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1
Woodward, B., and M. Kashtalyan. "Three-dimensional elasticity analysis of sandwich panels with functionally graded transversely isotropic core." Archive of Applied Mechanics 89, no. 12 (2019): 2463–84. http://dx.doi.org/10.1007/s00419-019-01589-y.
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Abstract In this paper, three-dimensional elastic deformation of rectangular sandwich panels with functionally graded transversely isotropic core subjected to transverse loading is investigated. An exponential variation of Young’s and shear moduli through the thickness is assumed. The approach uses displacement potential functions for transversely isotropic graded media and a three-dimensional elasticity solution for a transversely isotropic graded plate developed by the authors. The effects of transverse shear modulus, loading localisation, panel thickness and anisotropy on the stresses and displacements in the panel are examined and discussed.
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Leissa, A. W., and A. M. Saad. "Large Amplitude Vibrations of Strings." Journal of Applied Mechanics 61, no. 2 (1994): 296–301. http://dx.doi.org/10.1115/1.2901444.
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The study of nonlinear, free, undamped transverse vibrations of a stretched string may be traced back to an equation of motion developed by Kirchhoff more than a century ago. Subsequent studies have typically assumed small slopes and done little to incorporate longitudinal coupling effects. In the present work a new set of coupled equations is derived. These highly nonlinear equations are solved by means of a newly developed Galerkin procedure which determines variations of the transverse and longitudinal displacements in both space and time. Time variation is determined by incremental use of polynomials. Validity of solutions is verified by independent finite difference solutions. Numerical results are presented for three example problems wherein the string is displaced transversely into a half-sine wave, and released from rest. The problems include: (1) moderate strain (ε0 = 0.005) in the straight line equilibrium position and moderate transverse displacement (δ = 0.1L), (2) moderate strain and large displacement (δ = 0.4L), and (3) small strain (ε0 = 10 −5) and moderate displacement. Plots of transverse and longitudinal displacement with time are shown for all three examples. From these plots it is seen that higher modes are generated when only a single mode is initiated, and that the motion is definitely nonperiodic.
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Takeda, Nobuo, Shinji Ogihara, Satoshi Suzuki, and Akira Kobayashi. "Evaluation of Microscopic Deformation in CFRP Laminates with Delamination by Micro-Grid Methods." Journal of Composite Materials 32, no. 1 (1998): 83–100. http://dx.doi.org/10.1177/002199839803200105.
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Micro-grid methods were applied to measure displacements in 90° ply in CFRP cross-ply laminates with only transverse cracks or with both transverse cracks and delaminations. The COD (crack opening displacement) of the transverse cracks were also measured. Micro-grids were printed on the specimen edge surfaces by using the photo-lithography technique. The displacement fields of the specimen edge surface obtained from the experiment were compared with McCartney's [1] and Lee et al.'s [2] analyses which predicted the displacement field of a cross-ply laminate with only transverse cracks. Furthermore these analyses were modified to consider the existence of delamination.
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Zhao, Hanwei, Youliang Ding, Satish Nagarajaiah, and Aiqun Li. "Longitudinal Displacement Behavior and Girder End Reliability of a Jointless Steel-Truss Arch Railway Bridge during Operation." Applied Sciences 9, no. 11 (2019): 2222. http://dx.doi.org/10.3390/app9112222.
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The long length and complex service load form conflicts with the low limits of longitudinal and transverse displacements of jointless bridge design. The longitudinal displacements of the Nanjing Dashengguan Yangtze River Bridge, a jointless steel-truss arch railway bridge, and its girder end reliability are investigated in this article. The time–frequency characteristics of the longitudinal displacements of bearings and expansion joints are analyzed using the empirical wavelet transform. The long-term characteristics of the longitudinal displacements of bearings and expansion joints in the operation period are explored. Furthermore, the relative transverse displacements of the bridge girder end are calculated using longitudinal displacement monitoring data. The mechanical behaviors of the expansion device under relative transverse displacements are studied. The reliability of expansion devices and crossing trains under the effects of relative transverse displacements is studied using kernel density estimation. The main results demonstrate that: (1) The longitudinal displacements of bearings and expansion joints are mainly influenced by environmental temperature. (2) The maximum relative transverse displacement of the expansion joint is close to 1 mm in long-term bridge operation, with the transverse rail deflection at the expansion device approaching 1 mm, which reduces the stability of cross high-speed trains.
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Xia, Yong Jun, and Qian Miao. "Large Deformation Geometric Nonlinear Beam Element Based on U.L. Format." Advanced Materials Research 446-449 (January 2012): 3596–603. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3596.
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Based on the geometric deformation of the Euler-Bernoulli beam element, the geometric nonlinear Euler-Bernoulli beam element based on U.L. formulation is derived. The element’s transverse first-order displacement field is constructed using the cubic Hermite interpolation polynomial, and the first-order Lagrange interpolation polynomial is used for the axial displacement field. Then the additional displacements induced from the rotation of the elemental are included into the transverse and longitudinal displacement fields, so those displacement fields are expressed as the quadratic function of nodal displacement. Afterwards the nonlinear finite element formulas of Euler-Bernoulli beam element under the form of U.L. formulation are derived using Cauchy strain tensor and the principle of virtual displacements. The total equilibrium equation and tangent stiffness for large displacement geometric nonlinear analysis of frame are obtained in the total coordinate system. The correctness of this element is proved by typical example.
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Patel, Virat, Alexandra Digenakis, and Ernest Leber. "Transverse patellar fracture with displacement." Visual Journal of Emergency Medicine 7 (April 2017): 22–23. http://dx.doi.org/10.1016/j.visj.2016.12.001.
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GHUGAL, YUWARAJ M., and ATTESHAMUDDIN S. SAYYAD. "STRESS ANALYSIS OF THICK LAMINATED PLATES USING TRIGONOMETRIC SHEAR DEFORMATION THEORY." International Journal of Applied Mechanics 05, no. 01 (2013): 1350003. http://dx.doi.org/10.1142/s1758825113500038.
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A trigonometric shear deformation theory (TSDT) taking into account transverse shear deformation effect as well as transverse normal strain effect is presented. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in thickness coordinates is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The results of displacements and stresses for static flexure of simply supported symmetric and anti-symmetric cross-ply laminated square plates subjected to parabolic load and line load are obtained. The results obtained by present theory are compared with those of classical, first-order and higher-order plate theories.
