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This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

The purpose of this study is to adapt the incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence to manage the physical problem of double diffusion inside a porous L-shaped cavity including two fins.

The ISPH method solves the nondimensional governing equations of a physical model. The ISPH simulations are attained at different Frank–Kamenetskii number, Darcy number, coupled Soret/Dufour numbers, coupled Cattaneo–Christov heat/mass fluxes, thermal radiation parameter and nanoparticle parameter. An artificial neural network (ANN) is developed using a total of 243 data sets. The data set is optimized as 171 of the data sets were used for training the model, 36 for validation and 36 for the testing phase. The network model was trained using the Levenberg–Marquardt training algorithm.

The resulting simulations show how thermal radiation declines the temperature distribution and changes the contour of a heat capacity ratio. The temperature distribution is improved, and the velocity field is decreased by 36.77% when the coupled heat Cattaneo–Christov heat/mass fluxes are increased from 0 to 0.8. The temperature distribution is supported, and the concentration distribution is declined by an increase in Soret–Dufour numbers. A rise in Soret–Dufour numbers corresponds to a decreasing velocity field. The Frank–Kamenetskii number is useful for enhancing the velocity field and temperature distribution. A reduction in Darcy number causes a high porous struggle, which reduces nanofluid velocity and improves temperature and concentration distribution. An increase in nanoparticle concentration causes a high fluid suspension viscosity, which reduces the suspension’s velocity. With the help of the ANN, the obtained model accurately predicts the values of the Nusselt and Sherwood numbers.

A novel integration between the ISPH method and the ANN is adapted to handle the heat and mass transfer within a new L-shaped geometry with fins in the presence of several physical effects.

This paper aims to employ a multivariate nonlinear regression analysis to establish a predictive model for the final fracture area, while accounting for the impact of individual parameters.

This analysis is based on the numerical simulation data obtained, using the hybrid finite element–discrete element (FE–DE) method. The forecasting model was compared with the numerical results and the accuracy of the model was evaluated by the root mean square (RMS) and the RMS error, the mean absolute error and the mean absolute percentage error.

The multivariate nonlinear regression model can accurately predict the nonlinear relationships between injection rate, leakoff coefficient, elastic modulus, permeability, Poisson’s ratio, pore pressure and final fracture area. The regression equations obtained from the Newton iteration of the least squares method are strong in terms of the fit to the six sensitive parameters, and the model follow essentially the same trend with the numerical simulation data, with no systematic divergence detected. Least absolutely deviation has a significantly weaker performance than the least squares method. The percentage contribution of sensitive parameters to the final fracture area is available from the simulation results and forecast model. Injection rate, leakoff coefficient, permeability, elastic modulus, pore pressure and Poisson’s ratio contribute 43.4%, −19.4%, 24.8%, −19.2%, −21.3% and 10.1% to the final fracture area, respectively, as they increased gradually. In summary, (1) the fluid injection rate has the greatest influence on the final fracture area. (2)The multivariate nonlinear regression equation was optimally obtained after 59 iterations of the least squares-based Newton method and 27 derivative evaluations, with a decidability coefficient R2 = 0.711 representing the model reliability and the regression equations fit the four parameters of leakoff coefficient, permeability, elastic modulus and pore pressure very satisfactorily. The models follow essentially the identical trend with the numerical simulation data and there is no systematic divergence. The least absolute deviation has a significantly weaker fit than the least squares method. (3)The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

The floating ring generates elastic deformation as the film pressure for high-speed floating ring bearings (FRBs). The purpose of this study is to investigate the influence of ring elastic deformation on the performance of a hydrodynamic/hydrostatic FRB, including floating ring equilibrium and minimum film thickness.

The finite element method and finite difference method are used to solve thermohydrodynamic (THD) lubrication models, including the Reynolds equation, energy equation and temperature–viscosity equation. The deformation matrix method is applied to solve the elastic deformation equation, and then the deformation distribution, floating ring equilibrium and minimum film thickness are investigated. The maximum pressure is compared with the published article to verify the mathematical models.

