Transverse Deformation Research Articles

A New Design Method of Shield Tunnel Based on the Concept of Minimum Bending Moment

As the soil-resistance coefficient in a soft soil area is small, overlarge bending moment may cause exceeding transverse deformation for the shield tunnel and cause structural diseases and waterproof failure at the longitudinal segment joints. Hence, a new idea of cross-section design for a minimum bending moment shield tunnel was proposed. This article has first put forward the concept of a zero bending moment shield tunnel. Then, based on rational and feasible hypotheses, a structural mechanical model and an analytical expression of axis for the cross-section of the zero bending moment shield tunnel was obtained, and computational formulas of internal force and key geometry parameters were given. Based on the case of the metro shield tunnel constructed in the Shanghai soft soil area, the zero bending moment shield tunnel was designed, and its characteristics were analyzed. Considering only one cross-section of shield tunnel can be adopted in one metro line, the design method and procedure of the minimum bending moment shield tunnel were put forward. Finally, taking one of the Shanghai metro lines as an example, a cross-section of a minimum bending moment shield tunnel was designed, and its bending moment was compared with the bending moment of a circular section shield tunnel, which had the same horizontal diameter. The comparison revealed that the cross-section of the minimum bending moment can significantly reduce the bending moment of shield tunnel.

Displacement-based seismic performance assessment of multi-span steel truss bridges

Simplified mechanics-based approaches for the seismic performance analysis are used for the risk assessment of large bridge portfolios. This study evaluates the applicability and effectiveness of displacement-based assessment (DBA) and nonlinear static procedures for multi-span railway steel truss bridges. Although built in the first part of the last century, these historical bridges are currently in service within the European railway networks, and their seismic performance is poorly investigated in the literature. Direct DBA algorithms and pushover-based procedures aimed at seismic performance assessment and fragility analysis of bridges are presented and tested within a set of case studies parametrically generated by using an archetype steel truss bridge. The first part of this study focuses on the seismic analysis of steel braced towers which, in many situations, compose the substructure of steel truss multi-span bridges. A simplified pseudo-pushover and an accurate equivalent viscous damping formulation are proposed to be used for the approximate performance displacement assessment of these structural components. The second part discusses the accuracy of the investigated approaches for multi-span steel truss bridges through comparisons with nonlinear time history analysis. The results of the parametric analysis are used to propose recommendations for an appropriate DBA or pushover-based strategy for the deterministic performance assessment and fragility analysis with reference to the damage state of the supporting towers or bridge serviceability in terms of superstructure transverse deformation.

Study on modeling and dynamic performance of a planar flexible parallel manipulator based on finite element method.

The application of a high-speed parallel manipulator necessitates the adoption of a lightweight design to reduce dead weight. However, this increases the elastic deformation of certain components, affecting the dynamic performance of the system. This study examined a 2-DOF planar flexible parallel manipulator. A dynamic model of the parallel manipulator composed of fully flexible links was established using a floating reference coordinate system and a combination of the finite element and augmented Lagrange multiplier methods. A dynamic analysis of the simplified model under three driving torque modes showed that the axial deformation was less than the transverse deformation by three orders of magnitude. Further, the kinematic and dynamic performance of the redundant drive was significantly better than that of the non-redundant drive, and the vibration was well suppressed in the redundant drive mode. In addition, the comprehensive performance of driving Mode 2 was better than that of the other two modes. Finally, the validity of the dynamic model was verified by modeling via Adams. The modular modeling method is conducive to the extension to other models and programming. Furthermore, the dynamic model of the established fully flexible link system can aid in optimizing the lightweight design and dynamic performance of the parallel manipulator.

