasticity, however, during its treatment, there are some regression parameters. The dependence of manufacturing parameters on the quality of the chemical treatment was confirmed. The aim of this work is to improve the properties of the fabric through the development of manufacturing technology appropriately. Finally for the treatment of the strip pancake 100% cotton, a treatment method is recommended.

Keywords: elastic, cotton, processing, torsion

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49 Extension-Torsion-Inflation Coupling in Compressible Magnetoelastomeric Tubes with Helical Magnetic Anisotropy

Authors: Darius Diogo Barreto, Ajeet Kumar, Sushma Santapuri


We present an axisymmetric variational formulation for coupled extension-torsion-inflation deformation in magnetoelastomeric thin tubes when both azimuthal and axial magnetic fields are applied. The tube's material is assumed to have a preferred magnetization direction which imparts helical magnetic anisotropy to the tube. We have also derived the expressions of the first derivative of free energy per unit tube's undeformed length with respect to various imposed strain parameters. On applying the thin tube limit, the two nonlinear ordinary differential equations to obtain the in-plane radial displacement and radial component of the Lagrangian magnetic field get converted into a set of three simple algebraic equations. This allows us to obtain simple analytical expressions in terms of the applied magnetic field, magnetization direction, and magnetoelastic constants, which tell us how these parameters can be tuned to generate positive/negative Poisson's effect in such tubes. We consider both torsionally constrained and torsionally relaxed stretching of the tube. The study can be useful in designing magnetoelastic tubular actuators.

Keywords: nonlinear magnetoelasticity, extension-torsion coupling, negative Poisson's effect, helical anisotropy, thin tube

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48 Determination of Friction and Damping Coefficients of Folded Cover Mechanism Deployed by Torsion Springs

Authors: I. Yilmaz, O. Taga, F. Kosar, O. Keles


In this study, friction and damping coefficients of folded cover mechanism were obtained in accordance with experimental studies and data. Friction and damping coefficients are the most important inputs to accomplish a mechanism analysis. Friction and damping are two objects that change the time of deployment of mechanisms and their dynamic behaviors. Though recommended friction coefficient values exist in literature, damping is differentiating feature according to mechanic systems. So the damping coefficient should be obtained from mechanism test outputs. In this study, the folded cover mechanism use torsion springs for deploying covers that are formerly close folded position. Torsion springs provide folded covers with desirable deploying time according to variable environmental conditions. To verify all design revisions with system tests will be so costly so that some decisions are taken in accordance with numerical methods. In this study, there are two folded covers required to deploy simultaneously. Scotch-yoke and crank-rod mechanisms were combined to deploy folded covers simultaneously. The mechanism was unlocked with a pyrotechnic bolt onto scotch-yoke disc. When pyrotechnic bolt was exploded, torsion springs provided rotational movement for mechanism. Quick motion camera was recording dynamic behaviors of system during deployment case. Dynamic model of mechanism was modeled as rigid body with Adams MBD (multi body dynamics) then torque values provided by torsion springs were used as an input. A well-advised range of friction and damping coefficients were defined in Adams DOE (design of experiment) then a large number of analyses were performed until deployment time of folded covers run in with test data observed in record of quick motion camera, thus the deployment time of mechanism and dynamic behaviors were obtained. Same mechanism was tested with different torsion springs and torque values then outputs were compared with numerical models. According to comparison, it was understood that friction and damping coefficients obtained in this study can be used safely when studying on folded objects required to deploy simultaneously. In addition to model generated with Adams as rigid body the finite element model of folded mechanism was generated with Abaqus then the outputs of rigid body model and finite element model was compared. Finally, the reasonable solutions were suggested about different outputs of these solution methods.

Keywords: damping, friction, pyro-technic, scotch-yoke

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47 Prediction of Nonlinear Torsional Behavior of High Strength RC Beams

Authors: Woo-Young Jung, Minho Kwon


Seismic design criteria based on performance of structures have recently been adopted by practicing engineers in response to destructive earthquakes. A simple but efficient structural-analysis tool capable of predicting both the strength and ductility is needed to analyze reinforced concrete (RC) structures under such event. A three-dimensional lattice model is developed in this study to analyze torsions in high-strength RC members. Optimization techniques for determining optimal variables in each lattice model are introduced. Pure torsion tests of RC members are performed to validate the proposed model. Correlation studies between the numerical and experimental results confirm that the proposed model is well capable of representing salient features of the experimental results.