The deformation value increases with the growth of shaft speed; owing to elastic deformation on the film reaction force and friction moment, the ring achieves equilibrium at a new position, and the inner eccentricity increases while the ring-shaft speed ratio declines. The minimum film thickness declines with the growth of inlet temperature, and the outer film tends to rupture considering elastic deformation at a higher temperature.

The floating ring elastic deformation is coupled with the THD lubrication equations to study ring deformation on the hydrodynamic/hydrostatic FRB lubrication mechanism. The elastic deformation of floating ring should be considered to improve analysis accuracy for FRBs.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2023-0139/

As the crucial support component of the propeller power system, the reliability of the operation of submersible pumps is influenced by the lubrication performance of water-lubricated thrust bearings. When the water-lubricated thrust bearings are under start-stop or heavy load conditions, the effect of surface morphology is crucial as the mixed lubrication regime is encountered. This paper aims to develop one mixed lubrication model for the water-lubricated thrust bearings to predict the effects of surface skewness, kurtosis and roughness orientation on the loading carrying capacity and tribological behavior.

This paper developed one improved mixed lubrication model specifically for the water-lubricated thrust bearing system. In this model, the hydrodynamic model was improved by using the height of the rough surface and its probability density function, combined with the average flow model. The asperity contact model was improved by using the equation for the Pearson system of frequency curves to characterize the non-Gaussian aspect of surface roughness distribution.

According to the results, negative skewness, large kurtosis and lateral surface pattern can improve the tribological performance of water-lubricated thrust bearings. Optimizing the surface morphology is a reasonable design method that can improve the performance of water-lubricated thrust bearings.

In this paper, one mixed lubrication model specifically for the water-lubricated thrust bearing with the effect of surface roughness into consideration was developed. Based on the developed model, the effect of surface morphology on tribological behavior can be evaluated.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2023-0247/

The contact and lubrication performances, which were previously estimated assuming a Gaussian surface, are insufficient due to the non-Gaussian surface characteristics of the honing liner. The purpose of this study is to analyze the liner honing surface and examine its effects on the contact and flow performance.

The fast Fourier transform (FFT) method was used to generate the liner honing texture. Subsequently, an elastoplastic contact model based on boundary element theory was constructed and simulated for the honing surface. The results were compared with those obtained using a Gaussian surface. In addition, flow factors of the honing surfaces were also compared.

The contact pressure and flow factors demonstrate significant disparities when dealing with non-Gaussian surfaces. In the deterministic model, the pressure exhibits considerably diminished magnitudes and a more evenly distribution. Moreover, when the gap between surfaces is narrow, the discrepancy in flow factor across different directions on the real honing surface becomes more prominent compared with the Gaussian surface.

The model incorporates the influence of the non-Gaussian honing surface, thereby enabling more accurate prediction.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0198/

This paper aims to present the approximate limit pressure solutions for thin-walled shape-imperfect 90° pipe bends. Limit pressure was determined by finite element (FE) limit analysis with the consideration of small geometry change effects.

The limit pressure of 90° pipe bends with ovality and thinning has been evaluated by geometric linear FE approach. Internal pressure was applied to the inner surface of the FE pipe bend models. When von-Mises stress equals or just exceeds the yield strength of the material, the corresponding pressure was considered as the limit pressure for all models. The current FE methodology was evaluated by the theoretical solution which has been published in the literature.

Ovality and thinning produced a significant effect on thin-walled pipe bends. The ovality weakened pipe bend performance at any constant thinning, while thinning improved the performance of the bend portion at any constant ovality. The limit pressure of pipe bends under internal pressure increased with an increase in the bend ratio and decreased with an increase in the pipe ratio. With a simultaneous increment in bend radius and reduction in wall thickness, there was a reduction in limit pressure. A new closed-form empirical solution was proposed to evaluate limit pressure, which was validated with published experimental data.