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Khandelwal, R. P., A. Chakrabarti, and P. Bhargava. "A New C0 2D Fe Model Based on Improved Higher Order Zigzag Theory for the Analysis of Soft Core Sandwich Plate." International Journal of Applied Mechanics and Engineering 18, no. 2 (2013): 395–423. http://dx.doi.org/10.2478/ijame-2013-0024.
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An efficient C0 continuous finite element (FE) model is developed based on a combined theory (refine higher order shear deformation theory (RHSDT) and least square error (LSE) method) for the static analysis of a soft core sandwich plate. In this (RHSDT) theory, the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zig-zag linearly varying displacement field with a different slope in each layer. The transverse displacement assumes to have a quadratic variation within the core and it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements. In order to calculate the accurate through thickness transverse stresses variation, the Least Square Error (LSE) method has been used at the post processing stage. The proposed combined model (RHSDT and LSE) is implemented to analyze the laminated composites and sandwich plates. Many new results are also presented which should be useful for future research.
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Huang, Hui Rong, Ji Ping Hao, Hai Xia Zhang, and Yi Huang. "Displacement Fundamental Equations and Analysis of Governing Equations of the Circular Moderately Thick Shallow Spherical Shells." Advanced Materials Research 291-294 (July 2011): 2071–75. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.2071.
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Displacement fundamental equations of moderately thick shallow spherical shells in polar coordinates concerning five independent variables, i.e. five middle surface displacements are established, based on the displacement fundamental equations of the moderately thick shells by transverse shearing deformation and basic hypothesis on shallow shells. Four assistant displacement functions are introduced to solve displacement fundamental equations of circular moderately thick shallow spherical shells , which are tenth-order differential equations with variable coefficient, then the decoupled governing differential equations are built up, and five displacement components through four assistant displacement functions are obtained.
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Jones, Norman. "Damage of Plates due to Impact, Dynamic Pressure and Explosive Loads." Key Engineering Materials 535-536 (January 2013): 35–39. http://dx.doi.org/10.4028/www.scientific.net/kem.535-536.35.
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It is the purpose of this study to present design equations which can be used to predict the damage of ductile plating when subjected to mass impact, dynamic pressure or impulsive loadings. The external loadings are sufficiently severe to produce inelastic material behaviour and produce finite transverse displacement, or geometry change, effects. The damage is characterised as the final or permanent transverse displacement of a plate. The theoretical method predicts values for the maximum permanent transverse displacements which agree reasonably well with the corresponding experimental results generated on aluminium alloy circular, square and rectangular plates. Thus, the equations presented in this article are valuable for preliminary design purposes and for forensic studies, while the experimental data can be used for validating numerical schemes.
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Xiao, Feng, Weiwei Zhu, Xiangwei Meng, and Gang S. Chen. "Parameter Identification of Frame Structures by considering Shear Deformation." International Journal of Distributed Sensor Networks 2023 (August 16, 2023): 1–12. http://dx.doi.org/10.1155/2023/6631716.
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This paper presents a method to identify the damages in frame structures with slender beams. This method adjusts the parameters of the structure to match the analytical and the measured displacements. The effect of transverse shear deformation on the nodal analytical displacement is analyzed, and the parameter identification of frame structures with slender beams is performed. The results demonstrate that parameter-identification accuracy can be considerably improved by considering the transverse shear deformation in the frame structure with slender beams. The proposed method can accurately identify the damages in frame structures with slender beams using displacement measurements.
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Adepoju, Olaoluwa O., Larry W. Lake, and Russell T. Johns. "Investigation of Anisotropic Mixing in Miscible Displacements." SPE Reservoir Evaluation & Engineering 16, no. 01 (2013): 85–96. http://dx.doi.org/10.2118/159557-pa.
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Summary Dispersion (or local mixing) degrades miscibility in miscible-flood displacements by interfering with the transfer of intermediate components that develop miscibility. Dispersion, however, also can improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible-flood performance. This paper investigates longitudinal and transverse local mixing in a finite-difference compositional simulator at different scales (both fine and coarse scale) using a 2D convection-dispersion model. All simulations were of constant-mobility and -density, first-contact miscible flow. The model allows for variations of velocity in both directions. We analyzed local (gridblock) concentration profiles for various miscible-displacement models with different scales of heterogeneity and permeability autocorrelation lengths. To infer dispersivity, we fitted an analytical 2D convection-dispersion model to the local concentration profile to determine local longitudinal and transverse dispersivities simultaneously. Streamlines of simulation models were traced using the algorithm proposed by Pollock (1988). To our knowledge, this is the first systematic attempt to numerically study local transverse dispersivity. The results show that transverse mixing, which is usually neglected in the 1D convection-dispersion model of dispersion, is significant when the flow direction changes locally as a result of heterogeneity. The computed streamlines, which highlight the variation in flow directions, agree with the computed transverse-dispersivity trends. We find that both transverse and longitudinal dispersion can grow with travel distance and that there are several instances in which transverse dispersion is the larger of the two. Often, the variations in the streamlines are suppressed (homogenized) during upscaling. This paper gives a quantitative and systematic procedure to estimate the degree of transverse mixing (dispersivity) in any model. We conclude that local mixing, including transverse mixing, should be considered when upscaling a fine-scale model for miscible displacement to ensure proper preservation of fine-scale sweep and displacement efficiency and ultimate oil recovery for miscible-displacement simulations.
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Sapkas, George S., Andreas F. Mavrogenis, and Panayiotis J. Papagelopoulos. "Transverse sacral fractures with anterior displacement." European Spine Journal 17, no. 3 (2007): 342–47. http://dx.doi.org/10.1007/s00586-007-0528-2.
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Gupta, Rajani Rani. "Reflection of waves in micropolar transversely isotropic thermoelastic half space of GN type II and III." Journal of the Mechanical Behavior of Materials 23, no. 1-2 (2014): 27–35. http://dx.doi.org/10.1515/jmbm-2014-0004.
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AbstractThe present paper deals with the reflection of waves incident at the surface of a transversely isotropic micropolar medium under the theory of thermoelasticity of GN types II and III. The wave equations are solved by imposing proper conditions on the components of displacement, stresses, and temperature distribution. It is found that there exist four different waves, viz. quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement (qTD) wave, quasi-transverse microrotational (qTM) wave, and quasi-thermal (qT) wave. The amplitude ratios of these reflected waves are presented, when different waves are incident. Numerically simulated results have been depicted graphically for the different angles of incidence with respect to the frequency. Some special cases of interest also have been deduced from the present investigation.
