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Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds.

The paper opted the tensor calculus on manifolds to find the solution of the CPE.

In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting.

The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.

When establishing a mathematical model to simulate solid mechanics, considering realistic geometries, special tools are needed to translate measured data, possibly with noise, into idealized geometrical entities. As an engineering application, wheel-rail contact interactions are fundamental in the dynamic modeling of railway vehicles. Many approaches used to solve the contact problem require a continuous parametric description of the geometries involved. However, measured wheel and rail profiles are often available as sets of discrete points. A reconstruction method is needed to transform discrete data into a continuous geometry.

The authors present an approximation method based on optimization to solve the problem of fitting a set of points with an arc spline. It consists of an initial guess based on a curvature function estimated from the data, followed by a least-squares optimization to improve the approximation. The authors also present a segmentation scheme that allows the method to increment the number of segments of the spline, trying to keep it at a minimal value, to satisfy a given error tolerance.

The paper provides a better understanding of arc splines and how they can be deformed. Examples with parametric curves and slightly noisy data from realistic wheel and rail profiles show that the approach is successful.

The developed methods have theoretical value. Furthermore, they have practical value since the approximation approach is better suited to deal with the reconstruction of wheel/rail profiles than interpolation, which most methods use to some degree.

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.

The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.

An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.

The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.

Although green logistics has become a new focus of cooperation between government and enterprises under environmental constraints, how local governments formulate subsidy policies to effectively guide the green transformation of regional logistics and how to facilitate the reasonable cost-sharing are rather critical. This paper will deeply explore the dynamic process of the tripartite participation (government, platform, and logistics enterprises) in the selection of regional green logistics strategy, and reveal the evolutionary game relationship of the three parties.

To explore the dynamics involving the government, platform and logistics enterprises for the green logistic transformation, and reveal the evolutionary gaming among the three parties, based on the bounded rationality premise, this study constructs the tripartite asymmetric evolutionary game models, uses the stability theorem of differential equation to explore the evolution and stability strategy of the system in different cases and explicates the paths of influence on the tripartite behaviors via simulations.

Results of this study indicate that there exist stable equilibrium strategies among the three parties regarding the regional green logistics, and they are affected by different factors. The government's subsidy, subsidy intensity and the platform's cost-sharing proportion can generate positive effects, but the latter two can also impact negatively beyond the effective ranges. The findings provide a theoretical basis for local governments, platforms and logistics enterprises to formulate justifiable subsidy intensity and determine reasonable sharing proportion.

Firstly, considering the significant relevance of local government, it is included in the evolution model, and the tripartite game (among government, platform and enterprises) is explored; Secondly, by comparing the equilibrium results under different game conditions, this paper analyzes the evolution of each party's game strategy to achieve the optimal return under bounded rationality and the important factors determining the strategic selection; Finally, the key factor of platform cost sharing is involved, and to what extent the change of platform cost sharing ratio will influence the systematic stability is explored.

This paper aims to study the motion trajectory of the oil seal for shaft in eccentric state and derive equation of lip motion trajectory.

This paper analyzes the force during the motion of the eccentric lip by considering the material viscoelasticity, and a cam-plate mechanism is established as an equivalent model for the motion between the shaft and the lip; according to this, the equation of lip motion trajectory is derived.

The trajectory of the lip lags that of the shaft in the eccentric state because the viscoelasticity-affected lip recovery velocity is lower than the shaft recovery speed. The lip trajectory enters the lag phase earlier and the lag phase’s duration is longer with the increase of the eccentricity and rotational speed, because the deviation of the recovery velocities between the lip and the shaft will be exacerbated.

Innovatively, by considering the viscoelasticity of the material, the cam-plate mechanism is used to equivalent the motion of the shaft-lip to derive the equation for the radial motion trajectory of the eccentric lip. The regularity of lip motion is the key to determining the performance of oil seals, and the eccentric lip trajectory research method revealed in this paper provides a research basis for the performance research and optimization of eccentric oil seals.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0161/

This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

This paper aims to introduce a new numerical model that predicts the flashover voltage (FOV) value in the presence of polluted air surrounding a high-voltage insulator. The model focuses on simulating the propagation of arcs and aims to improve the accuracy and reliability of FOV predictions under these specific conditions.

This arc propagation method connecting the high voltage fitting and the grounded insulator cap involves a two-step process. First, the electric field distribution in the vicinity of the insulator is obtained using finite element method analysis software. Subsequently, critical areas with intense electric field strength are identified. Random points within these critical areas are then selected as initial points for simulating the growth of electric arcs.

by increasing the electric voltage applied to the insulator fittings, the arc path is, step by step, generated until a breakdown occurs on the polluted air surrounding the insulator surface, and thus a prediction of the FOV value.

The proposed model for the FOV prediction can be a very interesting alternative to dangerous and costly experimental tests requiring an investment in time and materials.

Some works were done trying to reproduce discharge propagation but it was always with simplified models such as propagation in one direction from a point to a plane. The difficulty and the originality of the present work is the geometry complexity of the insulator with arc propagation in three distinct directions that will require several proliferation conditions.

This paper aims to study the magnetohydrodynamic (MHD) wall jet of a hybrid nanofluid flow over a moving surface with a thermally convective surface, wall moving with suction/injection.

On using appropriate similarity transformations, the governing equations that describe the model are converted into a system of nonlinear ordinary differential equations. These equations are solved both analytically and numerically using standard two-point boundary-value problem solvers and Chebyshev pseudospectral differentiation matrix method, respectively.

These results show that the HNF is heating/cooling with growth of the positive/negative values of the parameter measuring the velocity of the moving surface. The temperature distributions increase, where the thermal boundary layer gets thicker, as the magnetic field strengthens and with an increase in the absolute value of the Biot number.

The current findings for the HNFs are new and original. They generalize successfully the problems investigated previously by different researchers for the cases of fluids and also nanofluids.

The present paper aims at the multi-objective optimization of a reentrant hexagonal cell auxetic structure. In addition, a parametric analysis will be carried out to verify how each of the design factors impact each of the responses.

The multi-objective optimization of five different responses of an auxetic model was considered: mass, critical buckling load under compression effort, natural frequency, Poisson's ratio and failure load. The response surface methodology was applied, and a new meta-heuristic of optimization called the multi-objective Lichtenberg algorithm was applied to find the optimized configuration of the model. It was possible to increase the failure load by 26.75% in compression performance optimization. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively. This paper addresses something new in the scientific world to date when evaluating in a multi-objective optimization problem, the compression and modal performance of an auxetic reentrant model.

It was possible to find multi-objective optimized structures. It was possible to increase the critical buckling load by 42.82%, and the failure load in compression performance by 26.75%. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%, and decrease the mass by 15.97%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, increase the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively.

There is no work in the literature to date that performed the optimization of 5 responses simultaneously of a reentrant hexagonal cell auxetic structure. This paper also presents an unprecedented statistical analysis in the literature that verifies how the design factors impact each of the responses.

This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C¹ basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.

The weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C⁰ non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C¹) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.

It is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.

Fourth-order PFM is implemented using C¹ non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.