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The paper presents an analytical model for travel time evaluation in double-deep, triple-deep, quadruple-deep and fivefold-deep tier-captive shuttle-based storage and retrieval system (SBS/RS). Under the assumption of the deepest location rule for the storage process and the nearest neighbour rule for the retrieval process, the expressions for single-command and dual-command cycle times of the shuttle vehicle and elevator are developed, from which the SBS/RS performance can be estimated. The model based on the probability theory enables the evaluation of all individual times that make up the cycle times and assessment of the average number of totes relocated during a retrieval process. Special attention is devoted to the modelling of the relocation of totes which block access to the requested tote during the retrieval process. The validity of the analytical model is examined via the developed simulation model. The given case study shows that the proposed analytical travel time model results match the results of the simulation model. The presented modelling strategy could be applied to bigger system racking depths following the same modelling logic. [ABSTRACT FROM AUTHOR]

Considering the storage increasing demand of 'multi-variety, small-batch' characteristic goods, we developed a new type of compact warehouse a three-dimensional double-ended compact storage system. Compared with the traditional three-dimensional automated storage and retrieval system (AS/RS) and existing three-dimensional compact AS/RS model, the storage system we designed exhibits excellent characteristics such as high density, high throughput efficiency, and more flexible configuration. There are three key points in our work listed as follows. Firstly, we establish the continuous travel time model under specific operating conditions in this new three-dimensional compact warehouse. Secondly, the three-dimensional size of the storage rack is optimised. The optimal three-dimensional proportion of the storage rack is obtained based on the model's optimal solution. Finally, numerical examples are given to analyse the influence of the I/O port layouts and related parameters on the system throughput efficiency. According to the optimisation results of the system model, a more reasonable rack dimension can be designed, which can provide an effective reference for the construction of a three-dimensional double-ended compact warehouse. [ABSTRACT FROM AUTHOR]

Travel time models for automated storage and retrieval systems (AS/RS) are used to define average travel times during storage/retrieval operations in an AS/RS. With an increasing depth of AS/RS racks, storage goods are stored in front of each other. This can lead to relocation operations of blocking goods causing higher travel times. This paper derives analytically and presents four travel time models for multi-deep AS/RS following four storage allocation strategies. Two models handle random strategies, one minimises the variance of storage channel fillings and the fourth maximises this variance. Evaluation and comparison of different models is followed by a discrete event simulation to verify these models. It is shown that the minimal variance strategy achieves the lowest relocation numbers and also the lowest total travel times, the random strategies perform between the minimal and maximal variance strategy. [ABSTRACT FROM AUTHOR]

In this study, an investigation on the acoustic performance of a simple expansion chamber muffler with side outlet has been presented. The investigation for the muffler is done in the 10–2400 Hz frequency range. The muffler is analyzed analytically, computationally, and experimentally. The computational and analytical modellings of the muffler have been done by using the finite element and transfer matrix methods, respectively for the determination of transmission loss. As the transfer matrix method is unable to capture the higher order modes above the cut-off frequency of the muffler, the finite element method has been adopted as the computational method. Additionally, the accuracy in the analytical and computational modelling of the muffler is checked with the experimental investigation. The two-load method is used in this study for muffler to determine the transmission loss and band power. The side outlet of the muffler introduces an extra impedance due to the shunt element and hence the effectiveness of the muffler can be improved. This muffler shows an overall improvement of 24.73 dB in the transmission loss when compared with the transmission loss of the simple expansion chamber muffler with an axial outlet in 10–2400 Hz frequency range. Specifically, the simple expansion chamber muffler with side outlet is more effective than the simple expansion chamber muffler with an axial outlet in 350–680 Hz, 1040–1350 Hz, 1570–1590 Hz, and 1850–2400 Hz frequency ranges. The comparison among the different techniques shows a fair agreement in the results. The transmission loss, variation of the band power in the 1/3rd octave band, and sound pressure level contours for the muffler at the selected frequencies have been presented. This study offers an advantage in the design of the automotive mufflers. [ABSTRACT FROM AUTHOR]

Inspection of defects in pipelines can be materialized by measuring ultrasonic guided waves the properties of which are conventionally analyzed with three-dimensional finite-element methods (FEM). They require complicated geometric discretization and memory consumption in a single analysis, thus are clumsy and limited to be used for field fast analysis. This work developed a systematic analytical approach to perform rapid assessment of mode-to-mode reflection for guided waves in a pipe owing to notches and used low-cost microprocessors for calculation. The mechanism of wave reflection was interpreted with the reciprocity theorem and a novel dynamic rigid-ring approximation. The theory successfully estimated the coefficient dependence of notch depths with an accuracy comparable to that obtained from a FEM, with the maximum error being less than 0.044. The developed algorithm was further implemented on an embedded system for computational complexity estimation. It shows the complete analytical theory sufficiently reduces computational memory and time cost by orders of magnitude while retaining good accuracy in determining mode-to-mode guided reflection by notches, which is a useful tool for practical pipeline applications. [ABSTRACT FROM AUTHOR]

