Additional Boundary Conditions Research Articles

Applicability and efficacy of Galerkin-based approximation for solving the buckling and dynamics of nanobeams with higher-order boundary conditions

In this research effort, the general nonlocal elasticity theory is applied to an axially-loaded Euler-Bernoulli nanobeam with varying boundary conditions. In applying the general nonlocal elasticity theory, a modified version of Eringen's nonlocal elasticity theory, a sixth-order partial differential equation is obtained for the transverse governing equation of motion. Obtaining the sixth-order equation created the need for additional non-classical beam boundary conditions. These boundary conditions are determined using the weighted residual approach and are physically interpreted as higher-order force and moment terms. This study investigates the buckling and dynamic responses of nanobeams using a Galerkin-based approximation with different trial mode shapes, as it relates to the exact solution. As such, comparisons are made between using three distinct types guess functions in the approximation, namely, the exact unloaded classical mode shapes, exact unloaded Eringen nonlocal mode shapes, and exact unloaded general nonlocal mode shapes. Unloaded mode shapes refer to the mode shapes in which the applied axial load is neglected or set to zero. Additional studies are conducted focusing on direct comparison between Eringen nonlocal and general nonlocal beams for both equal and unequal nonlocal parameters. It is shown that selection of an appropriate guess function that satisfies all boundary conditions is necessary for the approximate solution. Additionally, the response of Eringen and general nonlocal nanobeams with equal nonlocal parameters and hinged-hinged boundary conditions is identical using both the exact and approximate solutions. Finally, it is demonstrated that the general nonlocal dynamic response follows a different trajectory than the Eringen nonlocal dynamic response as a function of the applied axial load. The findings of this investigation may be used by other researchers to simplify analysis procedures and to better understand the fundamental relationships existing in the size-dependent governing equations and boundary conditions for nanobeam-based systems.

Single‐Molecule Fluorescence Enhancement by Plasmonic Core–Shell Nanostructures Incorporating Nonlocal Effects

AbstractMolecular fluorescence may strongly be affected by plasmonic environments, especially the ones with deep‐nanometer features, associated with the emergence of nonclassical effects. Such effects are largely investigated by a nonlocal hydrodynamic model with additional boundary conditions, describing the collective motion of the free electron gas in metals. The study of a fluorophore in the presence of the nano core–shell topology is performed, by employing the following models: the hard‐wall hydrodynamic model and the generalized nonlocal optical response. The analysis is conducted by investigating the fluorescence rates of the system, while considering the fluorophore located inside and outside the nanoparticle. It is demonstrated that the rates generated by the above models may considerably differ from the ones obtained via the classical approach. The optimal fluorescence enhancements for different size and material parameters are found both inside and outside the studied topology.

The influence of family firm image on access to financial resources in family SMEs: a signaling theory perspective

This study investigates whether a projected family firm image can affect access to financial resources, which is key to providing broader strategic options and meeting short-term financial needs, especially for small and medium-sized enterprises (SMEs). Building on the signaling literature, we consider the family SME leaders’ perspective and conceptually and empirically examine whether they believe a projected family firm image acts as a credible signal to the lender. We also examine additional boundary conditions influencing the family SME’s projected image–access to financial resources relationship, by specifically investigating whether firm age and size alter the degree of the signaling effect. Our unique data on 289 Spanish family SMEs reveal that projected family firm image can act as an attractive signal to lenders, leading to better access to financial resources for SMEs. Furthermore, firm size reinforces the role of the projected family firm image as a positive signal. These findings address an important practical issue in terms of family firm stakeholder perceptions, offering contributions to the corporate branding, family business, and financing literature.

On the Topological Structure of Nonlocal Continuum Field Theories

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field–matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

Investigation of the stress-strain state of a hollow cylinder with a coating based on the gradient model of thermoelasticity