Keywords: torsion, non-linear analysis, three-dimensional lattice, high-strength concrete

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46 Response of Concrete Panels Subjected to Compression-Tension State of Stresses

Authors: Mohammed F. Almograbi


For reinforced concrete panels the risk of failure due to compression -tension state of stresses, results from pure shear or torsion, can be a major problem. The present calculation methods for such stresses from multiple influences are without taking into account the softening of cracked concrete remains conservative. The non-linear finite element method has become an important and increasingly used tool for the analysis and assessment of the structures by including cracking softening and tension-stiffening. The aim of this paper is to test a computer program refined recently and to simulate the compression response of cracked concrete element and to compare with the available experimental results.

Keywords: reinforced concrete panels, compression-tension, shear, torsion, compression softening, tension stiffening, non-linear finite element analysis

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45 A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments

Authors: Haijie Li, Xuping Zhang


This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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44 Analysis of Cyclic Elastic-Plastic Loading of Shaft Based on Kinematic Hardening Model

Authors: Isa Ahmadi, Ramin Khamedi


In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C1 continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: cyclic loading, finite element analysis, Prager kinematic hardening model, torsion of shaft

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43 High Pressure Torsion Deformation Behavior of a Low-SFE FCC Ternary Medium Entropy Alloy

Authors: Saumya R. Jha, Krishanu Biswas, Nilesh P. Gurao


Several recent investigations have revealed medium entropy alloys exhibiting better mechanical properties than their high entropy counterparts. This clearly establishes that although a higher entropy plays a vital role in stabilization of particular phase over complex intermetallic phases, configurational entropy is not the primary factor responsible for the high inherent strengthening in these systems. Above and beyond a high contribution from friction stresses and solid solution strengthening, strain hardening is an important contributor to the strengthening in these systems. In this regard, researchers have developed severe plastic deformation (SPD) techniques like High Pressure Torsion (HPT) to incorporate very high shear strain in the material, thereby leading to ultrafine grained (UFG) microstructures, which cause manifold increase in the strength. The presented work demonstrates a meticulous study of the variation in mechanical properties at different radial displacements from the center of HPT tested equiatomic ternary FeMnNi synthesized by casting route, which is a low stacking fault energy FCC alloy that shows significantly higher toughness than its high entropy counterparts like Cantor alloy. The gradient in grain sizes along the radial direction of these specimens has been modeled using microstructure entropy for predicting the mechanical properties, which has also been validated by indentation tests. The dislocation density is computed by FEM simulations for varying strains and validated by analyzing synchrotron diffraction data. Thus, the proposed model can be utilized to predict the strengthening behavior of similar systems deformed by HPT subjected to varying loading conditions.

Keywords: high pressure torsion, severe plastic deformation, configurational entropy, dislocation density, FEM simulation

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42 A Method to Compute Efficient 3D Helicopters Flight Trajectories Based On a Motion Polymorph-Primitives Algorithm

Authors: Konstanca Nikolajevic, Nicolas Belanger, David Duvivier, Rabie Ben Atitallah, Abdelhakim Artiba


Finding the optimal 3D path of an aerial vehicle under flight mechanics constraints is a major challenge, especially when the algorithm has to produce real-time results in flight. Kinematics models and Pythagorian Hodograph curves have been widely used in mobile robotics to solve this problematic. The level of difficulty is mainly driven by the number of constraints to be saturated at the same time while minimizing the total length of the path. In this paper, we suggest a pragmatic algorithm capable of saturating at the same time most of dimensioning helicopter 3D trajectories’ constraints like: curvature, curvature derivative, torsion, torsion derivative, climb angle, climb angle derivative, positions. The trajectories generation algorithm is able to generate versatile complex 3D motion primitives feasible by a helicopter with parameterization of the curvature and the climb angle. An upper ”motion primitives’ concatenation” algorithm is presented based. In this article we introduce a new way of designing three-dimensional trajectories based on what we call the ”Dubins gliding symmetry conjecture”. This extremely performing algorithm will be soon integrated to a real-time decisional system dealing with inflight safety issues.