Effective Poisson’s ratio of tetrachiral mechanical metamaterial

The problem of computational determination of the effective Poisson’s ratio for a mechanical metamaterial having a tetrachiral structure is considered. The problem is solved numerically in the three-dimensional formulation based on the finite element method. The problem is that during uniaxial loading of the sample made of the considered metamaterial it is twisted. This makes it difficult to determine the transverse strain. For observation, 80 fixed points located on the ribs evenly along the length of the sample were selected. When looking at the four equidistant fixed points, it can be found that the deviations in the X-axis and Z-axes are commensurate. This indicates that the distance between the points on the straight line perpendicular to the axis of loading does not change, so there is no transverse deformation. From this, it was concluded that the value of the effective Poisson’s ratio is zero. The zero value can be explained by the fact that there are transverse elements in the structure. During longitudinal compression, the transverse edges do not twist, which could lead to a contraction in the cross-section of the rod.

Behavioral Study and Evaluation of Rubber Core Sandwich Beam Under Impact Loading

The shock resistance of structures is of current interest of academia and industry. Sandwich structures have been proposed as alternatives to conventional monolithic structures in order to enhance the shock resistance. Sandwich structures are widely used in many important fields, such as ship, aircraft, automotive and aerospace industries, packaging and construction engineering. In this study, a number of experiments were conducted to investigate the structural response of dynamically loaded on clamped (both end) 1mm thick monolithic aluminium beams and rubber core sandwich beams of 3.02 mm and 4.02 mm thicknesses impacted by a blunt nosed cylindrical projectile made of mild steel of diameter 12.8 mm, length 30.2 mm and mass 0.03018 Kg in sub ordinance velocity range (20 to 110 m/s). Sandwich structure consists of two face sheets of aluminium adhered to a low-density rubber core. The failure of composite specimens observed in the tests can be classified with respect to the front face sheet, core and back face sheet, respectively Different parameters like impact velocity, residual velocity, velocity drop, energy absorbed, kinetic energy, deflection, dimensionless external dynamic energy, and dimensionless maximum transverse permanent deformation were observed experimentally and calculated analytically with the help of work in the past. Three modes of failure of beams have been found during the experiment on monolithic and rubber core sandwich beams like mode-1: Fracture at the point of strike i.e. tearing; mode-2: Fracture at one or both support either on front face sheet or on back face sheet of beam i.e. end shear; mode-3: Fracture at the point of strike with bulging (cup shape) and after fracture beam turnaround from the support (in case of monolithic) or Fracture at the point of strike without bulging on front face sheet and after fracture on the back face sheet with bulging and beam turnaround from the support (in case of sandwich beam).

Towards the black hole uniqueness: transverse deformations of the extremal Reissner-Nordstr\xf6m-(A)dS horizon

We study all transverse deformations of the extremal Reissner-Nordström–(A)dS horizon in the Einstein-Maxwell theory. No symmetry assumptions are needed. It is shown, that for the generic values of a charge, the only allowed deformation is spherically symmetric. However, it is shown that for fine-tuned values of the charge, the space of deformations is larger, yet still finite-dimensional.

Elaboration and characterization of ferroelectric materials Sr2(1-x)Na(1+x)GdxNb5O15 synthesized by solid process

The solid solutions Sr2(1-x)Na(1+x)GdxNb5O15 (SNGN) with substitution rates of Sr2+ by Gd3+ varying between 0 and 1 were prepared and have undergone several heat treatments. The XRD spectra show that the powders calcined at 650 °C for 6 h exhibit a mixed structure consisting of orthorhombic-quadratic phases. On the other hand, calcination at 1200 °C for 12 h ensures complete crystallization of the SNGN compounds in the TTB structure of quadratic symmetry. The SEM images show grains of regular and spherical shapes. The Raman spectra of the solid SNGN solution calcined at 1200 °C (x = 0; 0.2; 0.4 and 0.6), show two broad bands attributed to the transverse deformation modes of the O-Nb-O bond and of elongation modes of the Nb-O bond of octahedra (NbO6). IR spectroscopy highlights the existence of absorption bands corresponding to the elongation and deformation vibrations of some bonds. The temperature measurements of the dielectric permittivity εr of the ceramic (SNN; x = 0) show for all the frequencies used, the presence of a narrow peak during the heating and the cooling phases with a maximum located respectively at the Curie temperature Tc ∼ 235.07 °C and Tc ∼ 224.84 °C. The dielectric losses tan (δ) values are very weak in the ferroelectric phase (T < Tc), then an increase, which reaches 2.3 for the lowest frequency, occurs in the paraelectric phase. The maximum permittivity ε'rmax undergoes a decrease as the frequency increases; this diffusive behavior can be associated to the domains walls in the micro-domains of the ferroelectric phase.

