Plate Of Finite Thickness Research Articles

Prediction of Coefficient of Restitution for Impact Elastoplastic Spheres Considering Finite Plate Thickness

Collisions between objects are a relatively common phenomenon in nature. Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts. The coefficient of restitution is a critical parameter in the analysis of collision processes. Many experiments have shown that the coefficient of restitution is closely related to the plate thickness, and the smaller the plate thickness, the more inaccurate the coefficient of restitution predicted by the existing model, which seriously affects the process of collision analysis. To remedy this shortcoming, this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable. The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness. Finally, the validity of the new model is verified using a large amount of experimental data.

Robust transport and topological valley refraction of fundamental symmetric lamb waves in perforated phononic crystal plates

Lamb waves can be divided into antisymmetric Lamb waves (type A) and symmetric Lamb waves (type S), which are widely used in health monitoring of engineering structures and nondestructive evaluation of materials. However, due to the fact that each mode of Lamb wave has the setting group velocity in a certain bandwidth range, it is easy to cause the aliasing of multi-mode Lamb waves, partly limiting the application scenarios of Lamb wave. In this paper, a hexagonal lattice meta-structure is designed and the zero-order symmetric (S0) Lamb wave in a finite thickness plate is successfully separated. By breaking the spatial C 3v symmetry, a valley topological phononic crystal (PnC) plate for the pure S0 mode is constructed, and its robust topological transports are demonstrated. Firstly, the valley topological phase transition of S0 mode is realized by changing the angle of scatterer in PnC plate and the valley edge state of S0 mode is obtained. Furthermore, by introducing structural mismatch, it is verified that the edge state of S0 mode is robust to various bends and defect. Finally, by changing the material property of the terminal, the valley refraction with different directionality is realized. The results offer a route to individually study the symmetric modes of Lamb waves, and have potential application prospects in rapid and accurate ultrasonic nondestructive testing based on Lamb waves.

3D stress concentration around circular hole under remote biaxial loading

In this study, a theoretical model is proposed to analyze the stress concentration in a plate of finite thickness containing a circular hole under remote biaxial loading. The stresses in a plate with a circular hole under remote biaxial loading is a superposition of the stresses in the unperforated plate and the released stresses induced by opening the hole. For the latter, the stresses at the edge of the hole can be further decomposed into a spherical component and a deviatoric component. The solution due to a spherical component can be readily obtained but the solution due to a deviatoric component is hard to find. According to the literature, the solution of three-dimensional stress distributions in a plate of finite thickness containing a circular hole can be found by four potential functions. The available fundamental solutions of the potential functions satisfying the boundary conditions on the surfaces of the plate contain numerous complicated integrals, which limits their application to the current problem. Nevertheless, these fundamental solutions can be found explicitly by constructing the orthogonal function, which is composed of the Bessel functions. A system of linear equations is established to satisfy the boundary conditions at the edge of the hole. Therefore, the stresses due to a deviatoric component are obtained by solving the linear simultaneous equations. The stress concentration factor calculated by the proposed model is validated with the available numerical and theoretical solutions. It is concluded that the stress ratio, the thickness of the plate, and Poisson's ratio have an important influence on the distribution of the stress concentration factor along the thickness of the plate, especially on the distribution near the surface. Moreover, the proposed model can be extended to analyze the stress concentration at the edge of a circular hole in a plate of finite thickness under remote bending. The model is efficient and reliable, and it can provide a powerful analytical method to analyze three-dimensional stress concentrations around holes under various remote loading in engineering.