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Chalak, Hanuman Devidas, Anupam Chakrabarti, Mohamad Asharaf Iqbal, and Abdul Hamid Sheikh. "Vibration of laminated sandwich beams having soft core." Journal of Vibration and Control 18, no. 10 (2011): 1422–35. http://dx.doi.org/10.1177/1077546311421947.
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Free vibration response of laminated sandwich beams having a soft core is studied by using a recently developed C0 finite element beam model. The model has been developed based on higher order zigzag theory where the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. Numerical examples on free vibration covering different features of laminated composite and sandwich beams are presented. Many new results are also presented which should be useful for future research.
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Chen, Ruijun, and Daniel F. Baldwin. "Displacement Theory for Fixturing Design of Thin Flexible Circuit Board Assembly." Journal of Electronic Packaging 123, no. 4 (2000): 388–93. http://dx.doi.org/10.1115/1.1371926.
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The compliant nature of flexible substrates subject to assembly forces can result in severe misregistration of the component leads and substrate bond pads, leading to assembly process defects. Specially dedicated tooling for fixturing thin flexible substrates in standard surface mount assembly equipment is gaining importance. This paper focuses on developing a theoretical foundation for implementing Smart Tooling of fixturing thin flexible substrates. The primary goals are to determine the impact of fixturing tooling on assembly process quality, to develop a displacement theory to predict transverse displacements, and to analyze the optimum perimeter fixturing configuration. The predictive capabilities of the transverse displacement model are verified.
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Mama, Benjamin Okwudili, Onyedikachi Aloysius Oguaghamba, and Charles IKE. "Deriving Ritz formulation for the Static Flexural Solutions of Sinusoidal Shear Deformable Beams." Journal of Civil Engineering Frontiers 5, no. 02 (2024): 49–54. http://dx.doi.org/10.38094/jocef50284.
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This paper presents the Ritz variational method for the static bending analysis of sinusoidal shear deformable beams. The theory accounts for transverse shear deformation and satisfies transverse shear stress-free conditions at the top and bottom surfaces of the beam. The total potential energy functional for the thick beam bending problem is formulated and minimized using a Ritz procedure. The problem considered simply supported boundary conditions and two cases of loading – uniformly distributed load over the span and point load at the center. The function is a function of two unknown displacement functions constructed in terms of unknown generalized displacement parameters and shape functions that satisfy the boundary conditions. Ritz minimization of the functional is used to find the generalized displacement parameters and then the displacements w(x) and The displacements and stresses are found for the loading distributions considered. It is found that the results obtained agree remarkably well with the exact results obtained using the theory of elasticity. The differences between the present results and the exact solutions are less than 0.3% for maximum transverse displacement for both cases of loading considered. For uniform load over the beam, the result for l/t = 10 is 0.112% greater than the exact solution. For the point load at the center, the result for l/t = 10 is 4.468% greater than the exact solution. The increased difference in the point load case is due to the singular nature of the point load problem.
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Huang, Hui Rong, Ji Ping Hao, Hai Xia Zhang, and Yi Huang. "Displacement Governing Equations of Moderately Thick Cylindrical Shallow Shells by Transverse Shearing Deformation and the General Solution." Advanced Materials Research 291-294 (July 2011): 2066–70. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.2066.
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Displacement fundamental equations of the moderately thick cylindrical shallow shells concerning five independent variables, i.e. five middle surface displacements are established based on the displacement fundamental equations of the moderately thick shells by transverse shearing deformation and basic hypothesis on shallow shells. Three assistant displacement functions are introduced to solve the equations, which are tenth-order differential equations with variable coefficient; and then five second-order differential equations are converted into a second-order differential equation and two fourth-order transition differential equations using the Cauchy-Riemann condition, afterwards another assistant displacement function is introduced to build its decoupled governing differential equations, finally five displacement components through four assistant displacement functions are obtained.
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Carrera, E. "Transverse Normal Stress Effects in Multilayered Plates." Journal of Applied Mechanics 66, no. 4 (1999): 1004–12. http://dx.doi.org/10.1115/1.2791769.
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An evaluation of transverse normal stress σzz effects in multilayered plate modeling is given in this paper. Mixed theories with continuous interlaminar transverse shear and normal stresses have been formulated on the basis of Reissner's theorem (Reissner, 1984). The case in which the number of the displacement variables preserves independence by the number of constitutive layers, N1, has been investigated. Classical models based on standard displacement formulations have been discussed for comparison purposes. The analysis of transverse stress effects has been conducted by allowing a constant, linear, and higher-order distribution of the transverse displacement components in the plate thickness directions. Related two-dimensional models are compared for the static response of symmetrically and unsymmetrically layered, simply supported plates made of isotropic as well as orthotropic layers. The conducted numerical investigation and comparison with available results have above all led to the following conclusions. The possibility of including σzz makes the used mixed theories more attractive that other available modelings. σzz plays a fundamental role in thick laminate plates analysis. Such a role increases in transversely anisotropic multilayered plate analysis. With an increase of the plate thickness, a very accurate description of σzz requires modelings whose number of independent variables depends on N1.
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King, W. W. "Displacement-Limited Buckling of an Optical Fiber." Journal of Electronic Packaging 115, no. 1 (1993): 39–43. http://dx.doi.org/10.1115/1.2909300.
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Buckling of an optical fiber within a confining connector housing is analyzed under the restriction that the transverse deflection profile be shallow. Fibers with pinned ends and with clamped ends are treated. The three stages of buckling are discussed: sufficiently small transverse displacements that contact is not made with the housing wall; point contact with the wall; and finite-length contact with the wall. Explicit expressions for responses as functions of relative longitudinal displacement of ends are obtained for the first and third stages. For the second stage, longitudinal displacement and maximum fiber curvature are expressed in terms of buckling load. Except for a portion of the point-contact stage, contact with a confining wall causes more severe stresses in the fiber than would otherwise be the case.
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Yang, Qihao, and Shuping Liu. "Strength Optimisation and Static Performance Analysis of Arch Ribs of Steel-tube Concrete Arch Bridge." Academic Journal of Science and Technology 11, no. 2 (2024): 90–95. http://dx.doi.org/10.54097/dpbtz946.