The study of the stress-strain state of a thermoelastic hollow cylinder with a homogeneous coating is carried out taking into account the scale effects. Aifantis' one-parameter gradient model is used to account for scale effects. Equilibrium equations and boundary conditions for a composite hollow thermoelastic cylinder are obtained on the basis of the Lagrange variational principle. In comparison with the classical formulation of the problem, additional boundary conditions and conjugation conditions are set for moment stresses and displacement gradients. The dimensionlessness of the task of thermoelasticity has been carried out. Solving the problem of uncoupled thermoelasticity begins with finding the radial temperature distribution of a layered cylinder on the basis of solving the problem of heat conduction in the classical formulation. The solution of the problem in displacements is presented as a sum of solutions in the classical formulation of the problem and additional boundary layer terms found on the basis of the asymptotic properties of the modified Bessel functions. Simplified analytical expressions are obtained for finding radial displacements, radial and circumferential Cauchy stresses, nonzero components of the tensor of moment and total stresses. On specific examples, calculations of the radial distribution of displacements and stresses of a composite cylinder in the case of both mechanical and thermal loading are carried out. The limits of applicability of the asymptotic solution of the problem are investigated. The difference between the radial distribution of displacements and stresses found on the basis of solutions to the problem in the classical formulation and in the gradient formulation is shown. It was found that the Cauchy radial stresses experience a jump at the boundary of the cylinder and the coating, which is explained by the continuity of radial displacements and their first derivatives. The components of the moment stress tensor either take on peak values or experience a jump at the interface. The moment stresses are proportional to the square of the gradient parameter, at small values of which they have values that are much less than the values of the total stresses. With an increase in the dimensionless scale parameter, the values of radial displacements and total circumferential stresses decrease, but moment stresses increase.

Well-posedness of singular-degenerate porous medium type equations and application to biofilm models

We show the well-posedness for a large class of degenerate parabolic equations with an additional singularity and mixed Dirichlet-Neumann boundary conditions on bounded Lipschitz domains. The proof is based on an L1-contraction result. In addition, we analyze systems where degenerate equations are coupled to semilinear reaction diffusion equations. This setting includes mathematical models for biofilm growth which are the motivation for our analysis.

A dynamic multiphase turbulence model for coarse-grid simulations of fluidized gas-particle suspensions

The Spatially-Averaged Two-Fluid Model (SA-TFM) is a functional multiphase turbulence model aimed at predicting the influence of unresolved meso-scale structures on the macro-scale flow properties in coarse-grid simulations of gas-particle flows. In this study, we highlight the general applicability of the SA-TFM model due to the dynamic estimation of the model coefficients through test-filters, the anisotropic treatment of the Reynolds-stresses and the drag force correction, and additional wall-friction boundary conditions for the particle-phase velocity, Reynolds-stress and turbulent kinetic energy. The dynamic approach derives information on the unresolved meso-scale flow properties from the resolved macro-scale variables without the need for any intensive prior considerations of the specific flow structure. Thereby, the drift velocity, a measure for the drag-reduction due to the presence of meso-scale structures is estimated from the turbulent kinetic energies of the phases and the variance of the solids volume fraction. We validate the dynamic anisotropic SA-TFM against highly resolved fine-grid Two-Fluid Model simulation data and experimental measurements of Geldart type A and B particles in bubbling to turbulent flow regimes. In the course of this extensive study, we find that the predictions for the macro-scale flow properties, such as slip-velocity, bed expansion, volume fraction distribution, and mass-flux, are in good agreement with the experimental and fine-grid simulation data in a vast number of cases, ranging from unbound fluidization to pilot-scale fluidized beds, thus, implying a wide applicability of the dynamic model independent of the underlying grid-size.

Dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena by the variable-node multiscale XFEM

This paper aims to develop a variable-node multiscale extended finite element method (V-XFEM) for dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. The general governing equations for the linearly uncoupled and coupled physical phenomena are presented in a compact form. The local mesh refinement technique for modeling cracks is used to improve the accuracy and efficiency, in which variable-node elements without modifying the system matrix or impose additional boundary conditions are taken to connect/link different scale elements. In addition, the time-dependent equations are solved by the unconditionally stable implicit Newmark time integration method, and the dynamic intensity factors (DIFs) are derived from the domain forms of the interaction integrals. Numerical results of the linearly elastic and piezoelectric problems show that V-XFEM is an efficient numerical approach to simulate the dynamic fracture problems of the linearly uncoupled and coupled physical phenomena.

Simulation of detection and scattering of sound waves by the lateral line of a fish

A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed. Within the framework of this model it is shown that the ratio of pressures on lateral lines on different fish flanks, as well as the cross section of sound scattering on both the lines, strongly depends on angles of incidence of incoming sound waves. The strong angular dependence of the pressure ratio seems to be sufficient for the fish to determine the directions from which the sound is coming.

Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges

We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbation is away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a "good" direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbation. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.

