Closed-form Relations Research Articles

Tunable metasurfaces for seismic Love wave manipulation: A theoretical study

Seismic Love waves are horizontally polarized surface waves propagating within an overlying layer, which have been shown to pose potential hazards to infrastructures. In this study, we propose an original analytical formulation to investigate the interaction between seismic Love waves and a metasurface that is composed of a cluster of tunable anti-plane resonators. The formulation utilizes the Green's function of a layered half-space subjected to a surface SH source, to describe both the source-induced incident field and the resonator-excited scattered field. Based on the multiple scattering theory, we obtain the total wavefield of the layered half-space equipped with surface resonators by coupling the incident field and the scattered field. Besides, a closed-form dispersion relation governing the hybrid Love waves is derived by utilizing the effective medium approximation. We demonstrate the capabilities of our analytical formulation by modelling Love waves propagating across a pair and a cluster of resonators, evidenced by some complex phenomena (e.g., surface-to-bulk wave conversion and higher-order hybridized surface modes). The hybridization features of different Love modes and metasurface resonances are clearly revealed. We anticipate the proposed tunable metasurface and the formulation can shed light on versatile control of Love wave propagation.

Modeling and analysis of dynamic load factor in a fail-safe crane mechanism equipped with a hydraulic equalizing cylinder

In the design and manufacturing of sensitive crane mechanisms, in particular, those utilized in nuclear facilities, safety is of utmost importance. A few designs are based on a hydraulic equalizing cylinder where the purpose is mainly to dampen the dynamic load factor generated by the sudden failure of the wire rope system. To the best of the authors' knowledge, design equations and engineering models for such an intricate dynamic mechanism are not reported anywhere in the literature. Toward achieving this goal, a model is proposed for the dynamic behavior of a hydraulic equalizing cylinder when coupled to a single-failure-proof cross-reeved crane hoist. The constitutive equations involve the time-dependent incompressible Navier-Stokes equations. These equations are coupled with the dynamics of the lower block and the elastic wire rope. A nonlinear second-order ordinary differential equation is obtained, which is solved analytically. This yields a closed-form relation for the dynamic load factor. The validity of the new model is investigated using experimental studies, which are presented in this work. The normalized root mean square error for the dynamic load factor obtained by the model compares favorably to the experimental results, where the maximum observed error is 3.9 percent. The results confirm that the current model can be used as a design equation by practitioners.

RCS reduction using grounded multi-height multi-dielectrics metasurfaces

In this paper, the PO method with the array theory are used to formulate the RCS of a grounded multi-height dielectric surface which can be employed in the design and optimization of a metasurface consisting of dielectric tiles with different heights and permittivities. The proposed closed form relations can be used instead of full wave simulation to design an optimized dielectric grounded metasurface, properly. Finally, three different RCS reducer metasurfaces are designed and optimized with three different dielectric tiles by using the proposed analytical relations. The results prove that the proposed ground dielectric metasurface achieve more than 10 dB RCS reduction at 4.4–16.3 GHz (114.9%) frequency range. This result proves the accuracy and effectiveness of the proposed analytical method which can be used in the RCS reducer metasurfaces design.

Lateral Static Response of Piles Based on a Full-Fledged Two-Parameter Foundation Model

A rigorous analytical continuum subgrade model translated into an equivalent two-parameter mechanical model of the Pasternak type is used to study the static response of piles to lateral loads. The model fully accounts for the soil shear missing in the conventional Winkler representation. The two parameters of the model are derived in advance. After conducting static analyses of a wide range of cases of the pile–soil system using both the proposed analytical model and finite-element models, closed-form relations are obtained for the adjustment factor left open in the model parameters that are found to mainly depend on the soil’s Poisson’s ratio. Back substitution of this factor showed that the model parameters take simple forms that depend only on a few factors such as the pile–soil stiffness ratio and the pile-end conditions. The model is validated by means of results of finite-element models. Closed-form pile head stiffness coefficients for various pile-end conditions are provided for both infinite- and finite-length piles. Expressions for a newly defined pile critical length are proposed for several combinations of pile-end conditions. It is demonstrated that the analytical approach employed is convenient and avoids the high degree of empiricity inherent in the conventional Winkler-based backward approach. The model has also the unique advantage of being convenient to conduct parametric studies, including the influence of soil shear resistance.

Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions

<abstract><p>Analyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type $ P(X < Y) $ when both $ X $ and $ Y $ follow a generalized extreme value (GEV) distribution with three parameters. At first, we derive new analytical and closed form relations in terms of the extreme value $ \mathbb{H} $-function, which have been obtained under fewer parameter restrictions compared to similar results in the literature. To show the performance of our results, we include a Monte-Carlo simulation study and we investigate the application of the reliability measure $ P(X < Y) $ in selecting financial assets with returns characterized by the distributions $ X $ and $ Y $. Therefore, rather than the conventional approach of comparing the expected values of $ X $ and $ Y $ based on modern portfolio theory, we delve into the metric $ P(X < Y) $ as an alternative parameter for assessing better returns.</p></abstract>

Artificial Intelligence Model for Risk Management in Healthcare Institutions: Towards Sustainable Development

This paper proposes an artificial intelligence model to manage risks in healthcare institutions. This model uses a trendy data source, social media, and employs users’ interactions to identify and assess potential risks. It employs natural language processing techniques to analyze the tweets of users and produce vivid insights into the types of risk and their magnitude. In addition, some big data analysis techniques, such as classification, are utilized to reduce the dimensionality of the data and manage the data effectively. The produced insights will help healthcare managers to make the best decisions for their institutions and patients, which can lead to a more sustainable environment. In addition, we build a mathematical model for the proposed model, and some closed-form relations for risk analysis, identification and assessment are derived. Moreover, a case study on the CVS institute of healthcare in the USA, and our subsequent findings, indicate that a quartile of patients’ tweets refer to risks in CVS services, such as operational, financial and technological risks, and the magnitude of these risks vary between high risk (19%), medium risk (80.4%) and low risk (0.6%). Further, several performance measures and a complexity analysis are given to show the validity of the proposed model.

Nonlinear thermo-electro-mechanical free vibrations of sandwich nanocomposite beams bonded with sensor layers considering pyroelectricity

An examination on the linear as well as nonlinear thermo-electro-mechanical free vibrations of a sandwich piezoelectric beam is performed in this research. Core layer has been strengthened with graphene platelets. Two piezoelectric layers as sensors are bonded to the bottom and top surfaces of the core layer. The formulation is developed for beams with general immovable end supports. A nonlinear integro-partial differential equation along with its nonlinear boundary conditions is discharged presuming a second order approximation for the nonlinear normal strain. The direct technique of multiple scales treats the nonlinear governing integro-partial differential equation along with its associated nonlinear boundary conditions. Subsequently, an analytical closed form relation is released for the estimation of amplitude dependent nonlinear natural frequencies. It is shown that the strengthening of a beam that is experiencing a thermal environment during its work with the graphene platelets becomes dysfunctional since it promotes the chance of static instability occurrence. On the other hand, it is seen that the pyroelectricity can postpone the static instability possibility. Furthermore, the pyroelectricity alleviates the hardening nonlinearity. Moreover, at large amplitude of vibrations, the influences of the temperature developing, the pyroelectricity, and the graphene platelet weight fraction decline.

Flexural waves at the edge of nonlocal elastic plate associated with the Pasternak foundation

In this article, an elastic foundation is used to study the characteristics of flexural edge waves propagating on a piezoelectric structure. The nonlocal elasticity theory is introduced to investigate the microscale effect on edge wave propagation. The traditional Kirchhoff plate hypothesis is used to determine the kinematics of the piezoelectric plate. By considering the sinusoidal waveform, a closed-form dispersion relation can be obtained. In the context of a flexural edge wave on a piezoelectric plate, an analytical and graphical comparison between the two boundary conditions (i.e. short circuit and open circuit) is discussed. In the presence of nonlocal elasticity, the dispersion relation is implied as an implicit function of frequency and wave number. A significant difference occurred between the dispersion curves for piezoelectric plates with different foundations and nonlocal parameters. Due to the Pasternak elastic foundation, an increasing rate of the fundamental mode of frequency is observed at the traction-free edge of a thin, semi-infinite piezoelectric plate. In contrast, the nonlocal elasticity tends to decrease this fundamental frequency mode for a particular wave number value. The corresponding phase velocity decreases rapidly within a short range of wave numbers.