This paper introduces a literature review of the accomplished research to calculate the strain concentration factor which shall be considered during the concrete coated subsea pipelines design. The strain concentration results from the discontinuity of the concrete coating which is applied to pipe joints to enhance the pipeline stability on the seabed. The paper introduces a definition of the strain concentration factor and a conclusive explanation of the work performed to calculate the strain concentration factor using the following three methods: full-scale tests, analytical models, and numerical models. The paper also introduces other works addressing the contribution of concrete coating to pipe stiffness. Literature indicates that while full-scale tests produce the most accurate values for the strain concentration factor, due to cost implications, the method is limited to a small range of pipe sizes and coating properties. Although the analytical method produces acceptable results, prediction of strain concentration factor due to concrete coating sliding and beyond steel yield stress and concrete crushing limit is unpredictable. The numerical method using finite element (FE) analysis indicates acceptable strain concentration factor values, however, careful consideration shall be taken due to possible modelling inaccuracies. The review shows that the strain concentration factor is mainly influenced by the thickness and strength of the concrete coating as well as the shear capacity of the external corrosion coating, whilst due to its low impact, the effect of the concrete coating reinforcement is not considered for most of the analysis due to low significance. [ABSTRACT FROM AUTHOR]

Thin polymeric films applied on stiff substrates are prone to delamination upon thermal loading. Different thermal expansion coefficients and different elastic properties can cause localized stress concentrations in the interface between applied layer and substrate. The present work proposes a variational approach to compute residual stresses and strains within the film. Using finite element calculations, it is shown that the presented closed-form analytical solution provides accurate interfacial stresses. Employing a critical distances failure criterion, these stresses are used to predict thermally induced crack nucleation. The proposed model is validated using experimental data of thermally loaded epoxy–glass specimens. It is in good agreement with the test data and provides predictions for thin-film delamination. [ABSTRACT FROM AUTHOR]

Background: Superficial targets require the use of the lowest energies within the available energy range in proton pencil‐beam scanning (PBS) technique. However, the lower efficiency of the energy selection system at these energies and the requirement of a greater number of layers may represent disadvantages for this approach. The alternative is to use a range shifter (RS) at nozzle exit. However, one of the concerns of using this beamline element is that it becomes an additional source of neutrons that could irradiate organs situated far from the target. Purpose: The purpose of this study is to assess the increase in neutron dose due to the RS in proton PBS technique. Additionally, an analytical model for the neutron production is tested. Methods: Two clinical plans, designed to achieve identical target coverage, were created for an anthropomorphic phantom. These plans consisted of a lateral field delivering an absorbed dose of 60 Gy (RBE) to the target. One of the plans employed the RS. The MCNP code was used to simulate the plans, evaluating the distribution of neutron dose equivalent (Hn) and the equivalent dose in organ. In the plan with the RS plan, neutron production from both the patient and the RS were assessed separately. Hn values were also fitted versus the distance to field edge using a Gaussian function. Results: Hn per prescription dose, in the plan using the RS, ranged between 1.4 and 3.7 mSv/Gy at the field edge, whereas doses at 40 cm from the edge ranged from 9.9 to 32 μSv/Gy. These values are 1.2 to 10 times higher compared to those obtained without the RS. Both this factor and the contribution of neutrons originating from the RS increases with the distance from field edge. A triple‐Gaussian function was able to reproduce the equivalent dose in organs within a factor of 2, although underestimating the values. Conclusions: The dose deposited in the patient by the neutrons originating from the RS predominantly affects areas away from the target (beyond approximately 25 cm from field edge), resulting in a neutron dose equivalent of the order of mSv. This indicates an overall low neutron contribution from the use of RS in PBS. [ABSTRACT FROM AUTHOR]

Recent experimental evidence has shown that wood–steel–wood dowel-type connections exhibit a semi-rigid behaviour even after 90 min of fire exposure. Because a semi-rigid behaviour influences the bending moment distribution among structural members, considering the moment–rotation relationships within frame analyses in which structural members are modelled as beam elements can enable a realistic fire response analysis that is significantly simpler than the three-dimensional finite element method. This study proposes an analytical methodology that accounts for the thermo-mechanical behaviour of timber and dowels, enabling the simulation of the non-linear moment–rotation relationships under fire conditions. The proposed analytical model divides dowels into a series of elements on an elastoplastic foundation and performs a direct stiffness method in a time-incremental procedure using an element stiffness matrix derived from beam-on-elastic-foundation theory. This study also presents the results of load-carrying tests on timber frames with dowel-type connections performed under ambient and fire conditions. The analytical results were consistent with the fire test results. Additionally, the analyses were also performed under three conditions in which the dowels were rigid, linear elastic, and elastoplastic bodies. These three results converged to the same value after 65 min of heating, which suggests that the ultimate states of beams with dowel-type connections exposed to fire can be modelled by assuming that dowels are rigid bodies. [ABSTRACT FROM AUTHOR]