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By means of finite element simulation, the axial compressive stiffness of different steel-tube concrete short columns was imported into the finite element model, and the effects of adopting new steel-tube concrete arch ribs on the mechanical properties of the key components of steel-tube concrete arch bridges, such as internal forces and displacements, were analyzed. The results show that: with the increase of the axial compressive stiffness of the arch rib chord, under different load combinations, the vertical displacement of the arch rib chord will increase, and the structure will be lifted up, with a maximum of 31.85%; the vertical displacement of the deck slab will also increase, with a maximum increase of 6.8%, which is smaller than the vertical displacement of the arch rib chord; the absolute value of the downward and transverse displacements of the arch rib chord will be reduced, with a maximum reduction of 7.1% respectively. The absolute values of the transverse and crossover displacements of the arch rib chord tube will be reduced, with the maximum reduction of 7.1% and 6.8%, respectively. In the project of arch bridge, the deflection and deformation of the arch rib, deck plate and other components of the more stringent restrictions, especially the vertical displacement, it is recommended to use the higher axial compressive stiffness of the steel pipe concrete arch rib.
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Muhammad, Ibrahim Dauda, and Mokhtar Awang. "Modeling the Bending Behavior of Single-Walled Cubic Zirconia Nanotubes." Journal of Nano Research 38 (January 2016): 88–95. http://dx.doi.org/10.4028/www.scientific.net/jnanor.38.88.
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The bending behavior of single-walled cubic zirconia nanotubes (CZNTs) is studied in this paper based on a three-dimensional finite element analysis with molecular bonds modeled as structural beam elements and positioned at the joints of beams as substitute of atoms. In order to simulate the bending effect of CZNTs, the free-end is exposed to varying transverse displacements and the maximum force along the cross section at the fixed end is recorded to estimate the bending elastic modulus. The result obtained indicates that the bending elastic modulus of CZNTs depends on chirality and magnitude of applied transverse displacement. The simulated bending modulus of CZNTs fluctuates with the optimum value obtained from the zigzag configuration when 0.5 – 1.0 nm transverse displacement was applied. The results follows similar trend with what was obtained in other studies for carbon nanotubes but at comparatively lesser magnitude.
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Cho, J. Y., and S. N. Atluri. "Analysis of shear flexible beams, using the meshless local Petrov‐Galerkin method, based on a locking‐free formulation." Engineering Computations 18, no. 1/2 (2001): 215–40. http://dx.doi.org/10.1108/02644400110365888.
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The problems of shear flexible beams are analyzed by the MLPG method based on a locking‐free weak formulation. In order for the weak formulation to be locking‐free, the numerical characteristics of the variational functional for a shear flexible beam, in the thin beam limit, are discussed. Based on these discussions a locking‐free local symmetric weak form is derived by changing the set of two dependent variables in governing equations from that of transverse displacement and total rotation to the set of transverse displacement and transverse shear strain. For the interpolation of the chosen set of dependent variables (i.e. transverse displacement and transverse shear strain) in the locking‐free local symmetric weak form, the recently proposed generalized moving least squares (GMLS) interpolation scheme is utilized, in order to introduce the derivative of the transverse displacement as an additional nodal degree of freedom, independent of the nodal transverse displacement. Through numerical examples, convergence tests are performed. To identify the locking‐free nature of the proposed method, problems of shear flexible beams in the thick beam limit and in the thin beam limit are analyzed, and the numerical results are compared with analytical solutions. The potential of using the truly meshless local Petrov‐Galerkin (MLPG) method is established as a new paradigm in totally locking‐free computational analyses of shear flexible plates and shells.
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Shen, C., and P. Fraundorf. "Lateral displacement microscopy of holograms using scanned tip image pairs." Proceedings, annual meeting, Electron Microscopy Society of America 51 (August 1, 1993): 534–35. http://dx.doi.org/10.1017/s0424820100148502.
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Tip displacements associated with lateral forces between specimen and tip can be quite large (e.g. microns in size) during repulsive force microscopy (SFM or AFM) and air-based scanning tunneling microscopy (STM) of soft samples. Both x and y components of the lateral tip displacement due specifically to drag between the specimen and tip, as separated from tfiose components of the tip's displacement due solely to the geometry of mechanical equilibrium between the tip and a tilted surface, may be inferred from STM or SFM image pairs of the same region taken with the tip traveling in different directions (e.g. with the tip fast scan going left versus up). We refer to this process of inferring displacement from image pairs as displacement mapping. By comparison, absolute measurements of lateral force like those obtained by imaging cantilever twists in Digital Instrument's commercial lateral force microscope: (a) don't remove equilibrium (purely geometric) components of the lateral displacement from the often more interesting friction components, (b) measure the lateral force in only one of the two transverse directions, and (c) require special hardware, not available on conventional STM's for example, to measure transverse deflection.
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Adepoju, Olaoluwa O., Larry W. Lake, and Russell T. Johns. "Anisotropic Dispersion and Upscaling for Miscible Displacement." SPE Journal 20, no. 03 (2015): 421–32. http://dx.doi.org/10.2118/166390-pa.
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Summary Dispersion is the irreversible mixing that occurs during miscible displacements. Dispersion can reduce local displacement efficiency by lessening solvent peak concentration or increase volumetric sweep efficiency by spreading of the injected solvent to more of the reservoir. Dispersion is therefore an important parameter in predicting and simulating miscible displacements. The difficulty of simulating miscible displacement and understanding the effect of dispersion is also compounded by numerical dispersion, which increases the apparent dispersion in finite-difference simulation models. This paper presents an approach to estimate the total longitudinal and transverse dispersion in large-scale media by use of continuous solvent injection in a medium of finite thickness. The simulations are based on the experimental arrangement of Blackwell (1962) to estimate transverse dispersion, with experiments consisting of coinjecting two miscible fluids into different sections of the medium at similar rates. This model arrangement, coupled with analytical solutions for the 2D convection/dispersion equation for a continuously injected solvent, allows us to determine longitudinal and transverse dispersivity simultaneously for the flow medium. In this manner, we investigate the effects of stochastic permeability distributions and other scaling groups affecting first-contact-miscible simulations on dispersion. Sensitivity analysis of dispersion in stochastic permeability fields confirms that both longitudinal and transverse dispersion are scale dependent. Results also show that the effect of increasing autocorrelation of cell permeability in the longitudinal direction (parallel to flow) is to increase longitudinal dispersion, as solvent travels through more continuous layers, while reducing transverse dispersion. Increasing autocorrelation in the transverse direction reduces dispersion in both directions. This reduction is caused by equilibration of solvent concentrations in continuous sections of the reservoir, resulting in reduced solute fingering and channeling. Finally, we developed a simple procedure to use the estimated dispersivities to determine a priori the maximum gridblock size that will maintain an equivalent level of dispersion between fine-scale models and upscaled coarse models. Large gridblock sizes can be used for highly heterogeneous and layered reservoir models. Nonuniform coarsening (upscaling) methods were also recommended and validated for reservoir models with sets of sequential but different permeability distributions. The procedure was extended to multicontact miscible simulations. The sweep and recovery from upscaled multicontact miscible simulations were comparable with those of fine-scale models.