The influences of structural deformation (ovality and thinning) in the limit pressure analysis of 90° pipe bends have not been investigated and reported.

Studying the shear stress and pressure resulting on the walls of blood vessels, especially during high-pressure cases, which may lead to the explosion or rupture of these vessels, can also lead to the death of many patients. Therefore, it was necessary to try to control the shear and normal stresses on these veins through nanoparticles in the presence of some external forces, such as exposure to some electromagnetic shocks, to reduce the risk of high pressure and stress on those blood vessels. This study aims to examines the shear and normal stresses of electroosmotic-magnetized Sutterby Buongiorno’s nanofluid in a symmetric peristaltic channel with a moderate Reynolds number and curvature. The production of thermal radiation is also considered. Sutterby nanofluids equations of motion, energy equation, nanoparticles concentration, induced magnetic field and electric potential are calculated without approximation using small and long wavelengths with moderate Reynolds numbers.

The Adomian decomposition method solves the nonlinear partial differential equations with related boundary conditions. Graphs and tables show flow features and biophysical factors like shear and normal stresses.

This study found that when curvature and a moderate Reynolds number are present, the non-Newtonian Sutterby fluid raises shear stress across all domains due to velocity decay, resulting in high shear stress. Additionally, modest mobility increases shear stress across all channel domains. The Sutterby parameter causes fluid motion resistance, which results in low energy generation and a decrease in the temperature distribution.

Equations of motion, energy equation, nanoparticle concentration, induced magnetic field and electric potential for Sutterby nano-fluids are obtained without any approximation i.e. the authors take small and long wavelengths and also moderate Reynolds numbers.

This study aims to propose a series of numerical and surrogate models to investigate the aerodynamic pressure inside cracks in high-speed railway tunnel linings and to predict the stress intensity factors (SIFs) at the crack tip.

A computational fluid dynamics (CFD) model is used to calculate the aerodynamic pressure exerted on two cracked surfaces. The simulation uses the viscous unsteady κ-ε turbulence model. Using this CFD model, the spatial and temporal distribution of aerodynamic pressure inside longitudinal, oblique and circumferential cracks are analyzed. The mechanism behind the pressure variation in tunnel lining cracks is revealed by the air density field. Furthermore, a response surface model (RSM) is proposed to predict the maximum SIF at the crack tip of circumferential cracks and analyze its influential parameters.

The initial compression wave amplifies and oscillates in cracks in tunnel linings, resulting from an increase in air density at the crack front. The maximum pressure in the circumferential crack is 2.27 and 1.76 times higher than that in the longitudinal and oblique cracks, respectively. The RSM accurately predicts the SIF at the crack tip of circumferential cracks. The SIF at the crack tip is most affected by variations in train velocities, followed by the depth and length of the cracks.

The mechanism behind the variation of aerodynamic pressure in tunnel lining cracks is revealed. In addition, a reliable surrogate model is proposed to predict the mechanical response of the crack tip under aerodynamic pressures.

This paper explores the empirical relationship between population age structure and bilateral trade.

The author includes age structure in both log and Poisson pseudo-maximum likelihood (PPML) formulations of the gravity equation of trade. The author studies relative age effects, using differences in the demographic structure of each country-pair.

The author finds that a relatively larger share of population in working age increases bilateral exports. This is robust to various estimation models, as well as to changes in the method of specifying the demographic controls. Old-age shares have a negative, but less robustly estimated impact on trade. Estimating instead the balance of trade between trading partners produces similar results, with positive effects of age structure peaking later in working life.

Global populations are poised to undergo a massive transition. Trade a crucial way that the demographic deficits of one country may be offset by the dividends of another as comparative advantages shift along with the size and strength of their underlying workforce.

The author’s work is among the first to quantify the effect of relative age structure between two countries and their bilateral trade flows. Focusing on the aggregate flows, relative age shares and PPML estimates of the trade relationship, this paper provides the most comprehensive picture to date on how age structure affects trade.