Radial Displacement Distributions Research Articles

Strain rate-dependent failure mechanics of the intervertebral disc under tension/compression and constitutive analysis

BackgroundThe intervertebral disc exhibits not only strain rate dependence (viscoelasticity), but also significant asymmetry under tensile and compressive loads, which is of great significance for understanding the mechanism of lumbar disc injury under physiological loads. ObjectiveIn this study, the strain rate sensitive and tension-compression asymmetry of the intervertebral disc were analyzed by experiments and constitutive equation. MethodThe Sheep intervertebral disc samples were divided into three groups, in order to test the strain rate sensitive mechanical behavior, and the internal displacement as well as pressure distribution. ResultsThe tensile stiffness is one order of magnitude smaller than the compression stiffness, and the logarithm of the elastic modulus is approximately linear with the logarithm of the strain rate, showing obvious tension-compression asymmetry and rate-related characteristics. In addition, the sensitivity to the strain rate is the same under these two loading conditions. The stress–strain curves of unloading and loading usually do not coincide, and form a Mullins effect hysteresis loop. The radial displacement distribution is opposite between the anterior and posterior region, which is consistent with the stress distribution. By introducing the damage factor into ZWT constitutive equation, the rate-dependent viscoelastic and weakening behavior of the intervertebral disc can be well described.

Modeling on displacement response and damage mechanism of contact interface during installation for composites sleeved interference joint

Interference-fit has remarkable advantages in improving the load-bearing performance of the structure, but the interface damage caused by interference installation becomes a weakness in the reliable application of composite joints. Therefore, a reliable and effective physically-based numerical model to reveal the displacement response and damage mechanism of contact interface during installation for composites sleeved interference joint was developed by combining the physically-based LaRC05 criterion and the energy-based linear softening law in this paper. The Partition Golden Section Search algorithm was employed to balance the accuracy of damage prediction and computational efficiency. The interference installation simulations with different geometric parameters were carried out and validated by experiments. Results show that the larger the bolt-sleeve interference-fit percentage, the more severe the non-uniform plastic deformation of the sleeve in the installation. Increasing the sleeve thickness can improve the uniformity of radial displacement distribution of the sleeve and alleviate the interface damage, but it cannot eliminate the connection gap. Choosing the appropriate sleeved fastener with taper can effectively avoid the aforementioned gap, improving the uniformity of displacement distribution and even reducing the interface damage.

An optimized zonal deformation prediction model for super-high arch dams

The previous zonal deformation prediction models for super-high arch dams focus on the measured deformation law, which cannot capture the trend, periodic and fluctuating characteristics. This greatly limits their physical interpretation and practical applications. To address this issue, this paper proposes an optimized zonal deformation prediction model. First, the variational mode decomposition algorithm is applied to split displacement into trend, periodic and fluctuating components. Representative environmental and load factors are determined by the hierarchical clustering on principal components, and then also decomposed into the trend, low- and high-frequency components according to their physical meanings. Second, an optimized dynamic time warping (DTW) based on shape-based distance is employed to divide the displacement components of measured points into different zones. The centroid sequences are calculated to capture the shared characteristics of the corresponding deformation zones. The zonal data sets of the centroid sequences of displacement components and their strongly related influencing factor components are established. Third, the optimized zonal deformation prediction models using three machine learning algorithms (random forest, least squares support vector machines, and boosted regression tree) and the improved hydrostatic-thermal-time model are constructed. The effectiveness of the optimized model is verified using the measured data collected from the Xiluodu dam. The case study shows that the optimized model can well explain the spatio-temporal characteristics of the trend, periodic and fluctuating displacements. Affected by the geological condition, the radial displacement distribution is not completely symmetrical under high reservoir water level.

Electro-thermo-mechanical stress analysis of smart sandwich cylindrical shell

In this paper, stress analysis of a multi-walled hollow cylinder made from a functionally graded material (POLYMER) sandwiched between two piezoelectric layers is investigated. This system is subjected to internal and external pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition, and a constant potential difference imposed on piezoelectric layers between its inner and outer surfaces or combination of these loadings. All mechanical and thermal properties except for the Poisson's ratio of Polymer layer are assumed to be power functions of the radial position. Using equilibrium equations, stress-strain relations and electromechanical coupling of piezoelectric layer, the constitutive differential equation in term of radial displacement is obtained. Considering electro-mechanical boundary conditions, this differential equation is analytically solved. The electro-thermo-mechanical stresses, electric potential and radial displacement distributions in three layers are obtained.