Deep borehole heat exchangers (DBHEs) with depths exceeding 500 m have been researched comprehensively in the literature, focusing on both applications and subsurface modelling. This review focuses on conventional (vertical) DBHEs and provides a critical literature survey to analyse (i) methodologies for modelling; (ii) results from heat extraction modelling; (iii) results from modelling deep borehole thermal energy storage; (iv) results from heating and cooling models; and (v) real case studies. Numerical models generally compare well to analytical models whilst maintaining more flexibility, but often with increased computational resources. Whilst in-situ geological parameters cannot be readily modified without resorting to well stimulation techniques (e.g. hydraulic or chemical stimulation), engineering system parameters (such as mass flow rate of the heat transfer fluid) can be optimised to increase thermal yield and overall system performance, and minimise pressure drops. In this active research area, gaps remain, such as limited detailed studies into the effects of geological heterogeneity on heat extraction. Other less studied areas include: DBHE arrays, boundary conditions and modes of operation. A small number of studies have been conducted to investigate the potential for deep borehole thermal energy storage (BTES) and an overview of storage efficiency metrics is provided herein to bring consistency to the reporting of thermal energy storage performance of such systems. The modifications required to accommodate cooling loads are also presented. Finally, the active field of DBHE research is generating a growing number of case studies, particularly in areas with low-cost drilling supply chains or abandoned hydrocarbon or geothermal wells suitable for repurposing. Existing and planned projects are thus presented for conventional (vertical) DBHEs. Despite growing interest in this area of research, further work is needed to explore DBHE systems for cooling and thermal energy storage. [ABSTRACT FROM AUTHOR]

Accurate prediction of the hydraulic effect of hydrate deposition and plug location is critical to the safety and operability of natural gas transport pipelines, especially for gas-dominant subsea pipelines where maintenance and intervention activities are more difficult. To achieve this, the present work improved an existing two-phase pressure drop relation due to friction, by incorporating the hydrates deposition rate into the equation. In addition, a model has been developed to predict the pipeline plugging time. The transient pressure drop predictions in the present study for all six cases at high and low velocities are within 4% mean relative error. Similar predictions by Di Lorenzo et al. are within 40% maximum relative error, while the mean relative error of the transient pressure drop predictions by Zhang et al. was 7.43%. In addition, the plugging flowtime model underpredicts the plugging time by a mean relative error of 9%. [ABSTRACT FROM AUTHOR]

In recent years, the proliferation of self‐established and third‐party online tourism platforms has impacted the visitor economy and social welfare sustainably. Tourism enterprises face the key decision of whether to join third‐party platforms or sell tourism services/products directly to consumers. Some researchers have addressed issues about online tourism platforms, but none analyse the internal mechanism and operational management, or the impact of the online tourism platform on sustainable economic growth and social welfare. To fill this gap, we establish an analytical model to explore the optimal tourism marketing and operational management of online tourism platforms for non‐profit tourist attractions and for‐profit tourism enterprises, which can help guide the decisions of managers. We construct a game‐theoretical model in which competing tourism attractions can choose only solo or dual online tourism platform promotion. When competition on a third‐party platform is intense, for‐profit tourism enterprises benefit from dual platforms. We further illustrate that with high competition, non‐profit tourist attractions provide higher social welfare when offering tourism products/services on both self‐established and third‐party tourism channels. However, with lower competition, third‐party tourism platforms harm social welfare if the tourism service/product quality is extremely high or low. Under a decentralised structure, we find that related tourism enterprises prefer to follow and collaborate with their tourist attractions' channel selection when competition in the third‐party platform is not fierce. This result indicates that a third‐party tourism platform improves the visitor economy and social welfare if the tourist attraction collaborates with its tourism‐related enterprises through the online tourism platform. [ABSTRACT FROM AUTHOR]