Simulation of gasketed-plate heat exchangers using a generalized model with variable physical properties

In this article, we present a new generalized model for the steady-state simulation of gasketed-plate exchangers handling single-phase fluids with properties varying with temperature. The model is based on differential balance equations that are discretized using a finite-difference scheme. The set of equations of the proposed model can simulate gasketed-plate heat exchangers with any configuration, encompassing any number of passes for each stream and including the variation of the streams’ physical properties with temperature. The selection of a given configuration is provided by a set of model parameters, without the need to modify the system of equations. Comparisons of the simulation results with closed-form relations valid for an infinite number of plates and with a numerical solution indicate average differences equal to 0.17 % and 0.075 %, respectively. The comparison with experimental data available in the literature indicates mean deviations smaller than 2 °C. The analysis of the simulation results of a typical heat exchanger shows that the models usually employed in the design optimization problems, based on uniform physical properties, may present large departures from the results of our detailed modeling, based on varying properties with temperature, which for its nature is considered more accurate. Moreover, when used in a design, we show that uniform physical properties may yield exchangers that are either oversized or undersized as compared to the use of our model. Therefore, the capacity of the proposed model to provide more accurate simulation results for any gasketed-plate heat exchanger configuration using a unique set of equations is an important contribution to future works involving heat exchanger design optimization.

Reconstruction of time-shifted hemodynamic response

Regression of voxel time course onto expected response is a standard procedure in functional magnetic resonance imaging that relies on exact onset time and shape of superimposed hemodynamic response functions. Elegant capture of time deviation by time derivative regressors appears complicated by shape distortion and limited to ±1 s, and is usually not exploited for reconstructing the true time-shifted response function together with its magnitude. This analysis of the time-derivative approach provides closed-form functional relations between time shift and regression coefficients that allow for hemodynamic shifts of ±5 s and can explain shape distortion and reconstruction behavior. Reliable absolute latencies were no smaller than 0.6 s in a best-case experiment. Confusions of latency are a previously undiscussed shortcoming where current limitation strategy may eliminate correct latencies and protect incorrect ones.

Distributed State Estimation for Continuous-Time Linear Systems With Correlated Measurement Noise

In this article, the problem of distributed state estimation for a continuous-time linear system with a sensor network is investigated, where each sensor can only communicate with its neighbors and contains time-correlated measurement noise. To solve this problem, a novel augmented leader-following information fusion strategy is first proposed to collect measurements and system matrices. Then, a class of distributed state estimators is developed with bounded estimation error covariances. Further, a closed-form relation between the designed distributed estimator and the centralized estimator is established. It is found that the estimation performance of the former converges to that of the latter when the consensus gain tends to infinity. The proposed estimator is further extended to the fully distributed case by introducing an adaptive law for the consensus gain without using any global information. Moreover, it is shown that the designed estimator is applicable for systems with deterministic noise. Finally, several comparative numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results.

Buckling behavior of spiral stiffened sandwich FGM cylindrical shells with porous core under axial compression using the FSDT

The linear buckling behavior of functionally graded cylindrical shells with porous core stiffened by spiral stiffeners under axial compression using the first-order shear deformation theory is presented in this paper. The improved Lekhnitskii’s smeared stiffeners technique is applied for shear deformable spiral FGM stiffeners. Approximate analytical solutions are assumed to satisfy the simply supported boundary conditions and the adjacent equilibrium criterion is applied to obtain closed-form relations of buckling loads. Effects of the number of FGM stiffeners, stiffener angle, volume fraction index and porosity coefficient on the buckling behavior of shells are numerically investigated.

Buckling behavior of spiral stiffened sandwich FGM cylindrical shells with porous core under axial compression using the FSDT

The linear buckling behavior of functionally graded cylindrical shells with porous core stiffened by spiral stiffeners under axial compression using the first-order shear deformation theory is presented in this paper. The improved Lekhnitskii’s smeared stiffeners technique is applied for shear deformable spiral FGM stiffeners. Approximate analytical solutions are assumed to satisfy the simply supported boundary conditions and the adjacent equilibrium criterion is applied to obtain closed-form relations of buckling loads. Effects of the number of FGM stiffeners, stiffener angle, volume fraction index and porosity coefficient on the buckling behavior of shells are numerically investigated.