Concrete Protective Layer Cracking Caused by Non-Uniform Corrosion of Reinforcements.

The volume expansion of reinforcement corrosion products resulting from the corrosion of steel reinforcement embedded into concrete causes the concrete’s protective layer to crack or spall, reducing the durability of the concrete structure. Thus, it is necessary to analyze concrete cracking caused by reinforcement corrosion. This study focused on the occurrence of non-uniform reinforcement corrosion in a natural environment. The characteristics of the rust layer were used to deduce the unequal radial displacement distribution function of concrete around both angular and non-angular bars. Additionally, the relationship between the corrosion ratio and the radial displacement of the concrete around the bar was established quantitatively. Concrete cracking due to the non-uniform corrosion of reinforcements was simulated using steel bars embedded in concrete that were of uneven displacement because of rust expansion. The distribution of the principal tensile stress around the bar was examined. A formula for calculating the critical radial displacement at the point when cracking began was obtained and used to predict the corrosion ratio of the concrete cover. The determined analytical corrosion ratio agreed well with the test result. The effect factor analysis based on the finite element method indicated that increasing the concrete strength and concrete cover thickness delays concrete cracking and that the adjacent rebar causes the stress superposition phenomenon.

Influence of Backfill Compaction on Mechanical Characteristics of High-Density Polyethylene Double-Wall Corrugated Pipelines

For flexible pipelines, the influence of backfill compaction on the deformation of the pipe has always been the focus of researchers. Through the finite element software, a three-dimensional soil model matching the exterior wall corrugation of the high-density polyethylene pipe was skillfully established, and the “real” finite element model of pipe-soil interaction verified the accuracy through field test. Based on the model, the strain distribution at any position of the buried HDPE pipe can be obtained. Changing the location and extent of the loose backfill, the strain and radial displacement distributions of the interior and exterior walls of the HDPE pipe under different backfill conditions when external load applied to the foundation were analyzed, and the dangerous parts of the pipe where local buckling and fracture may occur were identified. It is pointed out that when the backfill is loose, near the interface between the backfill loose region and the well-compacted region, the maximum circumferential strain occurs frequently, the exterior wall strain is more likely to increase greatly on the region near crown or invert, the interior wall strains increase in amplitude at springline, and the location of the loose region has a greater influence on the strain of the pipe than the size of the loose area.

The Improvement of Deformation Analysis for Circular Tunnel Based on Hoek-Brown Criterion in Strain-Softening Rock Mass

To overcome the defect that the support pressure is required to be measured or supposed in elasto-plastic analysis in strain-softening rock mass, by the connection of the support pressure imposed on surrounding rock mass, without assuming the support pressure is known a priori, an improved model of solving plastic radius and the distribution of radial displacement around the circular tunnel is proposed. Based on Hoek-Brown yield criterion, the results obtained by strain-softening model are compared with those of elastic perfectly brittle and elastic perfectly plastic models. The examples reveal that the difference of plastic radius obtained by the three models is comparatively smaller, but the difference of radial displacement is comparatively larger. The proposed model overcomes some defects of the previous studies in deformation analysis for tunnel.

Concrete Pipes Reinforced with AL2O3 Nanoparticles Considering Agglomeration: Magneto-Thermo-Mechanical Stress Analysis

Concrete pipes can be used in many industries which are exposed to different mechanical and thermal loadings. However, in the present work, stress analysis of concrete pipes reinforced with AL2O3 nanoparticles is presented considering agglomeration effects. The pipe is subjected to mechanical, magnetic and thermal loadings. All the equivalent mechanical and thermal properties of structure are obtained using the Mori–Tanaka model. Based on the equilibrium equation, the governing equation is derived. Using an exact solution, the stresses and radial displacement distributions of the structure are calculated. Presenting the effects of AL2O3 nanoparticles volume percentage and agglomeration on the stresses and radial displacement of concrete structure were the main novelties of this study. Numerical results indicate that with increasing 20% AL2O3 nanoparticles volume percentage, the effective stress decreases to 84.8%. Considering 75% agglomeration of AL2O3 nanoparticles leads to 19.54% increase in the effective stress of concrete structure. In addition, the dimensionless radial displacement of structure at the outer surface decreases to 92.49% with increasing 20% AL2O3 nanoparticles volume percentage and increases by 33.55% in the inner surface with considering 75% agglomeration effects.

