Boundary Conditions Research Articles

Powering Pro-Environment Behavior: The Impact of Unlocking Reward Strategy on Pro-Environmental Behavior

Global environmental challenges threaten both sustainable societal development and daily human life. As these issues intensify, promoting pro-environmental behaviors has become a key research priority. While reward strategies have been proven effective in encouraging such behaviors, most research has focused on the content of rewards, leaving the method of reward delivery underexplored. This study investigates the effects of an unlocking reward strategy on pro-environmental behavior, grounded in the Goal-Setting Theory, while also exploring the psychological mechanisms and boundary conditions that influence these effects. Three studies were conducted to test the hypotheses. Study 1 demonstrated that the unlocking reward strategy (compared to direct rewards) significantly increased pro-environmental behaviors. Study 2 showed that self-efficacy mediates this effect, as the unlocking reward strategy enhances self-efficacy, which in turn promotes pro-environmental behaviors. Study 3 revealed that commitment serves as a crucial moderator, amplifying the positive impact of the unlocking reward strategy. This research not only broadens the scope of reward strategy literature but also elucidates key drivers of pro-environmental behavior, offering practical insights for marketers, policymakers, and organizations aiming to foster sustainable practices.

Dynamics of a nonlocal phytoplankton species with nonlinear boundary conditions

Dynamics of a nonlocal phytoplankton species with nonlinear boundary conditions

Analogous Hawking Radiation in Dispersive Media

In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided.

Effects of transverse loading on the ultimate strength prediction of stiffened panels under biaxial loads: Potential improvements to the IACS rule formulation

The current International Association of Classification Societies (IACS) rule for designing stiffened panels was found in Wang et al. (2024) to conservatively predict the ultimate strength of panels when transverse loads predominate. This conservatism arises from the overestimation of bending moments acting on stiffeners by directly applying the beam analogy in both longitudinal and transverse directions in the rule formulation when evaluating stiffener yielding.To address this issue, this paper applies the orthotropic plate theory to calculate bending moments experienced by the stiffeners of panels under biaxial loads. Orthotropic properties are derived from equivalent sectional areas and moments of inertia. The predicted bending moments are validated through comparisons with numerical simulations. The effects of boundary conditions and deflection patterns with varying numbers of half-waves are discussed. Based on the analytical results, a modification of the IACS rule formulation is proposed by introducing a correction factor to account for transverse loading effects in the bending moment calculations. The factor is a function of the ratio between longitudinal and transverse loading.The modified IACS rule formulation is verified through numerical simulations of aluminium panels using ABAQUS and comparisons with results from existing literature on steel stiffened panels under various biaxial loading conditions. The modified rule formulation shows improved accuracy in predicting the ultimate strength of stiffened panels, particularly in cases with dominating transverse loads. The modified IACS rule formulation can be useful for more reliable and cost-effective design of ships and offshore structures.

Mathematical and Buongiorno nanofluid modelling to predict the thermal and solutal performance of magneto-bioconvective Casson nanofluid flowing in a rotatory disk

Abstract This study aims to improve how heat and mass move in systems that use viscoelastic nanofluids under magnetic fields. These systems are commonly used in industries like biotechnology, energy, and medical devices. The significance of this work lies in exploring the steady flow of magnetohydrodynamic (MHD) Casson nanofluids, incorporating the Buongiorno nanofluid model and swimming microorganisms. This research seeks to deepen the understanding of complex fluid behaviors by examining the effects of thermal radiation and chemical diffusion under thermal and solutal convective boundary conditions. The governing equations, which are inherently nonlinear due to the presence of multiple physical effects, are converted from two-dimensional partial differential equations (PDEs) to ordinary differential equations (ODEs) using a similarity transformation. A semi-analytical solution is derived using the collocation pseudo-spectral method within the MAPLE computational software. The study investigates how factors like Casson and magnetic parameters, Eckert number, Brownian motion, and thermophoresis affect the flow rate, temperature distribution, species concentration, and microorganism motility. These results are validated by comparing them with established benchmarks. The key findings reveal a pronounced oscillatory behavior in the temperature profile at higher Eckert number values, while increased Brownian motion and thermophoresis lead to greater nanoparticle dispersion near the disk surface. Higher Lewis and Peclet numbers lead to increased microorganism concentration, demonstrating stronger convective and advective effects. These insights are vital for optimizing drag force, thermal gradients, and mass transfer in engineering applications that involve rotating disks and magnetic fields.