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Wu, Ganggang, Xingming Xiao, Chi Ma, and Yuqiang Jiang. "Vision-based transverse vibration displacement measurement of hoisting vertical ropes in mine hoists." Advances in Mechanical Engineering 13, no. 7 (2021): 168781402110330. http://dx.doi.org/10.1177/16878140211033088.
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At present, there is no appropriate way to measure the transverse vibration response of moving hoisting vertical rope in hoist. Therefore, a vision-based measurement method combining the digital image correlation (DIC) and digital image processing (DIP) algorithms is proposed in this paper. In this method, a reference line perpendicular to the vertical ropes is added in image sequence by DIP algorithm to form some virtual cross targets, which makes the improved DIC algorithm with adaptive template updating (ATU) rule can track the moving hoisting vertical rope without any labels. Then for distinguishing all ropes in the measuring area, a displacement threshold is set to locate the current measured rope and exclude the other ropes. The transverse vibration displacements of the hoisting vertical rope in an actual mine hoist was measured in three background situations, verifying the feasibility of the proposed method. Moreover, in a laboratory artificial vibration test, the measurement results from the proposed vision method and a laser displacement sensor yielded a very good agreement. The two experimental results indicate that it is fairly reasonable and effective to measure the transverse vibration displacements of hoisting vertical ropes.
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KIKUCHI, FUMIO, KEIZO ISHII, and HIDEYUKI TAKAHASHI. "REISSNER-MINDLIN EXTENSIONS OF KIRCHHOFF ELEMENTS FOR PLATE BENDING." International Journal of Computational Methods 02, no. 01 (2005): 127–47. http://dx.doi.org/10.1142/s0219876205000363.
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A method of extending various existing Kirchhoff elements to Reissner-Mindlin elements for plate bending is developed and tested. The essential idea is to use independent transverse shear strains and a special mixed formulation. The Nedelec edge element is effective for assuming the shear strains. Furthermore, the displacements are carefully constructed so that the strain-displacement relations are strictly satisfied for the transverse shear strains. We present our approach for displacement-based three-node triangular elements including both conforming and non-conforming ones as the base Kirchhoff elements. It is also possible to reduce the shear variables from the element degrees of freedom by means of a special technique called the beam element approximation. Numerical results are obtained for some fundamental test problems and are generally reasonable over wide range of plate thickness. In particular, it is observed that the tested elements actually reduce to the base Kirchhoff element in the thin plate range and are free from transverse shear locking.
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Xu, Xin Xin, Sheng Jie Jiao, Jian Lian Cheng, and Jin Ping Li. "Study and Test of Coupled Axial and Transverse Vibrations on Drillpipe for Rotary Drilling Rig." Applied Mechanics and Materials 472 (January 2014): 73–78. http://dx.doi.org/10.4028/www.scientific.net/amm.472.73.
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In order to more accurately predict the vibration characteristics of drillpipe for rotary drilling rig, dynamic model of coupled axial and transverse vibrations was established based on Hamilton variation principle and finite element theory after discussing the vibration mechanism of drillpipe. The Newmark-β method was adopted to solve the dynamic equation and the simulated vibration responses of drillpipe were calculated. The results show that the axial models yield harmonic motion. The axial displacement is quite small and the maximum amplitude of the first section is about 6×10-4 m. The transverse displacement is much larger than the axial displacement and the maximum transverse amplitude of the first section is about 0.03 m. The drillpipe of the first section of rotary drilling rig was tested. Comparing simulation results and test results, trends of the responses of axial displacement and transverse displacement have a good agreement and the simulation model is verified by the experiment.
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Monastyrskyi, Vitalii, Serhii Monastyrskyi, Denis Nomerovskyi, and Borys Mostovyi. "Belt conveyor failure simulation at the design stage with transverse displacements of the belt." E3S Web of Conferences 168 (2020): 00056. http://dx.doi.org/10.1051/e3sconf/202016800056.
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To find possible conveyor failures at the design stage means to determine a transverse belt displacement and compare the obtained data with the permissible ones. The dynamic problem of the belt movement on the conveyor has been defined. Resistance and external forces, limits of the belt displacement have been determined. The transverse belt displacement can be described by partial differential equations. To solve the problem, the Fourier transform has been used. Change patterns in the transverse belt conveyor displacement dependent on conveyor’s parameters, type of load, and skewing of the idlers along the conveyor have been obtained. The results agree with experimental data. The method of adaptive control of the transverse belt displacement has been described. The essence of this method is to adapt the model of the moving belt in the conveying trough to changed conditions and to reveal the uncertainty of the control with the known parameters of the mathematical model.
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Belkaid, Khmissi, Nadir Boutasseta, Hamza Aouaichia, Djamel Eddine Gaagaia, Adel Deliou, and Badreddine Boubir. "A Simple and Efficient eight node Finite Element for Multilayer Sandwich Composite Plates Bending Behavior Analysis." Frattura ed Integrità Strutturale 16, no. 61 (2022): 372–93. http://dx.doi.org/10.3221/igf-esis.61.25.
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In this paper, a C0 simple and efficient isoparametric eight-node displacement-model based on higher order shear deformation theory is proposed for the bending behavior study of multilayer composites sandwich plates. Difficult C1-continuity requirement is overcome by extracting the seven degrees of freedom from strain relations for each element node: two displacements for in-plane behavior and five bending unknowns namely: a transverse displacement, two rotations and two shear angles, which results in a kinematic approximation formulation having only first order derivative requirement. The governing equations of the element (constitutive, virtual work and equilibrium equations) are implemented for the prediction of approximate solutions of deflections and stresses of sandwich plates linear elastic problems. Thereby, the formulation element is able to present a cubic in-plane displacement along both core and faces sandwich thickness, as well as, the shear stresses are found to vary as quadratic field without requiring shear correction factors and independent from any transverse shear locking problems. The accuracy and validity of the proposed formulation is verified through the numerical evaluation of displacements and stresses and their comparison with the available analytical 3D elasticity solutions and other published finite element results.
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Garg, Piyush, Roya Nasimi, Ali Ozdagli, et al. "Measuring Transverse Displacements Using Unmanned Aerial Systems Laser Doppler Vibrometer (UAS-LDV): Development and Field Validation." Sensors 20, no. 21 (2020): 6051. http://dx.doi.org/10.3390/s20216051.