Finite element modeling of concrete cover crack propagation due to non-uniform corrosion of reinforcement

Non-uniform corrosion of reinforcement causes concrete cracking in chloride contaminated RC structures. Due to an interaction existed between the concrete cover cracking and the ingress of aggressive agents in chloride environments, chloride ingress is significantly enhanced by cracks. Thus the investigation on the cracking paths and cracking propagation process resulting from steel corrosion is very essential. This work proposed a numerical model to study the cracking of cover concrete. The physical model was focused on the middle-located rebar corrosion, and the effect of the neighboring longitudinal reinforcing bars on the cracking of cover concrete was mainly considered. A damaged plasticity model for the study on the failure behavior of concrete cover was built. The non-uniform radial displacement distribution was adopted to simulate the corrosion expansion behavior of the rebar. The cracking propagation process of cover concrete with two neighboring longitudinal reinforcing bars embedded was simulated and monitored with the level of corrosion build-up. The present approach was verified by the available experimental observations. The influences of concrete cover thickness, rebar diameter and rebar spacing on the failure patterns of concrete cover and crack width propagation were examined. And limiting criteria for the cracking modes were established.

Magnetic Field Effects on the Elastic Behavior of Polymeric Piezoelectric Cylinder Reinforced with CNTs

In the present study, the magnetic field effects of the elastic response of the polymeric piezoelectric cylinder reinforced with the carbon nanotubes (CNTs) are studied. The cylinder is subjected to an internal pressure, a constant electric potential difference at the inner and outer surfaces, and the thermal and magnetic fields. The Mori-Tanaka model is used for obtaining the equivalent material properties of the cylinder. The governing differential equation of the cylinder is derived and solved analytically based on the charge and equilibrium relations. The main purpose of this paper is to investigate the effects of the magnetic field on the stresses, the electric potential, and the radial displacement distributions of the polymeric piezoelectric cylinder. The presented results indicate that the existence of the magnetic field can reduce the stresses of the nanocomposite cylinder.

Exact and Numerical Elastic Analysis for the FGM Thick-Walled Cylindrical Pressure Vessels with Exponentially-Varying Properties

Abstract Assuming exponential-varying properties in the radial direction and based on the elasticity theory, an exact closed-form analytical solution is obtained to elastic analysis of FGM thick-walled cylindrical pressure vessels in the plane strain condition. Following this, radial distribution of radial displacement, radial stress, and circumferential stress are plotted for different values of material inhomogeneity constant. The displacements and stresses distributions are compared with the solutions of the finite element method (FEM).

Multivariate Information Dynamic Monitoring System Application of Tunnel Construction Process Model Test

Abstract Geomechnical model testing has been widely applied as a kind of research technique in underground engineering problems. However, during the practical application process, due to the influence of many factors, the desired results cannot be obtained. In order to solve this problem, based on the measurement requirements of the model test, combined with FBG(Fiber Bragg Grating) sensor technology and traditional measurement methods, an FBG monitoring system, Micro-multi-point displacement test system, resistance strain test system and surrounding rock pressure monitoring system are developed. Applying the systems to a model test of the tunnel construction process, the displacement in advance laws of tunnel face, radial displacement distribution laws and surrounding rock pressure laws are obtained. Test results show that a multivariate information monitoring system has the advantage of high precision, stability and strong anti-jamming capability. It lays a solid foundation for the real-time data monitoring of the tunnel construction process model test.