Dynamic Response Analysis of Super Shallow‐Buried Rectangular Tunnel

Relying on the project of the open‐cut municipal tunnel undercrossing Ankang Freight V yard, the train dynamic response and seismic response of ultrashallow‐buried rectangular tunnel of the lower interchange are studied, respectively, by combining the method of field measurement and numerical simulation. The results show that under the action of train vibration load, the dynamic stress response of the top plate midspan and the upper end of the side wall of the tunnel cross section directly below the rail is the most significant, and the dynamic stress response of the bottom plate is the smallest. Under the rare earthquake, the tunnel structure has large transverse deformation, in which the transverse displacement of the tunnel roof is the largest. At the same time, there is a large stress concentration at the variable section of the tunnel.

Correction factors for in-plane shear strength and stiffness testing of flat angle-ply composite laminates with high Poisson’s ratios

In this paper, a method to obtain correction factors for in-plane shear properties in fibre-reinforced polymers with high Poisson’s ratio under biaxial load conditions and at high loads is presented. Experimental testing shows the deviations from classical laminate theory for such cases. The transverse deformation ratio is a general form of Poisson’s ratio and, for a ±45° angle-ply laminate, increases with strain. This effect is shown to exist for long and short test specimens, where significant biaxiality in the stress state is present. Reasons for this include fibre rotation at higher loads in tensile load conditions, and matrix plasticity and damage initiation. Test results show that the expanded formulas compensate errors in shear strength calculation of angle-ply laminates which arise from using nominal parameters with standard formulas. The results are also applicable to structures under biaxial load and when transverse contraction is inhibited, e.g. in shear panels. Further potential uses are in the presence of high shear strains and to detect the onset of damage under shear loading.

Dynamic modeling and analysis of center rigid body Timoshenko beam model based on unconstrained mode

The transverse deformation of the beam will lead to the longitudinal shortening deformation, and this transverse-longitudinal deformation coupling will bring the dynamic stiffening effect term on the generalized rigidity of the beam model. For the rotating beam structure, the centrifugal force will cause axial tension, with coupling axial and transverse deformation of the beam and bring additional geometric stiffness, which is more obvious for the thick short beam. The central rigid body-Timoshenko beam model with a large-range-motion center was investigated. Firstly, the dynamic model with centrifugal forces was established by means of the Timoshenko beam theory and the Hamilton principle. Secondly, the unconstrained mode concept was introduced, and the unconstrained mode shape functions and natural frequencies were solved with the Frobenius method. Finally, numerical simulations were carried out to explore the difference of generalized stiffness between the unconstrained mode and the constrained mode at different constant speeds, and the effects of centrifugal forces on the model under unconstrained mode condition were discussed.

Leveraging active-source seismic data in mining tailings: Refraction and MASW analysis, elastic parameters, and hydrogeological conditions

We applied active-source seismic method for the interpretation of elastic parameters in tailings facilities which is essential for evaluating stability and seismic response. The methodology uses different analysis methods on the same dataset, i.e., conventional seismic refraction (SR) to determine compressional-wave velocity (Vp) and multichannel analysis of surface wave (MASW) to estimate shear-wave velocity (Vs). Seismic velocities in conjunction with tailings physics approach revealed interpretable data in terms of elastic parameters and hydrogeological conditions. The results determined the empirical linear relationships between Vp and Vs that are particular to an unconsolidated media such as tailings and showed that variability of hydrogeological conditions influences the elastic seismic response (Vp and Vs) and the elastic parameters. The analysis of the elastic parameters identified the state condition of the tailings at the time of the survey. The Bulk modulus K that relates the change in hydrostatic stress to the volumetric strain was predominant between 1.0−2.0 GPa. The Young’s modulus E in the tailings media was in the low range of 0.15−0.23 GPa. Poisson’s ratio values in all sections were in the upper limit in the range of 0.37−0.49, meaning that the tailings media is highly susceptible to transverse deformation under axial compression.