Clay micromechanics: Numerical modelling of electrical double-layer interactions to develop particle-based models for clay

Discrete element modelling of clays requires defining the interaction energy between two particles. The Derjaguin, Landau, Verwey and Overbeek (DLVO) theory combining the effect of the van der Waals forces and the Coulombic forces due to the double layer of counterions provides a widely accepted framework to characterise the pair potential energy. Solutions of the Poisson-Boltzmann (PB) equation to quantify the Coulombic forces are only available for the case of infinitely extended and uniformly charged facing plates (1D conditions). However, these assumptions are not representative of a clay particle system. Particles should be represented by platelets of finite size and finite thickness, with different charges between the edge and the basal planes. This paper addresses the problem of deriving the Coulombic interaction forces for plates of finite size and thickness in 3D configuration by solving the Poisson-Boltzmann equation numerically via the Finite Element Method (FEM). It is shown that 2D particles (plates of infinitesimal thickness) provide an adequate representation of Coulombic interaction as long as the particles are uniformly charged. The advantage of 2D particles is to reconcile numerical modelling with analytical solutions available in the literature. The use of 2D particles is questionable when considering different charges between basal planes and edges.

Low-frequency still-air acoustic inertia of inclined circular aperture in an infinite flat plate of finite thickness

The acoustic inertia of the canonical configuration of inclined circular aperture(s) in a finite-thickness plate at the low frequency limit is investigated under the inviscid still-air condition. A hybrid approach combining modal expansion and boundary element method is applied to calculate the effective length of the aperture as a quantitative characterisation of its acoustic inertia. These calculations, covering different inclination angles up to 75°, are performed for a single isolated aperture with a selected range of plate thickness and the periodic aperture arrays of aligned and staggered arrangements with a selected range of aperture spacing respectively. The results are validated by the simulations carried out with the commercial software COMSOL. The parametric studies of geometric dimensions included in this work provide representative results for typical acoustic related engineering applications of finite-length inclined apertures. A link for access to the MATLAB programmes implementing the calculations is provided for interested readers. As an example of application, the hybrid method described in this work is used for the acoustic modelling of a representative multi-perforated liner studied in the literature for the problem of thermo-acoustic instability. The results compared well against those obtained from the Computational Fluid Dynamics simulations reported in the literature.

Dusty Gas Flow past Bodies under Scattering of Rebounded Particles

Two-phase gas-particle flow over a flat plate of finite thickness in a channel at a high subsonic velocity and supersonic transverse flow past a cylinder are considered. The leading edge of the plate is wedge-shaped or represents a smooth bluntness of constant radius. The wedge surface and the front bluntness are specified both smooth and rough. The roughness is modeled by a two-dimensional profile based on an experiment. Spherical particles and a mixture of particles in the form of ellipsoids of revolution, rectangular prisms, prisms with flat-cut vertices, and tetrahedrons are considered. The parameters of each of the forms vary. The impact interaction model proposed earlier and consistent with the experimental data on the coefficients of restitution of the center-of-mass velocity is used to determine the translational and rotational velocities of non-spherical particles after rebound. Along with monosized particles, a dispersed phase with a spread of particles in size is considered. The role of the studied factors of random nature which affect the flow pattern and the dispersed phase parameters is found.

Numerical fatigue modeling and simulation of interacting surface cracks in offshore wind structural connections

The structural integrity of marine structures is significantly influenced in many practical applications by their fatigue behavior, especially when dealing with dynamically sensitive structural systems, e.g., offshore wind substructures. The propagation of cracks found in structural components can be estimated through fracture mechanics-based methods, in which the crack growth under cyclic loading is mainly driven by the stress intensity factor (SIF). To simplify the computation of the SIF, closed-form solutions are often suggested in industrial standards, yet their applicability is limited to specific geometries and loading conditions. Overcoming the aforementioned constraints, we propose here a general methodology for numerically simulating the SIF and growth of multiple cracks by computing the SIF of adjacent cracks in an integrated finite element analysis, in which interaction effects are implicitly considered. In our proposed method, the coalescence of bordering cracks is also adequately modeled and fatigue failure is defined based on fracture mechanics principles. With the objective of enabling an efficient SIF computation, we also provide the necessary modeling details for the appropriate implementation of the corresponding finite element analysis. The proposed methodology is then tested and validated in a finite thickness plate under cyclic loading setting, whereas in a more practical case study, we investigate the fatigue analysis of interacting surface cracks in an offshore wind structural connection. The results emphasize the importance of considering interaction effects and crack coalescence when simulating the fatigue evolution of structural details in practical applications, and within the study, specific insights are additionally provided for the fatigue analysis of offshore wind structural components. With respect to the investigated fatigue failure criteria, the results show that a through-thickness limit state might yield slightly conservative fatigue life estimates compared to the fatigue limit that results when failure is defined based on the material fracture toughness.