Agglomeration effects on electro‐magneto‐thermo elastic behavior of nano‐composite piezoelectric cylinder

Agglomeration effect on the electro‐magneto‐thermo elastic response of a hollow piezoelectric circular cylinder reinforced with carbon nanotubes (CNTs) is the main contribution of present work. The cylinder is subjected to an internal pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition, a magnetic field in axial direction and a constant electric potential difference between its inner and outer surfaces or combination of these loadings. All the equivalent mechanical, thermal and piezoelectric properties of nano‐composite cylinder are obtained using Mori–Tanaka model considering agglomeration effects. The governing equation in polarized form is shown to reduce to a second‐order ordinary differential equation for the radial displacement. Considering mechanical boundary condition, this differential equation is analytically solved. The electro‐magneto‐thermo‐mechanical stresses, the electric potential and radial displacement distributions in the structure are discussed in detail. The presented results indicate that the agglomeration and volume percent of CNTs have significant influences on the electro‐magneto‐thermo‐mechanical behavior of the nano‐composite cylinder. POLYM. COMPOS., 39:1594–1603, 2018. © 2016 Society of Plastics Engineers

A novel approach to forced vibration behavior of thick-walled cylinders

This study is to investigate the effect of anisotropy on the forced vibration behavior of hollow cylinders under dynamic internal pressure. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin's numerical inversion method. Durbin's numerical inverse method into the analysis of transient thermal stresses in annular fins is a novel approach. Durbin's numerical inverse method successfully implements the boundary value problem which can be solved in Laplace space. Various material models from the literature are used and corresponding radial displacement distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained. The anisotropy constant is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution.

Investigation on the cracking behavior of concrete cover induced by corner located rebar corrosion

Non-uniform corrosion of reinforcement causes concrete cracking in chloride contaminated RC structures. Due to the special boundary conditions, the concrete cover with corner located rebar is often subjected to the attack of chloride ions in a marine environment from two directions, and thus the corresponding non-uniform corrosion distribution should be different from the one for side-located rebar. The aim of the work is to explore the effect of corner located rebar corrosion on the cracking of cover concrete. For corner located rebar, an improved non-uniform corrosion distribution model was established based on the analysis results of two-dimensional chloride diffusion in concrete. Considering the heterogeneities of concrete, a meso-scale mechanical model and method for the study on the failure behavior of concrete cover was built. In the analysis model and method, the non-uniform radial displacement distribution was adopted to simulate the corrosion expansion behavior of the rebar. The cracking of concrete cover with corner located rebar was simulated and studied. The present approach was verified by the available experimental observations. The influences of concrete heterogeneity, corrosion distribution types, rebar diameter and concrete cover thickness on the failure patterns of concrete cover and the expansive pressure were investigated. The simulation results indicate that the developed approach can well describe the cracking behavior of cover concrete and the corrosion-expansion behavior of steel rebar.

원판형 압전 변환기의 면내 방사 진동 특성 측정

이 논문은 원판형 압전 변환기의 면내 방사 진동 특성을 실험적으로 다룬다. 면내 방사 진동은 두께 방향으로 분극이 된 압전 원판에서 푸아송비로 인해 야기되는 것으로서, 레이저 면내 진동 측정기로써 측정되었고, 고유진동수는 임피던스 분석기로써 측정되었다. 실험 결과는 단순화된 이론적 해석과 유한요소 해석으로부터 얻어진 이론적 예측과 비교되었다. 원판형 압전 변환기의 기본 모드는 방사 모드이고, 중심으로부터 가장자리까지의 반경 방향 변위 분포는 단조 증가가 아니라 원주면에서 약간 떨어진 위치에서 최대 값을 나타낸다. 지름 대비 두께 비율이 작은 원판에서 이론적으로 계산된 기본 진동수는 유한요소 결과와 잘 일치하고, 두께/지름 비율 0.4까지 오차 7 % 이내로 정확하다. The paper experimentally deals with the radial in-plane vibration characteristics of disk-shaped piezoelectric transducers. The radial in-plane motion, which is induced due to Poisson's ratio in the piezoelectric disk polarized in the thickness direction, was measured by using an in-plane laser vibrometer, and the natural frequencies were measured by using an impedance analyzer. The experimental results have been compared with theoretical predictions obtained by simplified theoretical and finite-element analyses. It appears that the fundamental mode of a piezoelectric disk transducer is a radial mode and its radial displacement distribution from the center to the perimeter is not monotonic but shows maximum slightly apart from the perimeter. The theoretically-calculated fundamental frequencies agree well with the finite-element results for small thickness-to-diameter ratio, and they are accurate within 7 % error for the ratio up to 0.4.