Milling with minimum quantity lubrication (MQL) is a commonly used machining technique in the industry because of its advantage in lowering the cutting temperature and cutting force. Among its wide usage in machining, modeling for milling operations was particularly hard for its complexity. This paper proposed an analytical model for cutting force prediction in the end-milling process with MQL. The 3D milling operation was transferred into equivalent 2D orthogonal cutting at each rotational angle. Then the proposed model incorporated updated friction coefficients due to the MQL with boundary lubrication effect. Based on Oxley's orthogonal cutting model, the cutting force was calculated with an updated friction coefficient. Two sets of validations were done with experimental measurements using different cutting materials. The proposed model delivered reasonable accuracy for the force prediction with MQL, providing an adequate method for the industry. Based on the model investigation, the friction coefficient in cutting was also significantly affected by the droplet's layer thickness, which was presumably linearly correlated with the flow speed of the lubricant. [ABSTRACT FROM AUTHOR]

This paper discusses the analytical modelling of a segmented switched reluctance linear synchronous motor (SSRLSM) using a magnetic equivalent circuit (MEC) based on the permeance analysis method (PAM). The PAM is applied to obtain the MEC of the SSRLSM, considering the flux path pattern in the air gap region between the stator and mover. The PAM is used to create the air gap permeance model. The developed permeance model was transformed into a MEC. The MEC corresponds to an electrical circuit based on the geometry of the machine and the estimated magnetic flux path to solve the SSRLSM thrust performance analysis. The equation is derived from the MEC of the SSRLSM and used to analyse the characteristics of the thrust performance of the SSRLSM. The effect of mover position and phase current on the thrust is investigated and analysed. To validate the model of the SSRLSM, the thrust characteristics were compared with FEM and measurement results. The comparison shows good agreement.

ABSTRACTThe optimisation of selective laser sintering (SLS) of polymeric materials, based on analytical equations providing fast predictions, can broaden the SLS application area. However, the selection of SLS polymeric materials is currently rather limited, due to specific requirements regarding sufficient flowability and limited molecular degradation. The present work highlights that upgrading existing analytical equations, by incorporating a well-calculated overlay factor and correcting for pre-heating starting at ambient conditions, can accelerate SLS screening. Model validation is performed based on density, colorimetric, morphological and mechanical analysis of printed parts, focusing on the prediction of the laser power which corresponds to the onset of degradation, taking polyamide powder as a reference case. Furthermore, the optimised model is successfully applied for two other polymer powders, namely thermoplastic co-polyester and thermoplastic polyurethane powder, to highlight a better overall description of the SLS degradation mechanism.

AbstractIn this work an analytical as well as a numerical model are established for computing vibrations induced by a twin tunnel buried in a saturated poroelastic half-space. In the analytical solution the mechanical response for the half-space ground is expressed as a superposition of planar waves from the ground surface and cylindrical waves from two tunnel-soil interfaces. While in the numerical solution, three-dimensional saturated poroelastic finite element and multi-transmitting formula are formulated. The comparisons are made between the two methodologies, and the advantages and disadvantages of the two models are highlighted. Using the analytical one, the influence of the fluid in the soils, the reflection effect of the ground surface and the existence of a neighboring tunnel with or without a source on the mechanical response is investigated. By using the three-dimensional numerical model, the influence of various irregular tunnels on the surface vibration is investigated. The results suggest that: for the displacement and pore pressure response, the difference between one source tunnel and twin source tunnel can be up to 20 dB; the rectangular tunnels lead to the largest response followed by horseshoes and circular ones. [ABSTRACT FROM AUTHOR]

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Objective: Free vibration characteristics of the trapezoidal lattice sandwich composite panels are investigated based on a novel equivalent plate model. Methods: The equivalent shear modulus and the relative density of the graded lattice core are assumed to be thickness-dependent and these material properties are calculated based on the single-cell equivalence theory and the continuity assumption. Under the framework of the higher-order shear deformation theory (HSDT), the unknown displacement functions are expressed in terms of standard Fourier series and auxiliary functions to avoid discontinuities on the edges of lattice sandwich plate. Artificial spring technique is utilized to simulate arbitrary boundary conditions and the unknown coefficients in the displacement functions are obtained by Rayleigh–Ritz variational method. Results: The accuracy of the present method can be verified by comparing the obtained results with FEM results and those from literature. On this basis, a detailed parametric study concerning the effect of boundary conditions, aspect ratio a/b, tilt angle θ, and lamination schemes on the vibration frequencies of the trapezoidal lattice sandwich plate is also performed. [ABSTRACT FROM AUTHOR]

Most shell or beam models of anisotropic tubes under bending have no validity for thick-walled structures. As a result, the need to develop three-dimensional formulations which allow a change in the stress, strain and displacement distributions across the radial component arises. Basic formulations on three-dimensional anisotropic elasticity were made either stress- or displacement-based by Lekhnitskii or Stroh on plates. Lekhnitskii also was the first to expand these analytical formulations to tubes under various loading conditions. This paper presents a review of the stress and strain analysis of tube models using three-dimensional anisotropic elasticity. The focus lies on layered structures, like fiber-reinforced plastics, under various bending loads, although the basic formulations and models regarding axisymmetric loads are briefly discussed. One section is also dedicated to the determination of an equivalent bending stiffness of tubes. [ABSTRACT FROM AUTHOR]