Dynamics of a hot flexible cantilever plate under natural convection heat transfer in a square cavity

This study investigates the fluid-structure interactions of a flapping plate within a square cavity under four distinct boundary conditions, where two opposing walls are heated isothermally, and the others are adiabatic. These configurations are defined as case 1 (cooled side walls), case 2 (cooled top and bottom walls), case 3 (heated bottom and cooled top wall), and case 4 (heated top wall and cooled bottom wall). The effects of non-dimensional parameters, including Rayleigh number (Ra), Cauchy number (Ca), and mass ratio (β) on plate dynamics and convective heat transfer are analyzed. Numerical investigations are executed utilizing the SU2 open-source multi-physics computational fluid dynamics solver, with a fixed Prandtl number (Pr) set at 0.71 and dimensionless temperature difference (ϵ) established at 0.6. The results show that in cases 1 and 4, the plate exhibits no observable unsteadiness, while cases 2 and 3 reveal different oscillatory behavior within certain parameter ranges, including static mode, periodic flapping mode, quasi-periodic flapping mode, and chaotic flapping mode. In particular, the configuration in case 3 possesses higher inherent instability than case 2, causing the earlier onset of Hopf bifurcation. These findings provide valuable insights into the influence of boundary conditions on the behavior of flexible structures in fluid environments, highlighting the critical role of flow instabilities and boundary conditions in determining the dynamic response of the system.

Free vibration analysis of rectangular plates resting on an elastic foundation

Abstract Rectangular plate on elastic foundations is a common structural form in aerospace fields, while there still lacks a general analytical method for free vibration analysis of this kind of structure. Thus, the extended separation-of-variable method is used to obtain the analytical free vibration solutions for plates with all kinds of homogeneous boundary conditions. The mode functions are assumed to be in separation-of-variable form, and the natural frequencies of two-direction mode functions are mathematically independent. Then, the free vibration solutions are obtained according to the two-direction boundary conditions. The correctness of the present results is verified via numerical comparisons. Parameter study shows that the elastic foundation significantly affects the flexural vibration behaviors of rectangular plates, and the influence is dependent on boundary conditions and mode orders of rectangular plates.

Liquid and gas permeabilities of nanostructured layers: Three-dimensional lattice Boltzmann simulation

Liquid water and gas permeabilities in nanostructured catalyst layers (CLs) (pore size ∼10–150 nm) and microporous layers (MPLs) (pore size ∼50 nm-5 μm) are crucial to reduce the mass transport loss in proton exchange membrane fuel cells (PEMFCs). Experimental measurement of their permeabilities poses great challenges due to their brittle and thin characteristics. Presently, considerable discrepancy exists in the reported permeability values for CLs and MPLs in the literature with variation spanning several orders of magnitude. This study digitally reconstructed various nanostructures of similar pore size as CLs and MPLs to calculate their permeabilities using the Lattice Boltzmann Method (LBM) based on no-slip (e.g. for liquid water flow in MPL and CL's secondary pores) or slip condition (e.g. for gas flow in MPL). Analysis was performed to evaluate the range of pore size in nanostructures for the two boundary conditions. A comprehensive investigation was conducted under various parameters such as the Reynolds number (Re), sphere diameter, porosity, and pore structure. The results revealed that permeability exhibits an increasing trend with the diameter and porosity. The predicted permeability of randomly arranged spheres agrees well with established correlations. The random sphere structure demonstrates higher permeability than their body-centered cubic (BCC) and face-centered cubic (FCC) counterparts. Under slip boundary condition, the permeability was enhanced, compared to the no-slip condition. This study's novelty lies in using distinct boundary conditions to assess the permeabilities of liquid and air, based on flow pattern analysis in the CL and MPL pore structures. A new empirical correlation describing the influence of the Knudsen number (Kn) on the slip permeability was developed, exhibiting consistency with simulation across the entire porosity spectrum.