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Measurement of bridge displacements is important for ensuring the safe operation of railway bridges. Traditionally, contact sensors such as Linear Variable Displacement Transducers (LVDT) and accelerometers have been used to measure the displacement of the railway bridges. However, these sensors need significant effort in installation and maintenance. Therefore, railroad management agencies are interested in new means to measure bridge displacements. This research focuses on mounting Laser Doppler Vibrometer (LDV) on an Unmanned Aerial System (UAS) to enable contact-free transverse dynamic displacement of railroad bridges. Researchers conducted three field tests by flying the Unmanned Aerial Systems Laser Doppler Vibrometer (UAS-LDV) 1.5 m away from the ground and measured the displacement of a moving target at various distances. The accuracy of the UAS-LDV measurements was compared to the Linear Variable Differential Transducer (LVDT) measurements. The results of the three field tests showed that the proposed system could measure non-contact, reference-free dynamic displacement with an average peak and root mean square (RMS) error for the three experiments of 10% and 8% compared to LVDT, respectively. Such errors are acceptable for field measurements in railroads, as the interest prior to bridge monitoring implementation of a new approach is to demonstrate similar success for different flights, as reported in the three results. This study also identified barriers for industrial adoption of this technology and proposed operational development practices for both technical and cost-effective implementation.
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Kuo, Y. L., W. L. Cleghorn, and K. Behdinan. "STRESS-BASED FINITE ELEMENT METHOD FOR EULER-BERNOULLI BEAMS." Transactions of the Canadian Society for Mechanical Engineering 30, no. 1 (2006): 1–6. http://dx.doi.org/10.1139/tcsme-2006-0001.
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This paper presents a new technique, which can apply the stress-based finite element method to Euler-Bernoulli beams. An approximated bending stress distribution is selected, and then the approximated transverse displacement is determined by twice integration. Due to the satisfaction of compatibility, the integration constants are determined by the boundary conditions related to transverse displacement and rotation. To compare with the displacement-based finite element method, this technique provides the continuities of not only transverse displacement and rotation but also stress at nodes. Besides, the boundary conditions related to stress are satisfied. Two numerical examples demonstrate the validity of this technique. The results show that the errors are smaller than those generated by the displacement-based finite element method for the same number of degrees of freedom.
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Pakhale, Rushikesh V., Bhausaheb R. Sontakke, Gajendra R. Gandhe, and Durgesh H. Tupe. "Mathematical Analysis of Transverse Displacement of Laminated Beam with Thermal Load." Indian Journal Of Science And Technology 15, no. 31 (2022): 1523–26. http://dx.doi.org/10.17485/ijst/v15i31.1105.
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Lee, J. "Comparison of the Two Formulations of w-u-v and w-F in Nonlinear Plate Analysis." Journal of Applied Mechanics 69, no. 4 (2002): 547–52. http://dx.doi.org/10.1115/1.1458556.
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In a moderately large deflection plate theory of von Karman and Chu-Herrmann, one may consider thin-plate equations of either the transverse and in-plane displacements, w-u-v formulation, or the transverse displacement and Airy function, w-F formulation. Under the Galerkin procedure, we examine if the modal equations of two plate formulations preserve the Hamiltonian property which demands energy conservation in the conservative limit of no damping and forcing. In the w-F formulation, we have shown that modal equations are Hamiltonian for the first four symmetric modes of a simply-supported plate. In contrast, the corresponding modal equations of w-u-v formulation do not exhibit the Hamiltonian property when a finite number of sine terms are included in the in-plane displacement expansions.
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KHANDELWAL, RAVI PRAKASH, ANUPAM CHAKRABARTI, and PRADEEP BHARGAVA. "VIBRATION AND BUCKLING ANALYSIS OF LAMINATED SANDWICH PLATE HAVING SOFT CORE." International Journal of Structural Stability and Dynamics 13, no. 08 (2013): 1350034. http://dx.doi.org/10.1142/s021945541350034x.
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Free vibration and buckling of laminated sandwich plate having soft core is studied by using an efficient C0 continuous finite element (FE) model based on higher-order zigzag theory (HOZT). In this theory, the in-plane displacement field for both the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly varying displacement field with a different slope in each layer. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the plate. The nodal field variables are chosen in an efficient manner to overcome the problem of C1 continuity requirement of the transverse displacement. Numerical examples on free vibration and buckling covering different geometric and material features of laminated composite and sandwich plates are presented. Many new results are also presented which should be useful for future research.
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Pandit, M. K., A. H. Sheikh, and B. N. Singh. "Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 8 (2008): 1443–52. http://dx.doi.org/10.1243/09544062jmes985.
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This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.
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Nguyen, Trung-Kien, and Ngoc-Duong Nguyen. "Effects of transverse normal strain on bending of laminated composite beams." Vietnam Journal of Mechanics 40, no. 3 (2018): 217–32. http://dx.doi.org/10.15625/0866-7136/10959.
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Effect of transverse normal strain on bending of laminated composite beams is proposed in this paper. A Quasi-3D beam theory which accounts for a higher-order variation of both axial and transverse displacements is used to consider the effects of both transverse shear and normal strains on bending behaviours of laminated composite beams. Ritz method is used to solve characteristic equations in which trigonometric shape functions are proposed. Numerical results for different boundary conditions are presented to compare with those from earlier works, and to investigate the effects of thickness stretching, fibre angles, span-to-height ratio and material anisotropy on the displacement and stresses of laminated composite beams.
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Liu, Can, Zhi Ping Zeng, Bin Wu, Jia Yu Yuan, and Xian Feng He. "Experimental Study on the Transverse Stiffness of WJ-8 Rail Fastening." Applied Mechanics and Materials 596 (July 2014): 3–6. http://dx.doi.org/10.4028/www.scientific.net/amm.596.3.
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The study of WJ-8 rail fastening is about the relationship between lateral horizontal force and rail’s lateral displacement, and the rail fastening’s transverse stiffness was obtained since the rail slipped. The rail lateral displacement was measured by using the loading device of rail’s lateral horizontal force which was changed as needed. Moreover, when the lateral horizontal force changes, it was analyzed that how it affected rail’s lateral displacement and rail fastening’s transverse stiffness under different bolt torque conditions. Therefore, the recommended value of transverse stiffness is acquired which is based on analyzing the test results.
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Bhaskar, K., and T. K. Varadan. "Reissner’s New Mixed Variational Principle Applied to Laminated Cylindrical Shells." Journal of Pressure Vessel Technology 114, no. 1 (1992): 115–19. http://dx.doi.org/10.1115/1.2929001.