Coating GFRP bars with a layer of carbon fibers containing carbon/glass-hybrid-fiber-reinforced polymer (HFRP) bars has been proven to improved interlaminar shear durability. Thus, the bond performance of the HFRP bar-concrete interface depends on the behavior of the HFRP-reinforced concrete structure. In this context, the study investigates the effects of the compressive strength of concrete and the embedded length of HFRP bars on the bond behavior of the HFRP bar-concrete interface and compares the results with the data on the interfacial bond of GFRP bar to concrete. The results demonstrate that all the specimens fail at the FRP bar–concrete interface under the pullout. The bond strength and bond stiffness of the HFRP bar–concrete composites decrease with an increase in the embedded length of the HFRP bar from 4 to 10 times its diameter. Raising the compressive strength of the concrete enlarges the bond strength and bond stiffness of the HFRP bar–concrete composites. Furthermore, the outer layer of carbon-fiber on the GFRP bar decreases the impact of the embedded length of the HFRP bar on the bond strength and bond stiffness of the HFRP bar–concrete composites. Finally, the improved modified mBPE model can accurately predict the bond stress–slip relationship of GFRP/BFRP/HFRP bar–concrete composites. [ABSTRACT FROM AUTHOR]

Lattice structures are useful in the aerospace, automotive, infrastructural, and medical fields due to the way they incorporate a lightweight design and good mechanical properties, because of their hollow shapes. This review paper documents work carried out using various analytical models for lattice structures designed with different polygon hollow shapes, for loading in the in-plane and out-of-plane directions, in order to advise their ranking in terms of mechanical behaviour. A primer on lattice structures and polygon hollow shapes is first provided. This is followed by a review of relevant analytical models applied to lattice structures with various polygon hollow shapes that are available in the literature, and then a ranking of the polygon hollow structures in terms of their mechanical properties is performed. Following on from this, a review of the mechanical properties of polygon hollow structures is given. Engineering applications of different polygon hollow structures are then identified. A next-generation structural optimisation and design guide is then highlighted, and some of the primary prospective areas to be focused on when designing lattice parts are pointed out. The last section highlights current challenges, as well as recommendations for extending the use of design for the additive manufacturing of lattice parts. [ABSTRACT FROM AUTHOR]

The utilization of Riverbank Filtration Systems (RBF) presents a promising approach for obtaining potable water from rivers or streams. However, the effectiveness of this technique relies significantly on two key factors: the width of the river and the presence of a clogging layer beneath the streambed, both of which influence the degree of contamination in the extracted water. Prior studies have predominantly relied on numerical models or simplistic one-dimensional flow assumptions to address these variables. In contrast, this research introduces a 3D analytical model utilizing the Green's function approach to analyze the movement of contaminants from the river towards the extraction well within RBF systems. By accounting for the dynamic interaction between river width and the clogging layer, this model offers a more accurate depiction of contaminant transport in three-dimensional water flow scenarios. The accompanying MATLAB code facilitates numerical integration of model equations, producing graphical representations for various hydrological inputs. Validation against MODFLOW software demonstrates a remarkable agreement, with outcomes aligning at 98–99%. Key findings underscore the exacerbation of pollutant concentrations with heightened clogging, increased river width, and optimal well placement. Moreover, the analysis underscores better predictive accuracy achieved by incorporating actual river width values compared to simple linear approximations. Notably, the research reveals minimal impact on contaminant concentrations when the distance between the river and the well exceeds twice the river's width, offering valuable insights for system design and management.

The optimisation of selective laser sintering (SLS) of polymeric materials, based on analytical equations providing fast predictions, can broaden the SLS application area. However, the selection of SLS polymeric materials is currently rather limited, due to specific requirements regarding sufficient flowability and limited molecular degradation. The present work highlights that upgrading existing analytical equations, by incorporating a well-calculated overlay factor and correcting for pre-heating starting at ambient conditions, can accelerate SLS screening. Model validation is performed based on density, colorimetric, morphological and mechanical analysis of printed parts, focusing on the prediction of the laser power which corresponds to the onset of degradation, taking polyamide powder as a reference case. Furthermore, the optimised model is successfully applied for two other polymer powders, namely thermoplastic co-polyester and thermoplastic polyurethane powder, to highlight a better overall description of the SLS degradation mechanism. [ABSTRACT FROM AUTHOR]