Influence of the stress-strain state on the jerky flow effects and kinetics of the strain bands nucleation in Al-Mg alloy (A 95456)

The aim of the work is to develop a technique on the experimental study of inelastic deformation of structural metal materials in various types of stress-strain state. A technique is proposed based on the use of original samples of specialized complicated geometry, in the working zone of which a controlled biaxial stress state is realized, and the use of a contactless 3D digital image correlation measurement system Vic-3D for recording displacement and deformation fields. The authors proposed the use of original samples of variable thickness in the form of plates located inside a rigid circular rim and a rim of reverse curvature. Under uniaxial tension of these samples in the central area of the plate (working part of the sample), the plane stress state is realized with principal stresses of different signs, depending on the shape and rigidity of the rim. In the working part of the plate with a ring-shaped rim, tensile forces in the longitudinal direction and compressive forces in the transverse direction are realized due to the curvature of the circular rim and its narrowing in the transverse direction. In a plate with a rigid rim of reverse curvature, biaxial tension is realized in the working section. High efficiency of the proposed experimental technique has been shown to solve problems in the mechanics of solids, in particular, to study the processes of macroscopic localization of plastic flow in Al-Mg alloys (AlMg6) under the conditions of the Portevin - Le Chatelier effect. Using a video system, experimental data of the realized ratio of the deformation components (longitudinal and transverse deformations) in the working zone of the samples were obtained. The analysis of the kinetics of band formation and discontinuous yield strain occurring under conditions of a plane stress state has been carried out. The use of the Vallen Amsy-6 system made it possible to obtain data on the occurrence of acoustic emission signals accompanying the observed processes of inelastic deformation of the material. The graphs of the dependence of the energy parameter and frequency characteristics of acoustic emission signals on time have been constructed and analyzed.

Transverse Vibration of Viscoelastic Sandwich Structures: Finite Element Modeling and Experimental Study.

In the present work, the nonlinear vibration behavior of elastic-viscoelastic-elastic sandwich (EVES) beams is studied. A finite element (FE) equation taking intoaccount the transverse compression deformation of the viscoelastic core for the EVES beams is derived. In order toaccurately characterize the frequency-dependent feature of the viscoelastic materials layer, athird-order seven-parameter Biot model isused. A 2-node 8-DOF element is established to discretize the EVES beams. The experimental testing onEVES beams validates the numerical predication of the FE model. Numerical and analytical investigations are carried on a series of EVES beams with different thicknesses. The results indicate that the presented FE model has better accuracy in predicting the natural frequency of the sandwich beams, and in predicting damping, the accuracy is related to the thickness of each layer. The results of this paper have important reference values for the design and optimization of the viscoelastic sandwich structure.

Dynamic failure behavior of steel wire mesh subjected to medium velocity impact: Experiments and simulations

Considerable property damage is caused by windborne debris during extreme weather. The object of interest in this study, steel wire mesh, is an effective means of providing protection against windborne debris. However, the design and manufacture of security screens made of wire mesh typically depend on a laborious and imprecise trial-and-error process. Additionally, this anisotropic, inhomogeneous, and porous material comprising in-contact wires has rarely been examined in a comprehensive manner. Considering these issues, the current research experimentally tested the impact response of plain-weave steel wire mesh by firing a spherical projectile in a velocity regime ranging from 112 m/s to 152 m/s. The deformation and failure mechanisms of the wire mesh during the impact process were investigated via high-speed photography. The results showed that the wire mesh behaved as a membrane and failed mainly in tension over the impact velocity range of interest. Further, with a detailed finite element model consisting of interlaced warp and weft wires, additional virtual tests were carried out at a broader velocity range of 20–200 m/s. The findings indicated a linear relationship between residual velocity and impact velocity under a velocity range that exceeded the ballistic limit. The energy absorbed by the wire mesh increased with impact velocity (or impact energy) before the material reached peak absorption at the ballistic limit. Beyond this threshold, the energy absorption gradually declined to an asymptotic level. Such energy absorption was well correlated with the extent of transverse deformation in the wire mesh. Internal energy due to the deformation of wires and frictional energy associated with the interactions between sliding wires at their crossovers were two primary energy absorbing mechanisms. Moreover, the effects of impact location, clamped wire direction and projectile size were analyzed.