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Reissner’s new mixed variational theorem, which allows independent interpolation, through the thickness, of the three transverse stresses besides that of the three displacements, is applied here to derive a higher-order theory of laminated orthotropic cylindrical shells. The accuracy of the theory is verified by comparison with three-dimensional elasticity solutions. It is shown that Reissner’s principle does not directly lead to accurate transverse shear stress predictions, but requires the use of the equilibrium equations of three-dimensional elasticity as is common in the conventional displacement approach.
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Xiaoyu, Jiang. "3-D Vibration Analysis of Fiber Reinforced Composite Laminated Cylindrical Shells." Journal of Vibration and Acoustics 119, no. 1 (1997): 46–51. http://dx.doi.org/10.1115/1.2889686.
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In this paper, 3-D solutions of free vibrations are presented for isotropic and composite laminated cylindrical shells. The perturbation method and a variational principle are used to obtain the solutions which satisfy the 3-D differential equations of motion, the strain-displacement relations, the stress-strain relations, the boundary conditions and the continuity conditions at layer interfaces. The distributions of displacements and stresses in the shells are shown in figures. The free vibration frequencies are listed in tables. In the thickness direction of the shells, continuous displacements and stresses are obtained. And the importance of transverse shear stresses and transverse normal stress is analyzed.
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Luo, Zhanyou, Kuangqin Xie, Baoping Zou, Mingyao Jiang, and Wei Zheng. "Structural Dynamic Response of a Shield Tunnel under Aircraft Taxiing Load." Shock and Vibration 2021 (September 24, 2021): 1–9. http://dx.doi.org/10.1155/2021/3999948.
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Dynamic load is an important factor affecting the safety and stability of subway tunnel structures. To obtain the variation law of shield tunnel structure dynamic response under aircraft taxiing load, a three-dimensional numerical simulation of such tunnel under the action of aircraft taxiing load is performed on the basis of a project involving a shield tunnel orthogonal underpass taxiway. The effects of sliding speed and tunnel depth on the structure of the shield tunnel are also analyzed. The results show that the transverse displacement and acceleration response of tunnel segment exhibit evident time-space effect under the action of aircraft taxiing load. The transverse displacement and arch waist acceleration of the shield segment increase first and then decrease. The transverse displacement of the arch waist reaches its maximum when the aircraft taxis directly above the tunnel. The sliding speed exhibits an evident influence on the dynamic response of shield tunnel structure. The vertical and convergence displacements of tunnel segments increase with the increase in sliding speed. The dynamic response of tunnel structure is significantly affected by the factors of tunnel buried depth. The vertical and convergence displacements of tunnel segments decrease with the increase in tunnel buried depth. Therefore, the safety of the shield tunnel structure can be ensured by controlling the taxiing speed when the aircraft taxis directly above the tunnel. The measures of increasing the buried depth of the tunnel or strengthening the tunnel structure need to be considered when the taxiing speed is large.
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Tian, Longgang, and Ziling Cheng. "A Triangular Plate Bending Element Based on Discrete Kirchhoff Theory with Simple Explicit Expression." Mathematics 9, no. 11 (2021): 1181. http://dx.doi.org/10.3390/math9111181.
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A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular element, using the compatible trial function for the transverse displacement along the element sides, the construction of the present SDKT element is based on a specially designed trial function for the transverse displacement over the element, which satisfies interpolation conditions for the transverse displacements and the rotations at the three corner nodes. Numerical investigations of thin plate structures were conducted, using the proposed SDKT element. The results were compared with those by other prevalent plate elements, including the analytical solutions. It was shown that the present element has the simplest explicit expression of the nine-DOF (Degree of Freedom) triangular plate bending elements currently available that can pass the patch test. The numerical examples indicate that the present element has a good convergence rate and possesses high precision.
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Espinosa, H. D., M. Mello, and Y. Xu. "A Variable Sensitivity Displacement Interferometer With Application to Wave Propagation Experiments." Journal of Applied Mechanics 64, no. 1 (1997): 123–31. http://dx.doi.org/10.1115/1.2787262.
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The present paper introduces a variable sensitivity displacement interferometer (VSDI) used to monitor both normal and in-plane particle displacements in wave propagation experiments. The general system consists of two interferometers working in tandem. Normally reflected light is interfered with each of two symmetrically diffracted light beams generated by the specimen rear surface. In cases where the surface motion simultaneously exhibits both in-plane and normal displacements, the fringes represent a linear combination of the longitudinal and transverse components of motion. Decoupling of the normal and in-plane displacement histories may be achieved through a linear combination of the two VSDI records. Alternatively, it is always possible to decouple the components of motion by combining a VSDI record with an independent measurement of either component. Moreover, it is shown that in the case of pure normal motion, the VSDI system functions as a desensitized normal displacement interferometer (DNDI). Similarly, in situations involving purely in-plane motion, the VSDI is shown to function as a desensitized transverse displacement interferometer (DTDI). The DNDI and DTDI fringe sensitivities are in general shown to depend on the angle θ or equivalently, the frequency σ of a grating manufactured at the observation point and the order n of the diffracted beams. The variable sensitivity feature of the VSDI greatly desensitizes normal displacement measurements and is particularly well suited for wave propagation studies in which normal particle velocities in excess of 100 m/s are generated. Experimental results are presented which demonstrate the application of this technique to monitoring particle motion histories in plate impact recovery experiments.
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Wu, Ganggang, Xingming Xiao, Jiannan Yao, and Chunyang Song. "Machine vision–based measurement approach for transverse vibrations of moving hoisting vertical ropes in mine hoists using edge location." Measurement and Control 52, no. 5-6 (2019): 554–66. http://dx.doi.org/10.1177/0020294019842604.
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Hoisting vertical rope is a continuum of one-dimensional movement during operation of hoist, and there are no appropriate ways to measure its vibration displacement at present. In this paper, a non-contact and unmarked machine vision measurement method is proposed for measuring the transverse vibration displacement of hoisting vertical ropes. First, we construct the background image to extract the ropes by the background difference method. Subsequently, a novel row-column data statistics filtering algorithm is proposed and applied to the edge detection image for removing the edges of the unmeasured rope. Finally, Hough transformation is used to locate the two edge lines at the boundary of rope and obtain the line parameters, which can be used to calculate the vibration displacement of the measured points at different times. The transverse vibration displacement of a moving hoisting vertical rope in a mine hoist was measured by using the reported machine vision measurement method, verifying the feasibility of the method. In order to verify the validity of the method, a simulation experimental system was built. The proposed method and the laser displacement sensor were used to measure the artificial transverse vibration displacement of a vertical rope simultaneously. The two results are in good consistency, which indicates that the proposed method can be fairly reasonable and accurate to measure the transverse vibration displacement of vertical rope in mine hoists.
