Imperfect Boundary Conditions Research Articles

Investigating the Performance of CMIP6 Seasonal Precipitation Predictions and a Grid Based Model Heterogeneity Oriented Deep Learning Bias Correction Framework

AbstractClimate change is expected to alter the magnitude and spatiotemporal patterns of hydro‐climate variables such as precipitation, which has significant impacts on the ecosystem, human societies and water security. Global Climate Models are the major tools to simulate historical as well as future precipitation. However, due to imperfect model structures, parameters and boundary conditions, direct model outputs are subject to large uncertainty, which needs serious evaluation and bias correction before usage. In this study, seasonal precipitation predictions from 30 Coupled Model Inter‐comparison Project Phase 6 (CMIP6) models and Climate Research Unit observations are used to evaluate historical precipitation climatology in global continents during 1901–2014. A grid based model heterogeneity oriented Convolutional Neural Network (CNN) is proposed to correct the ensemble mean precipitation bias ratio. Besides, regression based Linear Scaling (LS), distribution based Quantile Mapping (QM) and spatial correlation CNN bias correction approaches are employed for comparison. Results of model performance evaluation indicate that generally precipitation prediction is more reliable in JJA than DJF on the global scale. Most models tend to have larger bias ratio for extreme precipitation. In addition, current CMIP6 models still have certain issues in accurate simulation of precipitation in mountainous regions and the regions affected by complex climate systems. Moreover, the proposed grid based model heterogeneity oriented CNN has better performance in ensemble mean bias correction than LS, QM, and spatial correlation CNN, which could consider the relative model performance and capture the features similar to actual climate dynamics.

Fourier transform approach to homogenization of frequency-dependent heat transfer in porous media

Purpose The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution. Design/methodology/approach The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes. Findings Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems. Originality/value The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.

Detection of transversal cracks in prismatic cantilever beams with weak clamping using machine learning

Because our infrastructure is aging and approaching the end of its intended functioning time, the detection of damage or loosening of joints is a topic of high importance in structural health monitoring. The most desired way to assess the health of engineering structures during operation is to use non-destructive vibration-based methods that can offer a global evaluation of the structure’s integrity. A comparison of using different modal data for training feedforward backpropagation neural networks for detecting transverse damages in beam-like structures that can also be affected by imperfect boundary conditions is presented in the current paper. The different RFS, RFSmin, and DLC training datasets are generated by applying an analytical method, previously developed by our research team, that uses a known relation, based on the modal curvature, severity estimation of the transverse crack, and the estimated severity for the weak clamping. The obtained dataset values are employed for training three feedforward backpropagation neural networks that will be used to locate transverse cracks in cantilever beams and detect if the structure is affected by weak clamping. The output from the three ANN models is compared by plotting the calculated error for each case.

A new approach for imperfect boundary conditions on the dynamic behavior

Real beams have non-ideal boundary conditions and it is necessary to use new models to determine the real modal parameters. Models that use ideal conditions do not fully reflect reality and can lead to unsatisfactory description of the dynamic behavior. The hinged – hinged boundary conditions, which is in the focus of the paper, are not analyzed as a single beam, but as a continuous beam with three spans, free at the ends. The continuous beam with three spans is analyzed for cases in which the intermediate supports can occupy any position along the length of the beam, by an analytical solution of the problem, with the example of cases when the intermediate supports are located very close at the free ends of the continuous beam, thus simulating the real case for an hinged beam at both ends; the situation in which the intermediate supports are very close to one of the ends of the beam, thus simulating the real case of the clamped beam, with an imperfect clamped end; and the situation in which the intermediate supports are very close located anywhere on the beam length, thus simulating the hypothetic case with a continuous beam free at the ends and fix on the hinged supports. The analytic results are compared with numerical results by using finite elements method.