THE PAPER PRESENTS A LINEAR ELASTIC ONE-DIMENSIONAL Discrete Layer--Wise (DLW) analytical model of a composite girder consisting of two beams bonded together with a layer of a flexible adhesive. The model takes into account both longitudinal and transverse deformation of component beams, the First Order Shear Deformation Theory (FSDT) for these adherends as well as extensibility of the adhesive layer. A system of governing equations is derived and a general solution is found with the use of the method of generalized eigenvectors. Two examples are analyzed both with the use of the considered 1D analytical model and a 3D Finite Element Analysis (FEA) in order to validate predictions of the introduced theory. Satisfactory agreement is found between theoretical and numerical results. [ABSTRACT FROM AUTHOR]

• Mathematical modelling – generalization of the analytical model of sandwich beam with an asymmetric structure analytical solution. • The individual nonlinear deformation function of a plane beam cross section – analytically developed. • Dimensionless deformation functions are determined based on the classical shear stress formula called the Zhuravsky stress. This paper is devoted to a sandwich beam with an asymmetric structure under uniformly distributed load. The first end of this beam is simply supported, while second end is clamped. The individual nonlinear deformation function of a plane beam cross section – the shear effect with consideration of the classical shear stress formula is analytically developed. Displacements, strains and stresses taking into account the individual nonlinear deformation function for successive layers of this beam are elaborated in detail. The system of two differential equation of equilibrium of this beam, based on the principle of stationary potential energy, is obtained. This system of equations is precisely solved analytically, according to the theory of differential equations. The individual nonlinear deformation functions, shear stresses and deflections of two cases of sample beams are determined in detail: the first with variable core porosity in the direction of the beam depth, the second with constant core porosity – standard sandwich structure. The calculations results specified in Tables and graphically presented in Figures. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement. [ABSTRACT FROM AUTHOR]

Theoretical models based on solutions of the conduction heat transfer equation have been widely proposed to calculate the thermal fields generated during laser welding, revealing simplification benefits and limitations in the accuracy of the results. In previous papers, the authors have introduced a parameterized analytical model based on the configuration of a virtual system of multiple mobile heat sources that simulates the effects of an actual keyhole welding mode by setting the system parameters so as to fit the calculated contours of the fusion zone in the weld cross-section of the experimental one. Even though a basic validation was already carried out by experimental detection, in order to further strengthen the model validity, this article deals with an extensive comparison between the results obtained by a multi-physics numerical simulation, performed by a commercial CFD software, and a theoretical one. The two different approaches were applied to the laser beam welding of butt-positioned AISI 304L steel plates. The investigation was focused on the effects of the keyhole on the main morphological features of the melt pool and fusion zone, and on the thermal fields obtained by the two models. The intrinsic differences between the two approaches, and how they are reflected in the corresponding results, were discussed. Satisfactory results were obtained by comparing the thermal fields, with a substantial convergence of the results, so as to validate the analytical model, assess the accuracy of its results, and define its application limits. [ABSTRACT FROM AUTHOR]

Main elements of the analytical modelling are presented for the laser cutting process. Analytical models consider the physical phenomena that occur and formulate balance equations. In current approaches, analytical modelling is integrated into simulation using software dedicated to this purpose. This moves away from the formation and knowledge of elementary models. The technological applicability of analytical modelling is reduced compared to the empirical one, through correlation formulas, because the analytical model is either too general or too particular. The sequential treatment of a complex processing process and the modelling of physical phenomena that have a significant contribution can be a way to exploit analytical modelling. [ABSTRACT FROM AUTHOR]

This work reports on the in-plane crushing behaviour of second-order hierarchical honeycombs with triangle substructures (SHT). Here, cell walls of a conventional hexagonal honeycomb were replaced with two-layer equilateral triangles as substructures. Finite element (FE) simulations and analytical modelling were conducted, and a good agreement was found between FE and analytical results. The response of SHT was compared with that of other patterned honeycombs. Three deformation modes were observed under different loading speeds, and critical velocities for mode transforming were obtained qualitatively. The effect of loading speed and relative density on crushing stress and energy absorption capacity was also discussed. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement.

Carbon nanotubes with their outstanding mechanical, physical and electrical properties have stimulated a significant amount of scientific and technological research due to their uniqueness compared to conventional materials. As a result, an extensive study on their mechanical properties has been conducted, and the static and dynamic behavior of single- walled and multi-walled carbon nanotubes has been examined using Euler-Bernoulli and Timoshenko beam models. The main objective of this paper is to study the free vibration behaviour of single-walled carbon nanotubes (SWCNT) using the nonlocal truncated Timoshenko beam theory. According to the Hamilton principle, the equation of motion of Timoshenko single-walled carbon nanotubes is calculated taking into account the truncated theory; and the general corresponding boundary conditions are derived. Finally, some numerical examples are performed to evaluate the effects of the nonlocal coefficient and the length of the nanotube. The obtained results are validated by comparing them with those found in the literature, and they show the accuracy and efficiency of the developed model. Particularly, the results demonstrate that the present formulation is highly efficient and capable of satisfactorily describing the behavior of nanobeams.