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Feng, Zhongju, Yunhui Guan, Suizhu Guo, et al. "Effect of spalling thickness on transverse axial bearing capacity of pile foundation under different corrosion depths." E3S Web of Conferences 198 (2020): 02019. http://dx.doi.org/10.1051/e3sconf/202019802019.
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The transverse and axial bearing characteristics of bridge pile foundation in salt marsh area are studied by numerical simulation. This paper mainly analyses the change of transverse and axial bearing characteristics of pile foundation caused by the change of spalling thickness of bridge foundation. The results show that the transverse and axial bearing capacity and displacement of pile foundation will be affected by the change of concrete spalling thickness under the condition of pile corrosion. When the peeling thickness is above 9.0cm, the transverse and axial bearing characteristics of pile foundation are obviously different with the change of corrosion depth of pile body. When the peeling thickness increases and the corrosion depth of the pile body is different, the negative displacement below the zero point of the first displacement of the pile body is continuously reduced, and the displacement curve above the first displacement zero point in the direction of the pile body begins to shift. When the peeling thickness reaches 15.0cm, the pile top displacement increases to 3.75mm. The research results are of great significance to the establishment of safety evaluation system of highway bridge pile foundation in alpine salt marsh area, and provide a basis for the structural design of highway bridge pile foundation in alpine salt marsh area.
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Shangguan, Wen-Bin, Xiao Feng, Haoting Lin, and Jiawei Yang. "A calculation method for natural frequencies and transverse vibration of a belt span in accessory drive systems." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 10 (2013): 2268–79. http://dx.doi.org/10.1177/0954406212474152.
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A method for modeling and calculation of natural frequencies of a belt span and transverse vibration displacement of a point in the belt span for an accessory drive system is presented in this article. In the model, the belt between two adjacent pulleys is simplified as an axial moving visco-elastic string, and the relation between stress and strain for the belt is modeled with standard visco-elastic constitutive model. The calculated natural frequencies from the axial moving string model are compared with estimated results from the pulley–string belt coupled model. It is shown that the natural frequencies can be obtained directly from axial moving string model. An experiment is carried out for getting the natural frequencies of a belt span and the transverse displacement of a point in a belt span in a generic engine front end accessory drive system. The measured natural frequencies and transverse displacements are compared well with calculated results, which validate the modeling and calculation methods presented in this article. Based on the axial moving visco-elastic string model, the influences of elastic stiffness and damping of a belt on the transverse deflections of a point in one belt span are investigated. It is shown that the transverse deflections of the belt decrease with the increasing of the elastic stiffness and damping of belt.
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Chen, Chong, Xing Fei Yuan, and Ruo Jun Qian. "Spatial Fine Beam Model Based on Vector Form Intrinsic Finite Element Analysis." Applied Mechanics and Materials 638-640 (September 2014): 238–43. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.238.
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Different from the Euler beam and Timoshenko beam, the spatial fine beam model considers some effects such as shear displacement, the additional axial displacement produced by lateral bending and the additional transverse displacement induced by reduced stiffness due to transverse shear deformation. In this paper the internal force formula of the spatial fine beam model, applying to Vector Form Intrinsic Finite Element (VFIFE) analysis, are derived and corresponding programs are developed. A spatial cantilever beam and a space frame are analyzed and the load-displacement curves are compared using different beam element models. The results show that when the depth-span ratio is relatively small, the load-displacement curves nearly have no difference. When the depth-span ratio becomes larger, the yield load gotten by the fine beam model is significantly smaller than that obtained by the Euler beam and Timoshenko beam. Therefore, when the deep beam is analyzed, the shear displacement, the additional axial displacement and the additional transverse displacement caused by stiffness reduction can’t be ignored. The spatial fine beam model proposed in this paper has good accuracy in the analysis of deep beam.
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Nwoji, C. U., D. G. Ani, O. A. Oguaghamba, and V. T. Ibeabuchi. "Static Bending of Isotropic Circular Cylindrical Shells Based on the Higher Order Shear Deformation Theory of Reddy and Liu." International Journal of Applied Mechanics and Engineering 26, no. 3 (2021): 141–62. http://dx.doi.org/10.2478/ijame-2021-0041.
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Abstract In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analysis for the displacements and stresses are presented for the simply supported shell. A comparison made to those of the Kirchhoff-Love theory for varying shell length to mean – radius of curvature ratios, shows good agreement for thin shells irrespective of the shell length to radius of curvature ratio (l / a). The transverse sharing effect is found to be noticeable in the deformation of thick shells, however, this effect diminishes with a continuous increase in l / a ratios.
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Yang, Bo, Xin Zhang, and Han Yu Yu. "Elasticity Solutions for Annular Plates of Functionally Graded Materials Subjected to a Uniform Load." Advanced Materials Research 261-263 (May 2011): 853–57. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.853.
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England (2006) proposed a novel theory to study the bending problem of isotropic functionally graded plates subjected to transverse biharmonic loads. His theory is extended here to functionally graded plates of transversely isotropic materials. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of the displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solutions may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory(CPT). The elasticity solutions of an FGM annular plate under a uniform load are derived. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity and radius-to-radius ratio on the plate deflection and stresses are studied numerically.
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Chen, Hong Kai, Ting Hu, Xiao Ying He, and Rong Can Liu. "Numerical Analysis of Concrete Arch Bridge on the Situation of Seismic Damage." Advanced Materials Research 446-449 (January 2012): 2783–90. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.2783.
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Based on the example, red-Flag Bridge in Chongzhou City, using the finite element to analyze the response spectrum of seismic performance for the concrete arch bridge under two conditions. Through the numerical analysis of vibrational damage on the whole bridge, reveals the nether structure and elements of bridge is affected by the seismic waves under the seismic effect and the great stiffness in upper structure, and posts that the anti-inertia in longitudinal direction is more powerful than the transverse and vertical ones. The deformation of arch ring is mostly affected by the displacement on transverse line, DY direction, and less in the longitudinal, vertical and rotational direction. According to the analysis of spectrum value displacement on abutment, finds out that the transverse direction of abutment is mostly affected by the displacement on DZ direction, for the abutment displacement, less in the middle, big in both sides. And for the vertical one, it is mostly affected by DY displacement, in the DY displacement of abutment, big in top, less in base.