Effects of homojunction on the reflected and transmitted waves at the interface between two thermoelastic semiconductor half spaces

It is systematically investigated that the influence of interface effect resulted from one homojunction on the reflected and transmitted thermoelastic waves between two bonded homogeneous isotropic thermoelastic semiconductor half spaces in this paper. Considering the geometrical and physical characteristics of homojunction, it is approximately treated as a two-dimensional isotropic imperfect interface without geometrical thickness mathematically but with elastic, thermal and semiconductor properties depicted through a dimensionless characteristic length factor physically. Considering the coupling effect of mechanical displacement, temperature change and charge carrier concentration perturbation, the imperfect interface boundary condition is established based on the generalized Green-Naghdi theory, the surface and interface elastic theory and the physical property of homojunction. The algebraic equation resulted from this imperfect interface boundary condition is solved to obtain the reflected and transmitted coefficients of thermoelastic waves expressed in the energy flux ratio, which are verified by the principle of energy conservation. The numerical calculation results demonstrate that the increase of geometrical thickness of homojunction and the angular frequency of thermoelastic waves can enhance the interface imperfect property and arise more evident influence of interface effect. Meanwhile, the interface effect has a more evident influence on the thermoelastic waves propagating along the interface normal direction. The physical mechanism revealed through the establishment of mathematical model provides a theoretical basis for using PN junction to regulate the propagation properties of thermoelastic waves in thermoelastic semiconductors.

A Wave Diffraction Problem with Higher Order Impedance Boundary Conditions

In this paper, we consider an impedance boundary transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. Operator theoretical methods and relations between operators are built to deal with the problem and, as consequence, a transparent interpretation of the problem in an operator theory framework are associated to the problem. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. At the end, we describe when the operators associated with the problem enjoy the Fredholm property in terms of the initial space order parameters.

Effects of Imperfect Simple Shear Test Boundary Conditions on Monotonic and Cyclic Measurements in Sand

AbstractThe direct simple shear (DSS) test is commonly used to assess the shear strength of soil, estimate liquefaction resistance, or calibrate constitutive models under the assumption of idealize...

Analytical study of electro-mechanical parameters on Love wave in an imperfectly bonded VPCM layered structure

This study is carried out to investigate the mechanical and electrical characteristics of Love waves in a visco-piezo-composite medium bounded between an orthotropic upper stratum and an elastic substrate of conducting type medium. The mechanically imperfect boundary conditions have been considered for both the interfaces of the sandwiched stratum. By solving coupled electromechanical field equations analytically, the electric potential, and mechanical displacement are obtained for the respective medium. After that, by using the relevant boundary conditions, the expression of dispersion has been established. The effect of various parameters such as viscosity, piezo-electric, dielectric, imperfection parameter, thickness ratio parameters on phase velocity, and attenuation coefficient of Love waves have been discussed. For the validation of our solution, the classical Love wave equation is obtained in the limiting sense (i.e. in the absence of piezoelectricity, upper surface, viscosity, imperfection parameters). To date, nobody has considered a Voigt-type viscous effect in composite piezo-structure to study Love wave propagation, even in the latest research works. Results indicate that the piezo-electric parameter possesses a great positive impact on phase velocity and attenuation coefficient. The attenuation co-efficient converges to some constant magnitude for different values of the thickness ratio parameter. The present investigation may find various applications in many problems of automatic remote control, space exploration, and piezoelectric ceramic devices. Moreover, it can be used in the investigation of the deformation and mechanical behavior of the sedimentary rock.

Deployment behavior of planar gossamer space structures made of plain-woven textile

Multifunctional membrane space structures have been developed in the past to realize solar arrays, array antennas, and other applications. However, the deployment of a folded membrane often requires fluctuating forces with high peaks, caused by the stiffness of the crease lines. This study proposes the use of a plain-woven textile as the base membrane for the planar deployment structures primarily because of its high packaging efficiency. The deployment forces required for the folded plain-woven textile structures to be employed in future space applications are experimentally measured. The deployment forces are compared between the proposed textile structures and the conventional film-based membranes to characterize the deployment behavior of the textile structures. Two types of experiments are conducted in this study for the one-dimensional deployment of v-folded membranes and the two-dimensional deployment of quarter Flasher origami structures, respectively. The advantages presented by the deployable textiles are as follows: (i) they require smaller and smoother deployment forces, and (ii) they are insensitive to imperfect boundary conditions. These features are important for the reliable deployment of future space structures.