Numerical modelling is particularly advantageous for analysing structures with complex behaviour. It is used to predict the mechanical properties of structures. Analytical modelling, on the contrary, has limited capacity for predicting the behaviour, particularly of structures, because it is based on mathematical equations that do not always exactly represent the geometry of the model. In such cases, numerical modelling is used for predicting structural bending, axial deformation, and buckling behaviour. This study documents numerical modelling of different types of polygon structures. To reduce computation costs, planar and extruded Ti6Al4V(ELI) hexagonal shell structures were used to predict stresses in the out-of-plane and in-plane directions. This was followed by numerical modelling of different types of planar polygon structures to predict their load-bearing capacity and stiffness. Thereafter, the hexagonal polygon was subjected to out-of-plane and in-plane uniaxial compression loads. This was done to compare the bending and buckling behaviour of finite element (FE) models to analytical models. The numerical and analytical results were then compared to determine how the ratio (t/L) of the wall thickness (t) and length of the polygon members (L) influenced the effective stiffness of the hexagonal polygon. The triangular polygon was seen to have the greatest load-bearing capacity and stiffness of all polygons that were modelled. The hexagonal model was observed to generate deformations due to compression, similar to those reported in literature. The critical buckling loads for the analytical honeycomb (HC) models were found to be below the yield stress for (1-, 1.125-, and 1.25-mm wall thicknesses) and above the yield stress for all FE HC models, respectively. The effective stiffness of the HC models were observed to increase with the increasing (t/L) ratio, for both the numerical and analytical models.

This work introduces a novel 3D formulation that presents helical motion within the framework of continuum mechanics. By leveraging the principle of virtual power, a comprehensive theoretical model is proposed, incorporating the extension-torsion coupling. The model establishes equilibrium equations and boundary conditions; its behavior is inspired from cable theory. Additionally, expressions are derived to establish the relationship between tensile stresses and torsion torques, based on the mechanical and geometric parameters. To shown case the influence of various parameters, such as helix pitch and torque, on mechanical stresses, illustrative examples are presented. These results are then compared with those obtained using the Cauchy continuum model. [ABSTRACT FROM AUTHOR]

The article presents the findings of a study that evaluates the feasibility of using an analytical model for a multi-service queuing system with a SDFIFO queuing service discipline and finite compression mechanism to approximate queuing systems with different queuing service disciplines (e.g., FIFO, cFIFO) while also incorporating finite compression. The evaluation involves comparing results obtained from an analytical model with those of simulation studies. The study considers the blocking probability and average queue length as factors. Additionally, two types of compressed traffic were analysed: elastic and adaptive. These are characteristic of modern telecommunications networks, particularly in multimedia applications. This paper is an extended version of our paper published in 4th CoBCom 2022. [ABSTRACT FROM AUTHOR]

Many of the carbon and natural fibres used in composite reinforcement have a non-circular cross section. Recently non-circular, or flat, cross section glass fibre products have become commercially available. This paper explores the potential effects that such non-circular fibre cross section shapes may have on the micromechanics of stress transfer at the composite fibre–matrix interface and the resulting changes in composite strength performance. Analytical modelling is used to show how the critical fibre length in composites with non-circular fibres is always less when compared to circular fibres with an equal cross-sectional area. This can result in significant changes to the strength performance of discontinuous fibre reinforced composites. Additionally, it is shown that the surface roughness found on natural and carbon fibres, many of which are also non-circular in cross section, can decrease the critical fibre length still further. These effects have important consequences for the use of single fibre micromechanical tests used for the characterisation of interfacial strength.

Lattice structures are useful in the aerospace, automotive, infrastructural, and medical fields due to the way they incorporate a lightweight design and good mechanical properties, because of their hollow shapes. This review paper documents work carried out using various analytical models for lattice structures designed with different polygon hollow shapes, for loading in the in-plane and out-of-plane directions, in order to advise their ranking in terms of mechanical behaviour. A primer on lattice structures and polygon hollow shapes is first provided. This is followed by a review of relevant analytical models applied to lattice structures with various polygon hollow shapes that are available in the literature, and then a ranking of the polygon hollow structures in terms of their mechanical properties is performed. Following on from this, a review of the mechanical properties of polygon hollow structures is given. Engineering applications of different polygon hollow structures are then identified. A next-generation structural optimisation and design guide is then highlighted, and some of the primary prospective areas to be focused on when designing lattice parts are pointed out. The last section highlights current challenges, as well as recommendations for extending the use of design for the additive manufacturing of lattice parts.