Effects of boundary conditions on the transmitral pressure gradient for numerical simulation of flow in a left heart model

The transmitral pressure gradient is a crucial clinical indicator for diagnosing mitral regurgitation and stenosis. Numerical simulation of specific patients can obtain the complete pressure distribution in the left heart system, which is an important approach to evaluate cardiac function. However, the results are sensitive to the boundary conditions used in the numerical simulations. In the present work, we constructed a left heart model and assessed the effects of four typical boundary conditions on the transmitral pressure gradient, which is computed based on the Bernoulli equation and the line probe, respectively. The results show that the transmitral pressure gradient obtained by the line probe is sensitive to the boundary conditions. The sensitivity is closely related to the pressure in the atrium but has negligible effect on the pressure in the ventricle. This study sheds light on evaluating the pressure gradient of patient-specific treatments based on the numerical simulation of a left heart model.

Mechanical performance analysis method for ribbed H-section aluminum alloy members with initial curvature and torsion angle

In this study, an experimental investigation was conducted on the axial compression performance of ribbed H-section aluminum alloy members with initial curvature and torsion angle under varying boundary conditions, including one end hinged with the other rigidly connected, and both ends rigidly connected. Ultimate bearing capacity and failure modes were identified under real loads and subsequently compared with previous findings from our research group on members with hinged ends. To account for initial imperfections introduced during processing and transportation, 3D scanning technology was utilized to capture the precise geometrical dimensions, constructing an accurate numerical simulation model. The experimental results were corroborated with numerical simulations, leading to the proposal of an analytical method for members with initial curvature and torsion angle. Furthermore, extensive parametric analysis elucidated the impact of initial curvature, torsion angle, and slenderness ratio on the ultimate bearing capacity, culminating in the formulation of the stability factor and calculated length factor based on numerical outcomes. The study discovered significant variances in bearing capacity under different boundary conditions, with one-end hinged and one-section rigidly connected, and two-end rigidly connected conditions exhibiting 1.4 and 2.1 times the capacity of the hinged-at-both-ends scenario. Under different boundary conditions, the axial compression members were subjected to flexural-torsional buckling failure. Moreover, when the ultimate bearing capacity was reached, the lower flange of the member and the web near the lower flange appeared obvious buckling phenomenon. The numerical analysis aligned well with experimental data, validating the simulation method's reliability and revealing the stress distribution and evolution during member failure. These findings offer vital theoretical insights and technical support for engineering design and practical applications.

Numerical modelling of pump-driven tsunami generation and fluid-structure-interaction in idealized urbanized coastal areas during run-up

Tsunami wave inundations are still one of the most devastating natural disasters worldwide. Tsunamis striking a settlement frequently devastate much of its infrastructure. In instances where infrastructure withstands the tsunami’s actions, it acts as a flow resistance for the wave’s run-up, altering inundation dynamics and flow depth. Accurately predicting the complex dynamics of tsunami wave run-up in densely populated urban areas is paramount for informing effective evacuation protocols and conducting comprehensive hazard and risk assessments. In pursuit of improving wave run-up prediction capabilities, this study delves into the three-dimensional numerical modelling of wave run-up of non-breaking, long tsunami waves in urbanized areas. Leveraging insights from a physical experiment with pump-driven wave generation and idealized infrastructure, a novel pressure-based wave generation boundary condition is developed. The boundary condition achieves an average of 4.9% accuracy in replicating the water surface elevation from experiments. Additionally, it attains an average 1.5% precision in reproducing flow velocities, furthermore reproducing the spatial flow dynamics accurately. Physical experiment wave run-up is modelled with an average 6.9% deviation for both simulations with and without idealized infrastructure. 63.0% higher non-linearity waves than in the physical experiments are additionally investigated to highlight the boundary conditions capabilities of high non-linearity wave generation, change in run-up reduction for higher non-linearity waves for infrastructure interaction and furthermore in-depth flow field characteristics during tsunami inundation. Finally, the study highlights deviations from analytically calculated wave run-up, emphasizing the necessity for numerical and physical experimental evaluation for both high non-linearity waves and tsunami infrastructure interaction, ultimately fostering both resilience and preparedness against tsunami hazards.