Keywords: robotics, aerial robots, motion primitives, helicopter

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41 Numerical Investigation of Beam-Columns Subjected to Non-Proportional Loadings under Ambient Temperature Conditions

Authors: George Adomako Kumi


The response of structural members, when subjected to various forms of non-proportional loading, plays a major role in the overall stability and integrity of a structure. This research seeks to present the outcome of a finite element investigation conducted by the use of finite element programming software ABAQUS to validate the experimental results of elastic and inelastic behavior and strength of beam-columns subjected to axial loading, biaxial bending, and torsion under ambient temperature conditions. The application of the rigorous and highly complicated ABAQUS finite element software will seek to account for material, non-linear geometry, deformations, and, more specifically, the contact behavior between the beam-columns and support surfaces. Comparisons of the three-dimensional model with the results of actual tests conducted and results from a solution algorithm developed through the use of the finite difference method will be established in order to authenticate the veracity of the developed model. The results of this research will seek to provide structural engineers with much-needed knowledge about the behavior of steel beam columns and their response to various non-proportional loading conditions under ambient temperature conditions.

Keywords: beam-columns, axial loading, biaxial bending, torsion, ABAQUS, finite difference method

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40 Fatigue Life Evaluation of Al6061/Al2O3 and Al6061/SiC Composites under Uniaxial and Multiaxial Loading Conditions

Authors: C. E. Sutton, A. Varvani-Farahani


Fatigue damage and life prediction of particle metal matrix composites (PMMCs) under uniaxial and multiaxial loading conditions were investigated. Three PMM composite materials of Al6061/Al2O3/20p-T6, Al6061/Al2O3/22p-T6 and Al6061/SiC/17w-T6 tested under tensile, torsion, and combined tension-torsion fatigue cycling were evaluated with various fatigue damage models. The fatigue damage models of Smith-Watson-Topper (S. W. T.), Ellyin, Brown-Miller, Fatemi-Socie, and Varvani were compared for their capability to assess the fatigue damage of materials undergoing various loading conditions. Fatigue life predication results were then evaluated by implementing material-dependent coefficients that factored in the effects of the particle reinforcement in the earlier developed Varvani model. The critical plane-energy approach incorporated the critical plane as the plane of crack initiation and early stage of crack growth. The strain energy density was calculated on the critical plane incorporating stress and strain components acting on the plane. This approach successfully evaluated fatigue damage values versus fatigue lives within a narrower band for both uniaxial and multiaxial loading conditions as compared with other damage approaches studied in this paper.

Keywords: fatigue damage, life prediction, critical plane approach, energy approach, PMM composites

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39 Effects of Variation of Centers in the Torsional Analysis of Asymmetrical Buildings by Performing Non Linear Static Analysis

Authors: Md Masihuddin Siddiqui, Abdul Haakim Mohammed


Earthquakes are the most unpredictable and devastating of all natural disasters. The behaviour of a building during an earthquake depends on several factors such as stiffness, adequate lateral strength, ductility, and configurations. The experience from the performance of buildings during past earthquakes has shown that the buildings with regular geometry, uniformly distributed mass and stiffness in plan as well as in elevation suffer much less damage compared to irregular configurations. The three centers namely- centre of mass, centre of strength, centre of stiffness are the torsional parameters which contribute to the strength of the building in case of an earthquake. Inertial forces and resistive forces in a structural system act through the center of mass and center of rigidity respectively which together oppose the forces that are produced during seismic excitation. So these centers of a structural system should be positioned where the structural system is the strongest so that the effects produced due to the earthquake may have a minimal effect on the structure. In this paper, the effects of variation of strength eccentricity and stiffness eccentricity in reducing the torsional responses of the asymmetrical buildings by using pushover analysis are studied. The maximum reduction of base torsion was observed in the case of minimum strength eccentricity, and the least reduction was observed in the case of minimum stiffness eccentricity.