In this work, we propose a geodetic model for the seismic sequence, with doublet earthquakes, that occurred in Bandar Abbas, Iran, in November 2021. A dataset of Sentinel-1 images, processed using the InSAR (Interferometric Synthetic Aperture Radar) technique, was employed to identify the surface deformation caused by the major events of the sequence and to constrain their geometry and kinematics using seismological constraints. A Coulomb stress transfer analysis was also applied to investigate the sequence's structural evolution in space and time. A linear inversion of the InSAR data provided a non-uniform distribution of slip over the fault planes. We also performed an accurate relocation of foreshocks and aftershocks recorded by locally established seismographs, thereby allowing us to determine the compressional tectonic stress regime affecting the crustal volume. Despite the very short time span of the sequence, our results clearly suggest that distinct blind structures that were previously unknown or only suspected were the causative faults. The first Mw 6.0 earthquake occurred on an NNE-dipping, intermediate-angle, reverse-oblique plane, while the Mw 6.4 earthquake occurred on almost horizontal or very low-angle (SSE-dipping) reverse segments with top-to-the-south kinematics. The former, which cut through and displaced the Pan-African pre-Palaeozoic basement, indicates a thick-skinned tectonic style, while the latter rupture(s), which occurred within the Palaeozoic–Cenozoic sedimentary succession and likely exploited the stratigraphic mechanical discontinuities, clearly depicts a thin-skinned style. [ABSTRACT FROM AUTHOR]

This article provides an analytical model to determine the suitable location of pumping well located between two polluted parallel sources. The first source is assumed to be a polluted river, while the second one is an arbitrary contaminant source such as landfill leachate site or wastewater. The location of the well is specified so that it gets the highest amount of river water that satisfies water quality requirements. To validate the model results, a numerical simulation is conducted using MODFLOW to calculate the concentration of contaminants at various locations determined by the proposed analytical model. The results confirmed the suitability of the analytical model to determine the location of pumping well. Additionally, it is found that any increase in pumping time, pumping rate or initial contaminant concentration increases the distance between river and well. [ABSTRACT FROM AUTHOR]

Carbon nanotubes with their outstanding mechanical, physical and electrical properties have stimulated a significant amount of scientific and technological research due to their uniqueness compared to conventional materials. As a result, an extensive study on their mechanical properties has been conducted, and the static and dynamic behavior of single- walled and multi-walled carbon nanotubes has been examined using Euler-Bernoulli and Timoshenko beam models. The main objective of this paper is to study the free vibration behaviour of single-walled carbon nanotubes (SWCNT) using the nonlocal truncated Timoshenko beam theory. According to the Hamilton principle, the equation of motion of Timoshenko single-walled carbon nanotubes is calculated taking into account the truncated theory; and the general corresponding boundary conditions are derived. Finally, some numerical examples are performed to evaluate the effects of the nonlocal coefficient and the length of the nanotube. The obtained results are validated by comparing them with those found in the literature, and they show the accuracy and efficiency of the developed model. Particularly, the results demonstrate that the present formulation is highly efficient and capable of satisfactorily describing the behavior of nanobeams. [ABSTRACT FROM AUTHOR]

The aim of this work is to propose a sandwich beam with stepped layer thickness in three parts along its length. The total depth, width of the cross-section and its mass are constant. The beam is under a uniformly distributed load. The system of two equilibrium equations was formulated for each part based on the literature. This system was analytically solved for the successive parts of the beam and the functions of the shear effect and deflection were determined in them. The effective stepped layer thicknesses was determined on the basis of the adopted criterion for minimizing the maximum deflection of the beam. The example calculations were made for two elected beams. The effective shapes of these beams are shown in the figures. Moreover, FEM numerical calculations of the deflections of these beams are performed. [ABSTRACT FROM AUTHOR]

Properly validated theoretical models are needed to understand the device and circuit level performance of MOSFET at high frequency. Analytical as well as compact models have special significance due to its SPICE simulator compatibility. Perhaps, most of the RF modelling approaches requires experimental Y, Z or S parameters to start with, which limits their acceptability in SPICE simulators. Considering this, under an innovative approach, starting from basic device physics, a complete generalized analytical RF model is developed for Semiconductor-On-Insulator MOSFET. Mathematical expressions for important MOSFET parameters valid at RF range are developed. Numbers of unique and justified mathematical formulations are adopted throughout the analysis to keep the parameter expressions simple but accurate. Parameters expressions are used to simulate and plot Y parameters with different structural and operational variables. These results are compared with reference results to check for validity. RF performance of current and upcoming Semiconductor-On-Insulator MOSFET structures are simulated and compared for better device selectivity. [ABSTRACT FROM AUTHOR]