A novel temporal finite element method to solve static viscoelastic problems

A novel temporal finite element method is presented to solve static viscoelastic problems, which is more flexible and appropriate to describe temporal variation of displacement than conventional finite difference or numerical integral methods. By using virtual work principle, a spatial finite element based governing equation is derived in terms of displacement and its derivatives. Then two temporal finite element models are developed using Gurtin variational principle and weighted residual technique. A kind of hybrid shape functions with polynomial and trigonometric basis is stressed to give more flexible descriptions of time varying variables. A criterion of stability analysis is derived, which can numerically be conducted when the constitution of shape functions and step size are prescribed. A recursive algorithm toward end is developed by which the temporal FE analysis can be conducted via a matrix power product with the initial condition, instead of step marching. The proposed approach is available for the viscoelastic model described by linear differential equations with order h ≤ 2, and can conveniently be combined with well-developed numerical algorithms to tackle with boundary value problems, such as FEM, SBFEM etc. Various numerical examples, including those with static/harmonic loads, creep, stress singularity and heterogeneous structures, etc. are provided to illustrate the efficiency of the proposed approaches, and impacts of the temporal FE model, constitution of shape functions, and step size, etc. are taken into account. Satisfactory results are achieved in comparison with analytical or ABAQUS-based solutions.

Boundary value problem of calculating ray characteristics of ocean waves reflected from coastline

A direct variational method for solving the problem of reflection of ocean waves ray paths from the coastline with given positions of the source and the point of registration is considered. It is shown that the original boundary value problem can be reduced to the direct search of stationary points of the functional. Information about the objective function in the area of solutions of the ray problem allows us to construct a systematic procedure for finding minima and saddle points. A feature of the proposed approach is the optimization of the ray reflection point along a given coastline.

Hygrothermoelastic analysis of the nano-circular plate with memory effect

In hygrothermal environments, the coupling effects of temperature and moisture substantially impact deflection and stresses play a significant role. This study presents a coupled hygrothermoelastic model with non-Fourier and non-Fick effects established by introducing relaxation times or phase lags of heat and moisture flux accompanied by memory-dependent derivatives. The boundary value problem is formulated by considering a thin circular plate as an exemplary example, where the perimetric edge is clamped. The upper and lower edges of the plate is subjected to zero temperature, whereas the curved surface is exposed to hygrothermal shock. The closed-form solution of temperature and moisture distribution is obtained via the integral transform approach. The Fourier series expansion approach is used to calculate the numerical Laplace inversion. The effects of both heat and moisture flux relaxation times on the thermal deflection/stresses of the plate are analyzed and illustrated graphically.

Topology optimization of link mechanisms for comprehensive synthesis of component arrangement and structure using micropolar elasticity model

This paper proposes a method for topology optimization of link mechanisms with multiple outputs, using a multi-material micropolar elasticity model. This approach allows for comprehensive optimization of both the arrangement and structure of the link mechanism components. By utilizing a continuum model that incorporates micropolar elasticity, we can specify bending stiffness independently from tensile stiffness, resulting in deformation characteristics that approximate a link mechanism. The optimization problem of designing link mechanisms for multiple outputs is reformulated as a boundary value problem within this model framework. The design goal is to synthesize a link mechanism that not only follows a desired path but also possesses the required degrees of freedom. To achieve this, the objective function is defined by the displacement error under external force and the strain energy in the links. The multi-material micropolar elasticity model is then optimized through a gradient-based optimization method, focusing on this objective function. The effectiveness and applicability of our methodology are demonstrated through several numerical case studies.

Double-eigenvalue bifurcation and multistability in serpentine strips with tunable buckling behaviors

Serpentine structures, composed of straight and circular strips, have garnered significant attention as potential designs for flexible electronics due to their remarkable stretchability. When subjected to stretching, these serpentine strips buckle out of plane, and previous studies have identified two distinct buckling modes whose order of appearance may interchange in serpentine structures with a single cell. In this study, we employ anisotropic rod theory to model serpentine strips as a multi-segment boundary value problem (BVP), with continuity conditions enforced at the interface between the straight and curved strips. We solve the BVP using methods of continuation, and our results reveal that: (1) the exchange of the two buckling modes in a single-cell serpentine strip is induced by a double-eigenvalue and associated secondary bifurcations, which also alter the stability of the two buckling modes; (2) a variety of stable states with reversible symmetry can be manually obtained in tabletop models and are found to be disconnected from the planar branch in numerical continuation. Furthermore, we demonstrate that modulating the strip thickness across different cells leads to the initiation of buckling in the thinnest section, thereby allowing for the tuning of buckling modes in serpentine strips. In structures with two cells, the sequence of the two buckling modes can also be controlled by designing serpentine strips with nonuniform height. This work could enhance the mechanical design of serpentine-interconnect-based flexible structures and could have applications in multistable actuators and mechanical memory devices.