Modeling isochoric and non-isochoric deformations in a polar elasto-plastic material

In this article, the response of an interfacial layer developed along a particulate–continuum interface is explored under two opposite normal confining constraints. To this end, a cohesionless granular strip subjected to both isochoric and non-isochoric conditions is monotonously sheared against an adjacent wall of different surface roughness values. Numerical simulations are performed using a finite element method formulated within an elasto-plastic polar continuum, equipped by granular rotation, couple stress, and average grain size. Along the wall in motion, the slide and rotation resistance of the first layer of boundary grains are innovatively determined by the additional polar boundary conditions, taking into account a ratio between slip and granular rotation along the wall, asperities of wall surface, and grain size. In particular, the combined interaction of material dilatancy constraint and wall roughness are examined on the frictional resistance and deformation of the interfacial layer. It is shown that the normal confinement and the roughness geometry of the wall surface have visible impacts on the stress-displacement response of the interfacial layer. The evolution of stresses and couple stresses is entirely different in isochoric and non-isochoric conditions. However, the stationary value of the interfacial strength is independent of how the bounding wall confines the granular body. Besides, the deformations manifested out of the interfacial layer are more pronounced in isochoric shearing than non-isochoric shearing. Nevertheless, the location and progression of the interfacial layer do not necessarily depend on the applied confining constraint after large shearing.

Does “CHALTA HAI”culture negatively impacts sustainability of business firms in India? An empirical investigation

PurposeChalta hai (it is fine or it is acceptable) is an Indian cultural phenomenon that influences attitude towards work and business and diachronically adversely affects both. The purpose of this study is to explore its impact on the sustainability of business firms operating in India.Design/methodology/approachThe research has firstly undertaken a theoretical study towards the development of appropriate hypotheses and a corresponding conceptual model, with emphasis on the effects of chalta hai culture as a moderator of the predictor-sustainability linkages. The model has been validated statistically through partial least square- structural equation modelling analysis of usable feedbacks from 349 respondents.FindingsThe research has concluded that the cultural notion of chalta hai impacts adversely the sustainability of business firms operating in India, with its effects being dominant.Research limitations/implicationsThe research has scholarly and executive implications, as well as socio-cultural implications. The sample, however, allows for conclusions to be drawn reliably but with limited generalizability. Additionally, only three predictors have been considered, bestowing upon future research the task of building on the present model through additional pertinent predictors and boundary conditions that will enhance its explanative power.Practical implicationsThe research has provided a scientifically developed model that guides Indian firm managers through appropriate steps that dissuade stakeholders from exhibiting the behavioural traits and attitudes of chalta hai culture, highlighting along the way its detrimental effects on Indian business sustainability.Originality/valueThere is little research on the business impacts of chalta hai and regarding the sustainability perspective/focus. In addition, this is in sharp contrast to the spread and impact of the phenomenon. This research and its findings, therefore, are valuable with regard to both their wider context (“chalta hai” business effects) and their specific focus (sustainability).

Design Technique for Shielded Multilayer Directional Coupler

The article discusses the implementation of directional couplers in a microstrip line, designed for communication lines in the frequency range of 2‒3 GHz, on a substrate made of a widely used and generally available material RO4350, with a coupling factor of 3‒7 dB. These directional couplers have been designed with additional boundary conditions to reduce the size of the device. In the course of numerical modeling, the correction factors used for preliminary analytical calculations were refined. The data of the numerical experiment were verified using the measurements prototype model.

Nonlocal Hydrodynamic Models for the Optical Response of Plasmonic Nanostructures

In order to model the interaction between light and plasmonic structures at deep-nanometer scale, which is governed by non-classical effects, a nonlocal hydrodynamic approach has been extensively studied. Several hydrodynamic models have been proposed, solving the coupled equations: the linearized hydrodynamic equation of motion and the electrodynamic Maxwell’s equations, by employing additional boundary conditions. This work compares four hydrodynamic models: the hard wall hydrodynamic model (HW-HDM), the curl-free hydrodynamic model (CF-HDM), the shear forces hydrodynamic model (SF-HDM), and the quantum hydrodynamic model (Q-HDM). The analysis is conducted for a metallic spherical nanoparticle, as an example. The above hydrodynamic models are also compared with experiments available in literature. It is demonstrated that HW-HDM and QHDM outperform the other two hydrodynamic models.