Thermoelastic Analysis For A Thick Plate Under The Radiation Boundary Conditions

A fractional Cattaneo model for studying the thermoelastic response for a finite thick circular plate with source function is considered. The thick plate is subjected to radiation-type boundary conditions on the upper and lower surfaces, and its curved surface is kept at zero temperature. The theory of integral transformations is used to solve the generalized fractional Cattaneo-type, classical Cattaneo-Vernotte and Fourier heat conduction model. The analytical expressions of displacement components using thermoelastic displacement potentials; and thermal-stress distribution are computed and depicted graphically. The effects of the fractional-order parameter and the relaxation time on the temperature fields and their thermal stresses are investigated. The findings show that the higher the fractional-order parameter, the higher the thermal response. The greater the relaxation period, the longer the heat flux propagates on thick structures.

Penetration performance and fragmentation mechanism behind target of tungsten fibre/zirconium-based bulk metallic glass matrix composite rod

A tungsten fibre/zirconium-based bulk metallic glass matrix composite (WF/Zr-MG) is a type of armour piercing material with significant development potential. When it penetrates a finite-thickness target plate, it results in damage different from those generated by W alloys. Therefore, the penetration of 80% WF/Zr-MG by volume fraction (the diameter of the W fibre is 0.3 mm) into a 120-mm-thick 45 steel target plate is investigated experimentally at an impact velocity of 1600 ± 20 m/s. Subsequently, the results are comp rod ared with those of a 91 Walloy (91 W) rod to investigate the penetration performance and damage ability behind the target of composite materials. The damage effects of the 45 steel target plate and after-effect target are analysed. The penetration performance and fragmentation mechanism of the two materials are analysed experimentally and based on theoretical calculations. The experimental results indicate that the WF/Zr-MG rod shows self-sharpening in the nose, a smaller average crater diameter, less kinetic energy loss, and better penetration performance compared with the 91 W rod. The bonding force between the phases of WF/Zr-MG is significantly lower than that of 91 W, and cracks formed easily in the material during the penetration process. Radial stress is released instantaneously after the WF/Zr-MG rod departs from the target; consequently, the WF/Zr-MG rod underwent radial expansion, fracture, and dispersion. The damaged areas of WF/Zr-MG measured 1734 and 1661 cm2, which exhibit fragment diffusion angles of 46.5° and 46.1°, respectively. However, the damaged areas of the W alloy are only 1017 and 1193 cm2, and the corresponding fragment diffusion angles are only 35.3° and 37.8°, respectively. The damage parameters of WF/Zr-MG behind the target are greater than those of the tungsten alloy, which increased its killing capacity behind the target.

FRACTIONAL MODEL IN THE THEORY OF GENERALIZED THERMOELASTIC DIFFUSION

A problem for thermoelastic thick plate of infinite extension and finite thickness is considered, where a permeating substance is in contact with one of the bounding planes in the context of generalized thermoelastic diffusion theory with fractional parameter. The upper surface is assumed to be traction-free, subject to time-dependent thermal shock, and the chemical potential is also assumed to be a known function of time. The lower surface of the plate is laid on an insulated rigid foundation. Laplace and Hankel transform techniques are used. Analytical solutions in the transform domain are obtained using direct methods. The inverse of the double transform is obtained using a numerical method based on the Fourier expansion technique. A general solution to the cylindrical region problem is obtained. The solution can calculate under any boundary conditions. All numerical results are in perfect agreement with earlier work in various thermoelastic theories. Numerical calculations are performed for two different time values and for three distinct fraction parameter values. Temperature, stress, displacement, concentration, and chemical potential are displayed graphically. Comparisons are made with the results of the previous theory.

Efficient Model Assisted Probability of Detection Estimations in Eddy Current NDT with ACA-SVD Based Forward Solver.