An experimental and finite element investigation of compression-after-impact (CAI) behaviour of biaxial carbon fibre non-crimp-fabric (NCF) based composites

The damage mechanisms of biaxial non-crimp-fabric (NCF) reinforced composites with a quasi-isotropic [(45/-45)(90/0)]4s layup subject to low-velocity impact (LVI) and compression-after-impact (CAI) loadings are investigated. Experimental results indicate that fibre compressive failure in the 0° plies controls the peak load during CAI, which is influenced by the out-of-plane transverse deformation of the impacted specimen. The study proposes a novel finite element (FE) model to predict the CAI strength of the NCF specimen. While the number of delaminations in the LVI model is less than the actual number of the multiple delaminations in the test specimen, the same out-of-plane transverse deformation measured by the experiment is still captured. The strength predicted from the subsequent CAI model is in good agreement with the experiment. The study provides a potential numerical design tool for the use of NCF materials in damage-tolerant structures.

Rub-impact dynamic analysis of a rotor with multiple wide-chord blades under the gyroscopic effect and geometric nonlinearity

In turbo-machinery, wide-chord blades are widely used due to the advantages of improving fan efficiency and aerodynamic performance. The rotor with multiple wide-chord blades is spaced from the outer casing. The small clearance may cause rub-impact fault between wide-chord blades and the casing, which induces different damage severity or the destruction of the whole machine. Numerical simulation is necessary to analyze this kind of rub-impact fault, but the solution process becomes complicated because of the coupling of geometric nonlinearity, local vibrations of wide-chord blades and gyroscopic motion of the rotor. This paper develops a rubbing rotor model with multiple wide-chord blades considering the gyroscopic effect and geometric nonlinearity induced by rub-impact. Based on the rub-impact model established for wide-chord blades, the high-order nonlinear governing equations of the bladed rotor are derived. Vibration responses are solved, and a series of dynamic characteristic analysis is carried out. The results reveal that high-order nonlinearity has a little effort on vibrations during slight rub-impact. But with the increase of transverse deformation induced by severe tip-rub, its influence cannot be ignored. Besides, localized rub-impact phenomenon of blades induced by external synchronous forces is found. Instead, external asynchronous force makes all blades rub, one after another along the circumferential direction of the disk, and there is a phase differenceΔφ=2π/Ω±ωNbbetween the vibration responses of adjacent blades. Then, we found that the swing motion intensifies the difference of transverse deformations along the chord direction of wide-chord blades with tip-rub, which may induce the edge failures. Also, the swing motion intensifies the steady rub-impact fault. It could weaken or eliminate its divergence and instability when the rotor with multiple wide-chord blades is unstable. The gyroscopic effect could weaken the swing motion, and then weakens the stable rub-impact fault.

Mechanical-Geometrical Modeling Of The Hyperelastic Materials At Uniaxial Stretching

Hyperelastic materials, such as rubber, occupy an important place in the design and operation of various technological equipment and machines. The article analyzed the deformation behavior of hyperelastic materials using a mechanical-geometric model. The method of mechanical-geometric modeling is a new method for obtaining constitutive relations and strain energy density functions for nonlinear elastic solids. It is based on physically and geometrically consistent prerequisites. The resulting models can describe broad classes of nonlinear elastic materials (both isotropic and anisotropic) depending on the mechanical and geometric properties “embedded” in them at the first stages of design. This paper discusses two basic types of models based on different initial geometry. The mechanical parameters of the models are constants, and the models themselves are considered in a statement corresponding to isotropic hyperelastic materials. The article presents the most common diagrams of deformation of artificial and natural rubbers, as well as steel. Hyperelastic materials, depending on the task, can be described in the nonlinear theory of elasticity as ideal incompressible, or as weakly compressible. Parameters of expressions of strain energy density functions of mechanical-geometric models obtained for cases of incompressible and weakly compressible continuous solids were identified. Stretch diagrams and diagrams of the transverse deformation function of the obtained mechanical-geometric models for the two cases mentioned above are plotted. The extension diagram for the model with parameters corresponding to the classic structural material of the steel type is also shown. Comments are given on the possibility of further paths of developing the method of mechanical-geometric modeling to obtain results not only in the field of nonlinear theory of elasticity, but also viscoelasticity.