Mantle-flow diversion beneath the Iranian plateau induced by Zagros\u2019 lithospheric keel

Previous investigation of seismic anisotropy indicates the presence of a simple mantle flow regime beneath the Turkish-Anatolian Plateau and Arabian Plate. Numerical modeling suggests that this simple flow is a component of a large-scale global mantle flow associated with the African superplume, which plays a key role in the geodynamic framework of the Arabia-Eurasia continental collision zone. However, the extent and impact of the flow pattern farther east beneath the Iranian Plateau and Zagros remains unclear. While the relatively smoothly varying lithospheric thickness beneath the Anatolian Plateau and Arabian Plate allows progress of the simple mantle flow, the variable lithospheric thickness across the Iranian Plateau is expected to impose additional boundary conditions on the mantle flow field. In this study, for the first time, we use an unprecedented data set of seismic waveforms from a network of 245 seismic stations to examine the mantle flow pattern and lithospheric deformation over the entire region of the Iranian Plateau and Zagros by investigation of seismic anisotropy. We also examine the correlation between the pattern of seismic anisotropy, plate motion using GPS velocities and surface strain fields. Our study reveals a complex pattern of seismic anisotropy that implies a similarly complex mantle flow field. The pattern of seismic anisotropy suggests that the regional simple mantle flow beneath the Arabian Platform and eastern Turkey deflects as a circular flow around the thick Zagros lithosphere. This circular flow merges into a toroidal component beneath the NW Zagros that is likely an indicator of a lateral discontinuity in the lithosphere. Our examination also suggests that the main lithospheric deformation in the Zagros occurs as an axial shortening across the belt, whereas in the eastern Alborz and Kopeh-Dagh a belt-parallel horizontal lithospheric deformation plays a major role.

Free high-frequency vibrations of nonlocally elastic beam with varying cross-section area

In the framework of the two-phase theory of nonlocal elasticity we study free high-frequency vibrations of nanobeams with varying cross section. Considering the Helmholtz kernel in the constitutive equation, we reduce the original integro-differential equation to an equivalent six-order differential equation with variable coefficients and derive the pair of additional boundary conditions accounting for the nonlocal edge effects. Applying WKB method, a solution of the boundary-value problem is constructed in the form of superposition of the outer expansion and edge effect integrals with high variability along the beam axis. As an example, a clamped nanobeam with a shape matching to the shape of a slab waveguide in a photonic crystal beam laser is considered. The derived relations for natural frequencies and performed calculations revealed strong effect of both the nonlocal model fraction and the cross-section variability on the correction to natural frequencies calculated within the classical beam theory

Investigating the effect of edge crack on the modal properties of composite wing using dynamic stiffness matrix

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

Solution of the gradient thermoelasticity problem for a cylinder with a heat-protected coating

The investigation of the stress-strain state of an infinitely long thermoelastic cylinder is carried out taking into account the scale effects. A thermal protective coating is applied to the outer side surface of the cylinder, the thermomechanical characteristics of which are functions of the radial coordinate. Thermal boundary conditions of the first kind are set on the stress-free side surfaces of the cylinder. To take into account the scale effects, the one-parameter gradient theory of thermoelasticity proposed by Aifantis is used. Additional boundary conditions and conjugation conditions for couple stresses are specified. The displacements and stresses are represented as the sum of the solutions of the thermoelasticity problem in the classical formulation and the gradient parts. After finding the radial temperature distribution, the thermoelasticity problem in the classical formulation with respect to radial displacements and stresses is solved numerically by the shooting method. Additional boundary layer terms for radial displacements at small values of the gradient parameter are found using the asymptotic method for solving linear differential equations with spatially varying coefficients (the Wentzel-Kramers-Brillouin method - WKB method). Calculations of radial displacements, Cauchy stresses, couple stresses and total stresses in the case of both homogeneous and inhomogeneous coatings are carried out using specific examples. It has been found that the Cauchy stresses and total stresses experience a jump at the boundary between the cylinder and the coating. The couple stresses at small gradient parameters are much less than the total stresses. An increase of the scale parameter reduces the values of radial displacements and total stresses. Deformations are continuous in both cases of coating (homogeneous and inhomogeneous). A comparative study of the influence of the value of the inhomogeneity parameter on the distribution of displacements and total stresses is carried out.

Studying free hight-frequency vibrations of an inhomogeneous nanorod based on the nonlocal theory of elasticity

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis of the nonlocal theory of elasticity. The upper part of spectrum with the wavelength comparable to the internal characteristic dimension of a nanorod is examined. An equations in the integral form with the Helmholtz kernel, incorporating both local and nonlocal phases, is used as the constitutive one. The original integro-differential equation is reduced to the forth-order differential equation with variable coefficients, the pair of additional boundary conditions being deduced. UsingWKB-method, a solution of the boundaryvalue problem is constructed in the form of the superposition of a main solution and edge effect integrals. As an alternative model, we consider the purely nonlocal (one-phase) differential model which allows estimating the upper part of spectrum of eigen-frequencies. Considering the nanorod with a variable cross-section area, we revealed a fair convergence of eigen-frequencies found in the framework of two models when the local fraction in the two-phase model vanishes.