Model assisted probability of detection (MAPoD) is crucial for quantifying the inspection capability of a nondestructive testing (NDT) system which uses the coil or probe to sense the size and location of the cracks. Unfortunately, it may be computationally intensive for the simulation models. To improve the efficiency of the MAPoD, in this article, an efficient 3D eddy current nondestructive evaluation (ECNDE) forward solver is proposed to make estimations for PoD study. It is the first time that singular value decomposition (SVD) is used as the recompression technique to improve the overall performance of the adaptive cross approximation (ACA) algorithm-based boundary element method (BEM) ECNDE forward solver for implementation of PoD. Both the robustness and efficiency of the proposed solver are demonstrated and testified by comparing the predicted impedance variations of the coil with analytical, semi-analytical and experimental benchmarks. Calculation of PoD curves assisted by the proposed simulation model is performed on a finite thickness plate with a rectangular surface flaw. The features, which are the maximum impedance variations of the coil for various flaw lengths, are obtained entirely by the proposed model with selection of the liftoff distance as the uncertain parameter in a Gaussian distribution. The results show that the proposed ACA-SVD based BEM fast ECNDE forward solver is an excellent simulation model to make estimations for MAPoD study.

Two-dimensional weight function for the determination of stress intensity factors for semi-elliptical surface cracks in finite-thickness and finite-width plates

In this study, a new two-dimensional (2D) weight function of stress intensity factors (SIFs) for semi-elliptical surface cracks in finite-thickness and finite-width plates subjected to arbitrary stress distributions was proposed. To determine the unknown coefficients in the weight function, parametric three-dimensional finite element (FE) models were developed to obtain the solutions of SIFs. The analysis matrix covers wide ranges of relative crack-length ratios 0.1 ≤ c/W ≤ 0.9, to consider the finite width effect, as well as aspect ratios 0.2 ≤ a/c ≤ 1.0 and relative crack-depth ratios 0.025 ≤ a/T ≤ 0.8. The present weight function was verified against the FE results and the solutions available in the literature. The maximum differences were within 6% for both the surface and deepest points. The proposed 2D weight function can be applied to calculate SIFs and predict the fatigue life of engineering structural components involving surface flaws.

Chiral standing spin waves in skyrmion lattice

This work studies the resonance excitations of the three-dimensional skyrmions lattice in the finite thickness plate of an isotropic chiral magnet using spin dynamics simulations. We found that the absorption spectra and resonance modes differ from those predicted by the two-dimensional model and the model of the unconfined bulk crystal. The features observed on the spectra can be explained by the formation of chiral standing spin waves, which, contrary to conventional standing spin waves, are characterized by the helical profile of dynamic magnetization of fixed chirality that is defined by the Dzyaloshinskii–Moriya interaction. In this case, the dynamic susceptibility becomes a function of the plate thickness, which gives rise to an interesting effect that manifests itself in periodical fading of the intensity of corresponding modes and makes excitation of these modes impossible at specific thicknesses.

Lamb waves in elastic–plastic plate containing voids

Abstract Propagation of Lamb waves has been studied in an infinite plate of finite thickness and composed of elastic–plastic material containing void pores. The plastic deformation in the plate material is considered through a single-plane and direction. Assuming a linear relation between the elastic and plastic parts of the change in void volume fraction and using the stress-free boundary surfaces of the plate, the dispersion relations corresponding to the symmetric and antisymmetric vibrations with respect to the mid-plane of the plate are derived. The corresponding dispersion relations of Lamb modes in the elastic–plastic plate have been reduced by neglecting the presence of voids. Some earlier known results are recovered from the present formulation under particular cases. The behaviour of symmetric and antisymmetric family of Lamb modes are depicted pictorially against the frequency, slip-angle, thickness of the plate and void parameters in a specific plate material. It is found that the plasticity and the presence of the voids in the plate material affect the propagation of Lamb modes. In particular, at the slip-angle $45^o$, the $S_0$- and $A_0$- modes exhibit symmetry, but $S_0$ is bell shaped and $A_0$ is parabolic.