Plane wave reflection/transmission in imperfectly bonded initially stressed rotating piezothermoelastic fiber-reinforced composite half-spaces

The effects of different types of imperfect interfaces, normal and shear initial stresses and rotation on the reflection and transmission characteristics of plane waves in two dissimilar piezothermoelastic fiber-reinforced composite (PTFRC) half-spaces are analytically studied in this article. The PTFRC structure is modeled employing the Strength of Materials (SM) technique with the Rule of Mixtures (RM) approach. Numerical studies are performed on two distinct PTFRCs comprised of CdSe–epoxy combination and PZT-5A-epoxy combination. Several reasons, like the inevitable presence of interfacial defects because of accumulative damages, have detrimental effects on the life expectancy and efficiency of structures manufactured using smart materials. For the same reasons, the bond between half-spaces is generally not perfect. Thus, the mechanical–electrical-thermally imperfect boundary is classified into seven types, viz. Normal Stiffness Boundary (NSB), Transverse Stiffness Boundary (TSB), Thermal Contact Conductance (TCC), Electrically Imperfect Boundary (EIB), Slip Boundary (SB), Completely Debonded Boundary (CDB) and Welded Contact (WC), which are analyzed individually. Initial stresses and rotation are also considered for making the present model more realistic. The closed-form expressions of amplitude ratios of reflected and transmitted quasi-longitudinal (qP), quasi-transverse (qSV), thermal (T-mode) and electro-acoustic (EA) waves are derived by means of appropriate mechanical–electrical-thermally imperfect boundary conditions. Using these, the energy ratios of all waves along with the interaction energy among various waves are obtained and the Law of Conservation of Energy is validated. Comparative analysis among the Classical dynamical coupled, Lord–Shulman and Green–Lindsay thermoelasticity theories is performed. The influences of the incident angle, imperfect interfaces, rotation, varying magnitudes of normal and shear initial stresses and thermal relaxation parameters on the energy ratios are illustrated graphically. Some special cases exclusive to this study are shown which validate the obtained results with extant literature and possible scientific and engineering applications of the present model are discussed.

A method to detect cracks in the beams with imperfect boundary conditions

Non-destructive testing of structures involving vibration-based damage detection methods implies knowing the beam’s boundary conditions. For perfect boundary conditions, numerous damage detection methods are developed and ensure more or less accurate estimation of the crack type, position, and severity. On the contrary, for imperfect boundary conditions, which are the real ones, there are only a few dedicated works. This paper presents a methodology that allows the identification of the weak clamping and the crack if both exist. The weak clamping is modelled as a defect that produces an identical relative frequency shift (RFS) for all vibration modes. Therefore, to find the two defects namely the real crack and defect simulating the weakly clamped end, we apply the principle of superposition. The method is implemented as an application written in the Python programming language. Tests show that defects are successfully identified even if there are uncertainties about the fixing of the beam.

Transient response of a concrete tunnel in an elastic rock with imperfect contact

The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated. Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design. The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock. Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series. To solve the transient problem, the Laplace transform and the associated Durbin’s algorithm are performed. To exhibit the dynamic responses, influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented. The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.

Anti-plane dynamic response of a non-circular tunnel with imperfect interface in anisotropic rock mass

In anisotropic rock mass, the dynamic response of a non-circular tunnel with imperfect interface is theoretically presented under an incidence of an anti-plane SH wave. For the anti-plane problem in anisotropic medium, three elastic constants can describe the characteristics of medium anisotropy according to the generalized Hooke’s Law. The wave function expansion method and the complex function are applied to express the wave fields with three unknown coefficients. By introducing the spring elastic model, the imperfect boundary condition around the tunnel lining can be satisfied to determine the coefficients. In numerical examples, effects of rock anisotropy and imperfect interface around the tunnel lining are discussed in detail, accompanied with incident angle and wave frequency. Analytical solutions show that both rock anisotropy and interface have considerable influence on the dynamic response of underground structures, which should be paid attention to for the design and construction of deep underground tunnels.

Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave

With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.

Experimental and computational investigation of the blast response of Carbon-Epoxy weathered composite materials

Abstract An experimental study with corresponding numerical simulations was conducted to investigate the blast response of weathered Carbon-Epoxy composite plates. The dynamic behavior of the composite plates with and without prior exposure to an aggressive marine environment was explored using a shock tube apparatus coupled with a high speed photography system. In order to simulate prolonged exposure in an aggressive marine environment, specimens were submerged in an elevated temperature, 3.5% salt solution for 0, 30 and 60 days. The saline solution temperature was maintained at 65 °C to accelerate the aging process. Finite Element Modeling (FEM) for the blast loading experiments was performed using the Ls-Dyna code. Models have been developed for both the simply supported and fixed boundary condition cases. Tensile and four point bend tests were performed to characterize the quasi-static mechanical behavior of the composite material before and after prolonged exposure to aggressive marine environments. After 30 and 60 days of submergence, the tensile modulus decreased by 11% and 13%, the ultimate tensile strength decreased by 12% and 13%, and the ultimate flexural strength decreased by 22% and 22%, respectively. Dynamic blast loading experiments were performed on simply supported and fully clamped specimens, to determine the effects of the boundary conditions on the Carbon-Epoxy specimen response. The Weathered (30 and 60 days) and Non-Weathered (0 day) specimens displayed dramatically different behavior after being subjected to a blast load. For the simply supported case, Non-Weathered specimens displayed an average maximum out of plane displacement of 20 mm and recovered elastically. Weathered specimens, both 30 and 60 days exhibited similar initial transient behavior but failed catastrophically due to through thickness cracking at the point of maximum deflection. For the fixed boundary condition, the Non-Weathered specimens displayed an average maximum out of plane displacement of 5.57 mm, whereas the 30 day and 60 day weathered specimens displayed a maximum out of plane displacement of 6.89 mm and 6.96 mm, respectively. The corresponding numerical simulations matched well with the experimental data. However, for the fixed boundary case, the beam vibration of the simulation was off phase with the experimental results due to imperfect boundary conditions in the experiments.

Acoustic emission based damage localization in composites structures using Bayesian identification

Acoustic emission based damage detection in composite structures is based on detection of ultra high frequency packets of acoustic waves emitted from damage sources (such as fibre breakage, fatigue fracture, amongst others) with a network of distributed sensors. This non-destructive monitoring scheme requires solving an inverse problem where the measured signals are linked back to the location of the source. This in turn enables rapid deployment of mitigative measures. The presence of significant amount of uncertainty associated with the operating conditions and measurements makes the problem of damage identification quite challenging. The uncertainties stem from the fact that the measured signals are affected by the irregular geometries, manufacturing imprecision, imperfect boundary conditions, existing damages/structural degradation, amongst others. This work aims to tackle these uncertainties within a framework of automated probabilistic damage detection. The method trains a probabilistic model of the parametrized input and output model of the acoustic emission system with experimental data to give probabilistic descriptors of damage locations. A response surface modelling the acoustic emission as a function of parametrized damage signals collected from sensors would be calibrated with a training dataset using Bayesian inference. This is used to deduce damage locations in the online monitoring phase. During online monitoring, the spatially correlated time data is utilized in conjunction with the calibrated acoustic emissions model to infer the probabilistic description of the acoustic emission source within a hierarchical Bayesian inference framework. The methodology is tested on a composite structure consisting of carbon fibre panel with stiffeners and damage source behaviour has been experimentally simulated using standard H-N sources. The methodology presented in this study would be applicable in the current form to structural damage detection under varying operational loads and would be investigated in future studies.