Buckling behavior of spiral stiffened sandwich FGM cylindrical shells with porous core under axial compression using the FSDT

The linear buckling behavior of functionally graded cylindrical shells with porous core stiffened by spiral stiffeners under axial compression using the first-order shear deformation theory is presented in this paper. The improved Lekhnitskii’s smeared stiffeners technique is applied for shear deformable spiral FGM stiffeners. Approximate analytical solutions are assumed to satisfy the simply supported boundary conditions and the adjacent equilibrium criterion is applied to obtain closed-form relations of buckling loads. Effects of the number of FGM stiffeners, stiffener angle, volume fraction index and porosity coefficient on the buckling behavior of shells are numerically investigated.

Computationally Efficient Region-Wise Potential- Based Extremely Closed-Form Analytical Modeling of B/N Substitution Doped GFETs

A simplified region-wise potential-based analytical model is established for boron (B) or nitrogen (N) substitution doped graphene field-effect transistor (GFET). The closed-form direct analytical relation between graphene channel potential and applied bias condition is developed by imposing the effective approximation for Fermi–Dirac integral function in various regions of operation. The boundary for distinct GFET operating regime is separated based on the position of Dirac point and Fermi energy level with respect to applied bias condition. The semiclassical drift and diffusive transport model is utilized to obtain the drain current. In addition to that, the drift component, diffusion coefficient, and its corresponding current component for B and N substitution doped GFETs have been modeled individually and their influence on total current is discussed. The proposed region-potential-based analytical model has shown good agreement with numerically solved self-consistent model. Also, the physical insights in device design, such as threshold voltage and saturation drain potential model with respect to various doping/device parameters, have been examined.

XFEM modeling of the effect of in-situ stresses on hydraulic fracture characteristics and comparison with KGD and PKN models

Increasing the permeability of hydrocarbon reservoirs by creating artificial cracks that are induced by injection of fluids under high pressure is called hydraulic fracturing (HF). This method is widely used in petroleum reservoir engineering. For design of Hydraulic Fracture operations, several analytical models have been developed. KGD and PKN are the first and most used analytical models in this area. Although number of advanced softwares are developed in recent years, KGD and PKN models are still popular and have even been used in a number of softwares. In both models the characteristics of the fracture namely: fracture length (L), fracture width (w), and fluid pressure at the crack mouth (p) are determined based on closed form relations using the reservoir rock shear stiffness, Poisson’s ratio, fluid injection rate, and injection time. Despite their ease of use, KGD and PKN models do not consider some important geo-mechanical and hydro-mechanical parameters and this shortcoming makes their results to be approximate. The aim of this study is evaluating the effects of in-situ stress on the fracture length, width, and fluid pressure employing XFEM method. In this study, tensile fracture mode and cohesive zone model are used for creation and propagation of cracks. In this paper, by conducting a series of numerical simulations using XFEM and after verification of the results, the accuracy of the analytical formulas of KGD and PKN models are examined. The results show that due to some simplifying assumptions used in KGD and PKN analytical models and neglecting some hydraulic and geomechanical parameters such as in-situ stresses, the length, width, and fluid pressure of the crack obtained from analytical formulas differ from the results of the numerical simulations. In this paper, the effects of in-situ stresses on hydraulic fracture characteristics (width, length, and crack mouth fluid pressure) are investigated and presented in the form of a number of correction (modification) factors that can be used for improvement of the results of KGD and PKN models. The findings of this study can help for more accurate design of hydraulic fracture process in oil industry for increasing the production of hydrocarbon reservoirs.

Generalized coupled thermoelasticity in an orthotropic rotating disk subjected to thermal shock

The problem of thermal shock in an orthotropic rotating disk is solved analytically using the Lord-Shulman coupled theory of thermoelasticity. Finite Hankel transform (Fourier-Bessel expansion) is used to present closed-form relations for the temperature and displacement fields. To simplify the problem, coupled equations of thermoelasticity are transferred into nondimensional form and the effects of the relaxation time on the history and the distribution of the temperature, displacement and stress components are investigated. Differences between boundary conditions in propagation and reflection of the elastic wave from boundaries are observed on figures. To show the effects of considering different mechanical properties in each principal direction, an orthotropicity factor is introduced and the stress components for different values of this factor are plotted. In order to validate the present work, the orthotropic disk is reduced to the isotropic one by considering the same material properties in different directions and the results are compared with a numerical study and an analytical solution, which show good agreement.

NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems

In this work, we establish a goal-oriented space–time finite element method for a class of dissipative heterogeneous materials. Those materials are modeled on both micro- and macroscale, with a scale transition of volume averaging type satisfying the Hill–Mandel condition. A nonuniform transformation field analysis is performed on the microscopic inelastic strain fields for a model reduction. Reduced variables are deduced from a space–time decomposition of those inelastic strain fields. Closed-form constitutive relations are derived from some dissipative considerations, thus resulting into a reduced order homogenization problem. The resulting model error is sufficiently small for the considered class of materials, thus leaving the discretization error of the finite element method as a main error source. For ease of error estimate, we rewrite the reduced order problem in a multifield formulation. Based on duality techniques, a backward-in-time dual problem is derived from a Lagrange method, rendering error representations of a user-defined quantity of interest. Combining a patch recovery technique, a computable error estimator is developed to quantify both spatial and temporal discretization errors. By means of a localization technique, local error estimators are used to drive a greedy adaptive refinement algorithm in space and time. The effectiveness of the resulting algorithm is confirmed by several numerical examples w.r.t. a prototype model.

Love-type surface wave propagation due to interior impulsive point source in a homogeneous-coated anisotropic poroelastic layer over a non-homogeneous extended substance

The paper is concerned with the effect of an impulsive point source on the Love-type surface wave propagation in an anisotropic poroelastic medium coated with an isotropic homogeneous thin layer over an infinite extent anisotropic non-homogeneous substance. The material properties of both the layer and extended medium are restricted on linear elasticity. Also, the transmissions of waves are considered as usually incidental transient. Infinitely extended medium is considered highly non-homogeneity with rigidity and density, which varies exponentially with depth. The closed-form equation of motion is formulated in each layered media depending on the conditional property of the surface seismic wave. Due to the presence of an impulsive point source at the interface of the intermediate layer and infinitely extended layer, a force density distribution function in the form of the Dirac-delta function is performed with the equations of motion. Green's function approach is demonstrated to obtain the closed-form dispersion relation of the Love-type wave. Attenuation analysis and numerical error analysis of the dispersive wave are performed for the complex quantity of the wavenumber and error percentage of the main dispersion. The validity of the Love-type dispersive wave is examined with the help of some particular cases. The theoretical prediction of phase and group velocities are illustrated numerically using MATLAB software. A short movie (link) of group velocity is created to show the changes of wave amplitude with porosity. It is observed that the phase/group velocity is highly affected by porosity, non-homogeneity, anisotropy, thickness of the layer, coated layer and attenuation coefficient. The derivation and analysis of the structural model bear the promise of having important applications in the field of seismology and civil engineering, particularly in the studies related to earthquakes and mechanical explosions on the near-surface of the Earth.

A multisymplectic Lie algebra variational integrator for flexible multibody dynamics on the special Euclidean group SE (3)

A multisymplectic Lie algebra variational integrator (MLAVI) for simulating the dynamics of a flexible multibody system is proposed. The flexible bodies are described by the geometrically exact beam elements established on the special Euclidean Lie group SE(3). A lemma is also provided to demonstrate that the used discrete compatibility equation can make temporal and spatial interpolation independent. Then, the reduced Lagrangian density on the Lie algebra is derived, and the discrete dynamics of motions are established by the discretization of the covariant variational principle. Furthermore, another novel closed-form equality relation lemma on the right tangent maps of the associated exponential map and Cayley map is originally proved, which greatly helps to simplify the Jacobi matrix of the proposed MLAVI in the Newton iteration process. The accuracy and efficiency of the proposed MLAVI are validated by six static and dynamic numerical examples. Numerical results show that the proposed MLAVI can preserve the system's symplectic structure, momentum, and energy for long-time simulation.