The prediction of the coefficient of restitution between impacting spheres and finite thickness plates undergoing elastoplastic deformations and wave propagation

The prediction of the coefficient of restitution between impacting spheres and finite thickness plates undergoing elastoplastic deformations and wave propagation

Analytical Model of Perturbed EMF in a Transmit-Receive Coil System Due to Thin Flaws

This work proposes a model based on the semianalytical boundary element method (BEM) to predict the perturbation of the voltage induced in an eddy current coil due to narrow opening flaws that are usually encountered in eddy current nondestructive tests. The modeling is performed for rectangular narrow opening flaws that are located on the surface of an aluminum plate of finite thickness. The excitation to the coil varies time harmonically and the BEM results are corroborated by experiments performed in a controlled environment in the laboratory.

The effect of specimen thickness on the dislocation-free zone model of fracture

We use the method of continuously distributed dislocations to study the dislocation-free zone (DFZ) model of fracture in an infinite plate of finite thickness under externally applied uniform anti-plane shear stress. We formulate the equilibrium condition in terms of a set of two coupled singular integral equations using the representation of the total interaction force between two screw dislocations in a thin plate obtained by Eshelby and Stroh (1951). This set of singular integral equations is then solved numerically using the Gauss-Chebyshev integration formula resulting in the dislocation distribution functions in the crack and in the two plastic zones, the total number of screw dislocations in the plastic zone, the DFZ condition for a crack in a thin plate and the local mode III stress intensity factor at the crack tip.

Точные формулы напряженности магнитного поля внутри и вне однородного эллипсоидального магнетика во внешнем однородном в области магнетика поле

The direct problem of magnetostatics is considered - the calculation of the resulting magnetic field strength inside and outside a homogeneous magnet in the form of an arbitrary ellipsoid placed in the area of uniformity of the external magnetic field. The final formulas for calculating the field strength containing elementary functions or incomplete elliptic integrals are given. From them, the strength formulas for the "limiting" cases of a magnet of the specified shape are obtained – a plate of finite thickness, an infinite circular cylinder and a cylinder with an elliptical cross section, a ball. A comparison with a number of known formulas for these cases is made.

Active learning-based KNN-Monte Carlo simulation on the probabilistic fracture assessment of cracked structures

The probability of fracture (POF) assessment of complex cracked structures is a difficult task in the reliability assessment of engineering structures. Due to the complexity of structure, balancing efficiency and accuracy is the top concern in POF calculation. In this study, a novel probabilistic solution method called AKNN-MCS (Active learning-based K-Nearest Neighbors-Monte Carlo Simulation) is proposed. Combining the active learning strategy and the KNN algorithm, this method could get accurate POF results using a few samples. In detail, POF calculation is treated as a classification problem. A learning function is proposed to select sample points near the limit state surface. Then the selected sample points are added into training data set T. A convergence criterion is defined to decide when to stop the enrichment of T. Thanks to the above active learning strategy, the trained KNN model could have a great generalization ability with only a few training samples required. The proposed method is validated by POF assessment of a finite thickness plate containing a surface semi-elliptical crack and POF assessment of the CT specimen. Results show that AKNN-MCS is three or four orders of magnitude more efficient than MCS for almost identical POF results.

Probability of detection modelling in eddy current NDE of flaws integrating multiple correlated variables

A new method to model the probability of detection (PoD) of flaws that takes into consideration the correlation between the flaw features as a function of the correlated flaw dimensions, the length and depth, is proposed in this work. Boundary element method was used to efficiently obtain the required flaw features. The features used are the maximum change in the amplitudes of the three components of the scattered magnetic flux density (Bx, By and Bz). Firstly, the magnetic-electric Green's function, for a finite thickness plate, is formulated. On knowing the distribution of the dipole density, the scattered fields at the axial center of the coil are computed. Experiments were conducted in a controlled environment to validate the predictions of the BEM. The features, from the BEM, computed for several flaw lengths and depths, were fit to a trivariate Gaussian distribution. The discrete form of the PoD was determined after identifying the sensor threshold. A continuous function is later obtained by linking the discrete PoD with a generalized logistic function.