Keywords: strength eccentricity, stiffness eccentricity, asymmetric structure, base torsion, push over analysis

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38 Femoral Neck Anteversion and Neck-Shaft Angles: Determination and Their Clinical Implications in Fetuses of Different Gestational Ages

Authors: Vrinda Hari Ankolekar, Anne D. Souza, Mamatha Hosapatna


Introduction: Precise anatomical assessment of femoral neck anteversion (FNA) and the neck shaft angles (NSA) would be essential in diagnosing the pathological conditions involving hip joint and its ligaments. FNA of greater than 20 degrees is considered excessive femoral anteversion, whereas a torsion angle of fewer than 10 degrees is considered femoral retroversion. Excessive femoral torsion is not uncommon and has been associated with certain neurologic and orthopedic conditions. The enlargement and maturation of the hip joint increases at the 20th week of gestation and the NSA ranges from 135- 140◦ at birth. Material and methods: 48 femurs were tagged according to the GA and two photographs for each femur were taken using Nikon digital camera. Each femur was kept on a horizontal hard desk and end on an image of the upper end was taken for the estimation of FNA and a photograph in a perpendicular plane was taken to calculate the NSA. The images were transferred to the computer and were stored in TIFF format. Microsoft Paint software was used to mark the points and Image J software was used to calculate the angles digitally. 1. Calculation of FNA: The midpoint of the femoral head and the neck were marked and a line was drawn joining these two points. The angle made by this line with the horizontal plane was measured as FNA. 2. Calculation of NSA: The midpoint of the femoral head and the neck were marked and a line was drawn joining these two points. A vertical line was drawn passing through the tip of the greater trochanter to the inter-condylar notch. The angle formed by these lines was calculated as NSA. Results: The paired t-test for the inter-observer variability showed no significant difference between the values of two observers. (FNA: t=-1.06 and p=0.31; NSA: t=-0.09 and p=0.9). The FNA ranged from 17.08º to 33.97 º on right and 17.32 º to 45.08 º on left. The NSA ranged from 139.33 º to 124.91 º on right and 143.98 º to 123.8 º on left. Unpaired t-test was applied to compare the mean angles between the second and third trimesters which did not show any statistical significance. This shows that the FNA and NSA of femur did not vary significantly during the third trimester. The FNA and NSA were correlated with the GA using Pearson’s correlation. FNA appeared to increase with the GA (r=0.5) but the increase was not statistically significant. A decrease in the NSA was also noted with the GA (r=-0.3) which was also statistically not significant. Conclusion: The present study evaluates the FNA and NSA of the femur in fetuses and correlates their development with the GA during second and third trimesters. The FNA and NSA did not vary significantly during the third trimester.

Keywords: anteversion, coxa antetorsa, femoral torsion, femur neck shaft angle

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37 Investigation of Flexural – Torsion Instability of Struts Using Modified Newmark Method

Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi


Differential equations are of fundamental importance in engineering and applied mathematics, since many physical laws and relations appear mathematically in the form of such equations. The equilibrium state of structures consisting of one-dimensional elements can be described by an ordinary differential equation. The response of these kinds of structures under the loading, namely relationship between the displacement field and loading field, can be predicted by the solution of these differential equations and on satisfying the given boundary conditions. When the effect of change of geometry under loading is taken into account in modeling of equilibrium state, then these differential equations are partially integrable in quartered. They also exhibit instability characteristics when the structures are loaded compressively. The purpose of this paper is to represent the ability of the Modified Newmark Method in analyzing flexural-torsional instability of struts for both bifurcation and non-bifurcation structural systems. The results are shown to be very accurate with only a small number of iterations. The method is easily programmed, and has the advantages of simplicity and speeds of convergence and easily is extended to treat material and geometric nonlinearity including no prismatic members and linear and nonlinear spring restraints that would be encountered in frames. In this paper, these abilities of the method will be extended to the system of linear differential equations that govern strut flexural torsional stability.

Keywords: instability, torsion, flexural, buckling, modified newmark method stability

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36 Noncommutative Differential Structure on Finite Groups

Authors: Ibtisam Masmali, Edwin Beggs


In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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35 Tool for Analysing the Sensitivity and Tolerance of Mechatronic Systems in Matlab GUI