Results on a nonlinear wave equation with acoustic and fractional boundary conditions coupling by logarithmic source and delay terms: Global existence and Asymptotic behavior of solutions

The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is notable for its capacity to model complex systems, contribute to the advancement of mathematical theory, and exhibit wide-ranging applicability to real-world problems. This paper investigates the global existence and general decay of solutions to a wave equation characterized by the inclusion of logarithmic source and delay terms, governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under various hypotheses, and the general decay behavior is established through the construction and application of a suitable Lyapunov function

Analytical prediction of electromagnetic performance for surface-embedded permanent magnet in-wheel machines considering iron’s nonlinearity

Accurate magnetic field calculation is the premise of electromagnetic performance prediction. Conventional subdomain (SD) techniques assume that the iron’s relative permeability is infinite, leading to falsely overestimated flux density. We propose an accurate magnetic field analytical model for permanent magnet (PM) in-wheel machines considering iron’s magnetization nonlinearity and saturation. Specifically, according to the excitation source and topology, the entire solution domain of the machine is divided into sub-regions such as stator slots/teeth, stator slot-openings/tooth-tips, air-gap, and rotor slots/teeth, etc. Poisson’s or Laplace’s magnetic vector potential (MVP) equations are solved using Maxwell’s electromagnetic theory and complex Fourier series methods in each sub-region. Specifically, in our approach, The Cauchy product theorem addresses the discontinuous magnetic permeability change at the slot and tooth interface. The machine’s magnetic saturation effect is considered by combining the actual magnetization characteristics of iron with an iterative algorithm. The general solution for the MVP is solved using the boundary conditions between adjacent subregions. Subsequently, electromagnetic properties such as air-gap flux density, back electromotive force (EMF), and electromagnetic torque are obtained. The accuracy of the analytical model is verified by finite element analysis (FEA) and prototype tests, which proved that the proposed analytical model can consider the iron’s nonlinearity and the magnetic saturation. In addition, the inaccurate overestimation of electromagnetic torque and air-gap magnetic flux density by the conventional SD techniques has also been proven.

Design and experimental verification of composite stiffened panel under combined compression-shear loads

Abstract As an important part of the aircraft, the panel structure accounts for a large proportion of the building block verification system. The real stress state of the aircraft panel is usually not a uniaxial compression or shear, but a combined loading condition in service. In the past, box structure was usually tested for structure selection in the aircraft’s preliminary design phase, which was limited by immature panel test methods and equipment. At present, a general panel test system considering the actual load form and boundary conditions was independently developed by the Aircraft Strength Research Institute of China. A large-scale composite stiffened panel was designed and tested on this test system in this paper. The whole process of the test was monitored by digital image correlation technology and strain gauge measurement. The test process and results were detailed and analyzed. Experimental results show that the failure modes of stiffened panels under combined compression-shear loads include mainly three forms. The first is in the upper part of the panel, which shows a typical shear failure mode and tears along the shear loading direction of the specimen. The second is the fracture of the reinforced piece in the bottom right-hand corner of the specimen due to compression loads. The third form is the large-scale cracking at the junction of the reinforced piece and skin, which may be related to the coupling effect of combined loading.

Analysis of guided and leaky modes of planar optical waveguides using transparent boundary conditions

We present a numerical approach to compute and characterize both guided and leaky modes in a multilayer planar optical waveguide made of any lossy and dispersive materials. Usually, in numerical calculations based on finite element methods, perfectly matched layers (PMLs) are used to truncate the unbounded substrate and cover layers. However, it is difficult to make such PMLs transparent for both guided and leaky modes at the same time, and often, different or even contradictory PML parameters are required for these two types of modes. In contrast, the transparent boundary conditions (TBCs) that we use in this work can terminate the unbounded waveguide and, simultaneously, provide perfect transparency for the modes. In addition, this type of boundary condition does not contaminate the solutions with non-existent modes, such as PML modes. More importantly, the TBC approach yields the nonlinear eigenvalue solutions that can be intrinsically mapped to the parameter space of transverse wavenumbers in the claddings. This allows us to uniquely determine the power flow properties of all the calculated modes. A finite element Python package is developed to treat a variety of planar waveguides in a robust and systematic way.