Dynamic Response of Lined Circular Tunnel in Linear Viscoelastic Medium Due to Moving Ring load

A two dimensional elasticity analysis for steady state axisymmetric dynamic response of an arbitrarily thick elastic homogeneous hollow cylinder of infinite length, which is imperfectly bonded to the surrounding viscoelastic soil, subject to an axially moving ring load, is presented. The soil is described with the model of Kelvin-Voigt model, and imperfect boundary condition for circular tunnel is adopted. The problem solution is derived in Laplace transform. Numerical solutions for the displacement, pore pressure and stresses are calculated by analytical inversion of the Laplace transformation with respect to the frequency.

Size-dependent bending modulus of nanotubes induced by the imperfect boundary conditions.

The size-dependent bending modulus of nanotubes, which was widely observed in most existing three-point bending experiments [e.g., J. Phys. Chem. B 117, 4618–4625 (2013)], has been tacitly assumed to originate from the shear effect. In this paper, taking boron nitride nanotubes as an example, we directly measured the shear effect by molecular dynamics (MD) simulations and found that the shear effect is not the major factor responsible for the observed size-dependent bending modulus of nanotubes. To further explain the size-dependence phenomenon, we abandoned the assumption of perfect boundary conditions (BCs) utilized in the aforementioned experiments and studied the influence of the BCs on the bending modulus of nanotubes based on MD simulations. The results show that the imperfect BCs also make the bending modulus of nanotubes size-dependent. Moreover, the size-dependence phenomenon induced by the imperfect BCs is much more significant than that induced by the shear effect, which suggests that the imperfect BC is a possible physical origin that leads to the strong size-dependence of the bending modulus found in the aforementioned experiments. To capture the physics behind the MD simulation results, a beam model with the general BCs is proposed and found to fit the experimental data very well.

Influence of imperfect end boundary condition on the nonlocal dynamics of CNTs

Imperfections that unavoidably occur during the fabrication process of carbon nanotubes (CNTs) have a significant influence on the vibration behavior of CNTs. Among these imperfections, the boundary condition defect is studied in this investigation based on the nonlocal elasticity theory. To this end, a mathematical model of the non-ideal end condition in a cantilever CNT is developed by a strongly non-linear spring to study its effect on the vibration behavior. The weak form equation of motion is derived via Hamilton’s principle and solved based on Rayleigh–Ritz approach. Once the frequency response function (FRF) of the CNT is simulated, it is found that the defect parameter injects noise to the FRF in the range of lower frequencies and as a result the small scale effect on the FRF remains undisturbed in high frequency ranges. Besides, in this work a process is introduced to estimate the nonlocal and defect parameters for establishing the mathematical model of the CNT based on FRF, which can be competitive because of its lower instrumentation and data analysis costs. The estimation process relies on the resonance frequencies and the magnitude of noise in the frequency response function of the CNT. The results show that the constructed dynamic response of the system based on estimated parameters is in good agreement with the original response of the CNT.

Interaction of two shallow non-circular tunnels with imperfect interfaces subjected to shear waves

The dynamic interaction of two non-circular shallow tunnels with imperfect interfaces subjected to anti-plane waves is investigated, and the semi-analytical solution of dynamic stress with the half-plane boundary effect is presented. The spring model is adopted to analyse the effect of imperfect interfaces between the tunnel and the rock mass on the dynamic stress. The half-plane boundary is modelled by an arc with a large radius to satisfy the traction-free boundary condition. Combining the wave function expansion method and conformal transformation method, the analytical solutions of stresses and displacements are expanded in terms of wave functions. The expanded coefficients are determined by satisfying the imperfect boundary conditions around the tunnels and the traction-free boundary condition at the surface. Some numerical examples are provided to discuss the imperfect interface effects on the dynamic stress under different depths of tunnels and different distances between the two tunnels. Comparison with existing numerical results validates this present dynamic model.