Authors: Bohuslava Juhasova, Martin Juhas, Renata Masarova, Zuzana Sutova


The article deals with the tool in Matlab GUI form that is designed to analyse a mechatronic system sensitivity and tolerance. In the analysed mechatronic system, a torque is transferred from the drive to the load through a coupling containing flexible elements. Different methods of control system design are used. The classic form of the feedback control is proposed using Naslin method, modulus optimum criterion and inverse dynamics method. The cascade form of the control is proposed based on combination of modulus optimum criterion and symmetric optimum criterion. The sensitivity is analysed on the basis of absolute and relative sensitivity of system function to the change of chosen parameter value of the mechatronic system, as well as the control subsystem. The tolerance is analysed in the form of determining the range of allowed relative changes of selected system parameters in the field of system stability. The tool allows to analyse an influence of torsion stiffness, torsion damping, inertia moments of the motor and the load and controller(s) parameters. The sensitivity and tolerance are monitored in terms of the impact of parameter change on the response in the form of system step response and system frequency-response logarithmic characteristics. The Symbolic Math Toolbox for expression of the final shape of analysed system functions was used. The sensitivity and tolerance are graphically represented as 2D graph of sensitivity or tolerance of the system function and 3D/2D static/interactive graph of step/frequency response.

Keywords: mechatronic systems, Matlab GUI, sensitivity, tolerance

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34 A Coupled Stiffened Skin-Rib Fully Gradient Based Optimization Approach for a Wing Box Made of Blended Composite Materials

Authors: F. Farzan Nasab, H. J. M. Geijselaers, I. Baran, A. De Boer


A method is introduced for the coupled skin-rib optimization of a wing box where mass minimization is the objective and local buckling is the constraint. The structure is made of composite materials where continuity of plies in multiple adjacent panels (blending) has to be satisfied. Blending guarantees the manufacturability of the structure; however, it is a highly challenging constraint to treat and has been under debate in recent research in the same area. To fulfill design guidelines with respect to symmetry, balance, contiguity, disorientation and percentage rule of the layup, a reference for the stacking sequences (stacking sequence table or SST) is generated first. Then, an innovative fully gradient-based optimization approach in relation to a specific SST is introduced to obtain the optimum thickness distribution all over the structure while blending is fulfilled. The proposed optimization approach aims to turn the discrete optimization problem associated with the integer number of plies into a continuous one. As a result of a wing box deflection, a rib is subjected to load values which vary nonlinearly with the amount of deflection. The bending stiffness of a skin affects the wing box deflection and thus affects the load applied to a rib. This indicates the necessity of a coupled skin-rib optimization approach for a more realistic optimized design. The proposed method is examined with the optimization of the layup of a composite stiffened skin and rib of a wing torsion box subjected to in-plane normal and shear loads. Results show that the method can successfully prescribe a valid design with a significantly cheap computation cost.

Keywords: blending, buckling optimization, composite panels, wing torsion box

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33 An Atomistic Approach to Define Continuum Mechanical Quantities in One Dimensional Nanostructures at Finite Temperature

Authors: Smriti, Ajeet Kumar


We present a variant of the Irving-Kirkwood procedure to obtain the microscopic expressions of the cross-section averaged continuum fields such as internal force and moment in one-dimensional nanostructures in the non-equilibrium setting. In one-dimensional continuum theories for slender bodies, we deal with quantities such as mass, linear momentum, angular momentum, and strain energy densities, all defined per unit length. These quantities are obtained by integrating the corresponding pointwise (per unit volume) quantities over the cross-section of the slender body. However, no well-defined cross-section exists for these nanostructures at finite temperature. We thus define the cross-section of a nanorod to be an infinite plane which is fixed in space even when time progresses and defines the above continuum quantities by integrating the pointwise microscopic quantities over this infinite plane. The method yields explicit expressions of both the potential and kinetic parts of the above quantities. We further specialize in these expressions for helically repeating one-dimensional nanostructures in order to use them in molecular dynamics study of extension, torsion, and bending of such nanostructures. As, the Irving-Kirkwood procedure does not yield expressions of stiffnesses, we resort to a thermodynamic equilibrium approach to obtain the expressions of axial force, twisting moment, bending moment, and the associated stiffnesses by taking the first and second derivatives of the Helmholtz free energy with respect to conjugate strain measures. The equilibrium approach yields expressions independent of kinetic terms. We then establish the equivalence of the expressions obtained using the two approaches. The derived expressions are used to understand the extension, torsion, and bending of single-walled carbon nanotubes at non-zero temperatures.