A procedure of strain-softening model for elasto-plastic analysis of a circular opening considering elasto-plastic coupling

A simple numerical procedure of strain-softening model for the elasto-plastic analysis of a circular opening is presented by modifying the procedure proposed by Lee and Pietruszczak (2008). The proposed procedure has two advantages over that of Lee and Pietruszczak (2008). One is that the elasto-plastic coupling can be considered, the other is that the equilibrium equation and compatibility equation need not be expressed with respect to the normalized radius. Through MATLAB programming, the accuracy and validity of the proposed procedure are demonstrated through some examples. The influence of elastic modulus and Poisson’s ratio evolution on the distribution of radial displacement and hoop stress, ground response curve (GRC) and plastic radius was investigated, and the results show that, with the decrease of elastic modulus evolutional ratio, the radial displacement, hoop stress and plastic radius all increase. With the increase of Poisson’s ratio evolutional ratio, the radial displacement, hoop stress and plastic radius all decrease. As for influence extent, the evolution of elastic modulus has great influence on the radial displacement; and the evolution of Poisson’s ratio has smaller influence on the radial displacement, both of them have very slight influence on the hoop stress near the excavation face but greater on the hoop stress near the interface of elastic and plastic region. And both of them have very slight influence on the plastic radius.

Analysis on the Finite Element of Electromechanic Coupling of Flexible Gear in Electromagnetic Harmonic Drive

In the harmonic electromagnetic drive motor, the rotating magnetic field may deform gear as well as the shape of interaction electromagnetic fields, thereby resulting in the interaction between electromagnetic field and the structure field. By analyzing the electromagnetic-structural coupling relationship of the system and conducting discretization, this paper established the finite element coupling equilibrium equations of electromagnetic field and structure field and discussed the coupling conditions between two fields as well as the boundary conditions of various fields, thus deducing the expression of the force and displacement transmission on the interface of two physical fields. By finite element simulation of the system, the law of the radial displacement distribution of flexible gear changing with the system parameters, which has provided a basis for further study of electromagnetic harmonic drive motor.

COMPLETE CLOSED-FORM SOLUTION FOR PRESSURIZED HETEROGENEOUS THICK SPHERICAL SHELLS

On the basis of plane elasticity theory (PET), the governing equations for axisymmetric thick spherical shells made of nonhomogeneous functionally graded materials (FGMs) subjected to internal and external pressure in general case are derived. It is assumed that the modulus of elasticity varies nonlinearly in the radial direction, and the Poisson’s ratio is constant. The analytical solution of the equations for real, double and complex roots are obtained. The radial stress, meridional stress and radial displacement distributions depending on an inhomogeneity constant are compared with those of the homogeneous case as well as with the solution using finite element method (FEM) and presented in the form of graphs. The obtained result shows that the property of FGMs has a significant influence to the stress distribution along the radial direction. Results are useful for engineers to design a sphere made of FGMs. DOI: http://dx.doi.org/10.5755/j01.mech.18.5.2702

CONSTRAINTS ON QUASAR LIFETIMES AND BEAMING FROM THE He II Lyα FOREST

We show that comparisons of HeII Lyman-alpha forest lines of sight to nearby quasar populations can strongly constrain the lifetimes and emission geometry of quasars. By comparing the HeII and HI Lyman-alpha forests along a particular line of sight, one can trace fluctuations in the hardness of the radiation field (which are driven by fluctuations in the HeII ionization rate). Because this high-energy background is highly variable - thanks to the rarity of the bright quasars that dominate it and the relatively short attenuation lengths of these photons - it is straightforward to associate features in the radiation field with their source quasars. Here we quantify how finite lifetimes and beamed emission geometries affect these expectations. Finite lifetimes induce a time delay that displaces the observed radiation peak relative to the quasar. For beamed emission, geometry dictates that sources invisible to the observer can still create a peak in the radiation field. We show that both these models produce substantial populations of "bare" peaks (without an associated quasar) for reasonable parameter values (lifetimes ~10^6-10^8 yr and beaming angles <90 degrees). A comparison to existing quasar surveys along two HeII Lyman-alpha forest lines of sight rules out isotropic emission and infinite lifetime at high confidence; they can be accommodated either by moderate beaming or lifetimes ~10^7-10^8 yr. We also show that the distribution of radial displacements between peaks and their quasars can unambiguously distinguish these two models, although larger statistical samples are needed.