Active multi-physical modulation of Poisson’s ratios in composite piezoelectric lattices: On-demand sign reversal

A large number of studies have been reported in literature to analyse various parameters that influence the Poisson’s ratios of multi-functional lattice materials. However, the major limitation in such lattices is that once the lattice is manufactured, the Poisson’s ratios and other elastic properties become fixed corresponding to the particular lattice configuration. This limits the application of such lattices in many advanced multi-functional structures and systems, where on-demand active property modulations are warranted. This paper proposes composite lattices comprising a substrate and piezoelectric materials, wherein it is possible to actively modulate the Poisson’s ratios and other elastic properties as a function of voltage. Considering both axial and transverse deformations of the cell walls along with a unit cell based approach, the exact closed-form expressions of Poisson’s ratios and equivalent Young’s modulus are derived in an expanded design space for the unimorph and bimorph configurations. The study reveals that a sign reversal of the Poisson’s ratios and Young’s modulus can be achieved for specific combinations of cell angle and applied voltage. Contrary to the conventional wisdom, such active sign reversal implies that re-entrant honeycomb lattices can exhibit positive Poisson’s ratios and vice versa.

Semianalytical Solution for Buried Pipeline Subjected to Horizontal Transverse Ground Deformation

For buried pipelines, it is not always possible to avoid active zones where there is a possibility of ground deformation either due to earthquake or topographical reasons, and hence it is necessary to understand the impact of ground deformation on buried pipelines. The present study derives a semianalytical solution for the case of a buried pipeline subjected to spatially distributed horizontal transverse ground deformation (HTGD). Governing differential equations are developed considering the pipe as a Timoshenko beam and surrounding soil as a two-parameter foundation. Firstly, the proposed semianalytical solution is validated with prior studies on the influence of HTGD on buried pipelines, and then a comprehensive parametric variation with various influential parameters such as peak ground deformation, pipe diameter, wall thickness of pipe, burial depth, backfill soil, width of HTGD zone, and type of HTGD pattern is studied to understand the effect on the behavior of buried pipelines. It is observed that the pipe stability increases with increasing the width of the HTGD zone and with decreasing peak ground deformation. Pipe responses significantly vary with the pattern of HTGD. Further, pipe failure against HTGD can be reduced by reducing pipe diameter or by increasing the pipe wall thickness and by providing loose backfill material. The present methodology will help to evaluate the displacement patterns of pipes and the qualitative behavior of an overall soil–pipe system subjected to spatially distributed HTGD without performing numerical analysis.

On The Stability of Solutions of Certain Classes of Initial-Boundary-Value Problems in Aerohydroelasticity

We study the stability of solutions to initial–boundary-value problems for coupled systems of partial differential equations that describe the dynamics of deformable structural elements interacting with a gas-liquid medium. The definitions of stability of deformable bodied adopted in this work correspond to the concept of the Lyapunov stability of dynamic systems. The stability of deformable elements of vibration devices interacting with subsonic and supersonic flows is examined. The influence of a gas or liquid (in the model of an ideal compressible medium) is determined from asymptotic equations of aerohydromechanics. For the description of the dynamics of elastic elements, we use nonlinear models of solid deformable bodies with transverse and longitudinal deformations. Models are described by coupled nonlinear systems of partial differential equations. The study of stability is based on the construction of positive-definite Lyapunov-type functionals corresponding to these systems; sufficient conditions for the stability of their solutions are obtained.