Keywords: thermoelasticity, molecular dynamics, one dimensional nanostructures, nanotube buckling

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32 Module Valuations and Quasi-Valuations

Authors: Shai Sarussi


Suppose F is a field with valuation v and valuation domain Oᵥ, and R is an Oᵥ-algebra. It is known that there exists a filter quasi-valuation on R; the existence of a quasi-valuation yields several important connections between Oᵥ and R, in particular with respect to their prime spectra. In this paper, the notion of a module valuation is introduced. It is shown that any torsion-free module over Oᵥ has an induced module valuation. Moreover, several results connecting the filter quasi-valuation and module valuations are presented.

Keywords: valuations, quasi-valuations, prime spectrum, algebras over valuation domains

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31 Structural Health Monitoring of Buildings–Recorded Data and Wave Method

Authors: Tzong-Ying Hao, Mohammad T. Rahmani


This article presents the structural health monitoring (SHM) method based on changes in wave traveling times (wave method) within a layered 1-D shear beam model of structure. The wave method measures the velocity of shear wave propagating in a building from the impulse response functions (IRF) obtained from recorded data at different locations inside the building. If structural damage occurs in a structure, the velocity of wave propagation through it changes. The wave method analysis is performed on the responses of Torre Central building, a 9-story shear wall structure located in Santiago, Chile. Because events of different intensity (ambient vibrations, weak and strong earthquake motions) have been recorded at this building, therefore it can serve as a full-scale benchmark to validate the structural health monitoring method utilized. The analysis of inter-story drifts and the Fourier spectra for the EW and NS motions during 2010 Chile earthquake are presented. The results for the NS motions suggest the coupling of translation and torsion responses. The system frequencies (estimated from the relative displacement response of the 8th-floor with respect to the basement from recorded data) were detected initially decreasing approximately 24% in the EW motion. Near the end of shaking, an increase of about 17% was detected. These analysis and results serve as baseline indicators of the occurrence of structural damage. The detected changes in wave velocities of the shear beam model are consistent with the observed damage. However, the 1-D shear beam model is not sufficient to simulate the coupling of translation and torsion responses in the NS motion. The wave method is proven for actual implementation in structural health monitoring systems based on carefully assessing the resolution and accuracy of the model for its effectiveness on post-earthquake damage detection in buildings.

Keywords: Chile earthquake, damage detection, earthquake response, impulse response function, shear beam model, shear wave velocity, structural health monitoring, torre central building, wave method

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30 A Study on Shear Field Test Method in Timber Shear Modulus Determination Using Stereo Vision System

Authors: Niaz Gharavi, Hexin Zhang


In the structural timber design, the shear modulus of the timber beam is an important factor that needs to be determined accurately. According to BS EN 408, shear modulus can be determined using torsion test or shear field test method. Although torsion test creates pure shear status in the beam, it does not represent the real-life situation when the beam is in the service. On the other hand, shear field test method creates similar loading situation as in reality. The latter method is based on shear distortion measurement of the beam at the zone with the constant transverse load in the standardized four-point bending test as indicated in BS EN 408. Current testing practice code advised using two metallic arms act as an instrument to measure the diagonal displacement of the constructing square. Timber is not a homogenous material, but a heterogeneous and this characteristic makes timber to undergo a non-uniform deformation. Therefore, the dimensions and the location of the constructing square in the area with the constant transverse force might alter the shear modulus determination. This study aimed to investigate the impact of the shape, size, and location of the square in the shear field test method. A binocular stereo vision system was developed to capture the 3D displacement of a grid of target points. This approach is an accurate and non-contact method to extract the 3D coordination of targeted object using two cameras. Two group of three glue laminated beams were produced and tested by the mean of four-point bending test according to BS EN 408. Group one constructed using two materials, laminated bamboo lumber and structurally graded C24 timber and group two consisted only structurally graded C24 timber. Analysis of Variance (ANOVA) was performed on the acquired data to evaluate the significance of size and location of the square in the determination of shear modulus of the beam. The results have shown that the size of the square is an affecting factor in shear modulus determination. However, the location of the square in the area with the constant shear force does not affect the shear modulus.

Keywords: shear field test method, BS EN 408, timber shear modulus, photogrammetry approach

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29 Classification of Tropical Semi-Modules

Authors: Wagneur Edouard


Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra

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