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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.

Due to the miniaturization of electronic devices, the increased current density through solder joints leads to the occurrence of electromigration failure, thereby reducing the reliability of electronic devices. The purpose of this study is to propose a finite element-artificial neural network method for the prediction of temperature and current density of solder joints, and thus provide reference information for the reliability evaluation of solder joints.

The temperature distribution and current density distribution of the interconnect structure of electronic devices were investigated through finite element simulations. During the experimental process, the actual temperature of the solder joints was measured and was used to optimize the finite element model. A large amount of simulation data was obtained to analyze the neural network by varying the height of solder joints, the diameter of solder pads and the magnitude of current loads. The constructed neural network was trained, tested and optimized using this data.

Based on the finite element simulation results, the current is more concentrated in the corners of the solder joints, generating a significant amount of Joule heating, which leads to localized temperature rise. The constructed neural network is trained, tested and optimized using the simulation results. The ANN 1, used for predicting solder joint temperature, achieves a prediction accuracy of 96.9%, while the ANN 2, used for predicting solder joint current density, achieves a prediction accuracy of 93.4%.

The proposed method can effectively improve the estimation efficiency of temperature and current density in the packaging structure. This method prevails in the field of packaging, and other factors that affect the thermal, mechanical and electrical properties of the packaging structure can be introduced into the model.

When the reinforced concrete beams are reinforced by bonding steel plates to the bottom, excessive use of steel plates will make the reinforced concrete beams become super-reinforced beams, and there are security risks in the actual use of super-reinforced beams. In order to avoid the occurrence of this situation, the purpose of this paper is to study the calculation method of the maximum number of bonded steel plates to reinforce reinforced concrete beams.

First of all, when establishing the limit failure state of the reinforced member, this paper comprehensively considers the role of the tensile steel bar and steel plate and takes the load effect before reinforcement as the negative contribution of the maximum number of bonded steel plates that can be used for reinforcement. Through the definition of the equivalent tensile strength, equivalent elastic modulus and equivalent yield strain of the tensile steel bar and steel plate, a method to determine the relative limit compression zone height of the reinforced member is obtained. Second, based on the maximum ratio of (reinforcement + steel plate), the relative limit compression zone height and the equivalent tensile strength of the tensile steel bar and steel plate of the reinforced member, the calculation method of the maximum number of bonded steel plates is derived. Then, the static load test of the test beam is carried out and the corresponding numerical model is established, and the reliability of the numerical model is verified by comparison. Finally, the accuracy of the calculation method of the maximum number of bonded steel plates is proved by the numerical model.

The numerical simulation results show that when the steel plate width is 800 mm and the thickness is 1–4 mm, the reinforced concrete beam has a delayed yield platform when it reaches the limit state, and the failure mode conforms to the basic stress characteristics of the balanced-reinforced beam. When the steel plate thickness is 5–8 mm, the sudden failure occurs without obvious warning when the reinforced concrete beam reaches the limit state. The failure mode conforms to the basic mechanical characteristics of the super-reinforced beam failure, and the bending moment of the beam failure depends only on the compressive strength of the concrete. The results of the calculation and analysis show that the maximum number of bonded steel plates for reinforced concrete beams in this experiment is 3,487 mm². When the width of the steel plate is 800 mm, the maximum thickness of the steel plate can be 4.36 mm. That is, when the thickness of the steel plate, the reinforced concrete beam is still the balanced-reinforced beam. When the thickness of the steel plate, the reinforced concrete beam will become a super-reinforced beam after reinforcement. The calculation results are in good agreement with the numerical simulation results, which proves the accuracy of the calculation method.

This paper presents a method for calculating the maximum number of steel plates attached to the bottom of reinforced concrete beams. First, based on the experimental research, the failure mode of reinforced concrete beams with different number of steel plates is simulated by the numerical model, and then the result of the calculation method is compared with the result of the numerical simulation to ensure the accuracy of the calculation method of the maximum number of bonded steel plates. And the study does not require a large number of experimental samples, which has a certain economy. The research result can be used to control the number of steel plates in similar reinforcement designs.

This paper presents the experimental and numerical results of the bending properties of low-height prestressed T-beams. The purpose is to study the bearing capacity, failure state and strain distribution of low-height prestressed T-beams.

First, two 13 m-long full-size test beams were fabricated with different positions of prestressed steel bundles in the span. The load–deflection curves and failure patterns of each test beam were obtained through static load tests. Secondly, the test data were used to validate the finite element model developed to simulate the flexural behavior of low-height prestressed T-beams. Finally, the influence of different parameters (the number of prestressed steel bundles, initial prestress and concrete strength grade) on the flexural performance of the test beams is studied by using a finite element model.

The test results show that when the distance of the prestressed steel beam from the bottom height of the test beam increases from 40 to 120 mm, the cracking load of the test beam decreases from 550.00 to 450.00 kN, reducing by 18.18%, and the ultimate load decreases from 1338.15 to 1227.66 kN, reducing by 8.26%, therefore, the increase of the height of the prestressed steel beam reduces the bearing capacity of the test beam. The numerical simulation results show that when the number of steel bundles increases from 2 to 9, the cracking load increases by 183.60%, the yield load increases by 117.71% and the ultimate load increases by 132.95%. Therefore, the increase in the number of prestressed steel bundles can increase the cracking load, yield load and ultimate load of the test beam. When the initial prestress is from 695 to 1,395 MPa, the cracking load increases by 69.20%, the yield load of the bottom reinforcement increases by 31.61% and the ultimate load increases by 3.97%. Therefore, increasing the initial prestress can increase the cracking load and yield load of the test beam, but it has little effect on the ultimate load. The strength grade of concrete increases from C30 to C80, the cracking load is about 455.00 kN, the yield load is about 850.00 kN and the ultimate load is increased by 4.90%. Therefore, the improvement in concrete strength grade has little influence on the bearing capacity of the test beam.

Based on the experimental study, the bearing capacity of low-height prestressed T-beams with different prestressed steel beam heights is calculated by finite element simulation, and the influence of different parameters on the bearing capacity is discussed. This method not only ensures the accuracy of bearing capacity assessment, but also does not require a large number of samples and has a certain economy. The study of prestressed low-height T-beams is of great significance for understanding the principle and application of prestressed technology. Research on the mechanical behavior and performance of low-height prestressed T beams can provide a scientific basis and technical support for the design and construction of prestressed concrete structures. In addition, the study of prestressed low-height T-beams can also provide a reference for the optimization design and construction of other structural types.

The ionization of the air surrounding the phase conductor in high-voltage transmission lines results in a phenomenon known as the Corona effect. To avoid this, Corona rings are used to dampen the electric field imposed on the insulator. The purpose of this study is to present a fast and intelligent surrogate model for determination of the electric field imposed on the surface of a 120 kV composite insulator, in presence of the Corona ring.

Usually, the structural design parameters of the Corona ring are selected through an optimization procedure combined with some numerical simulations such as finite element method (FEM). These methods are slow and computationally expensive and thus, extremely reducing the speed of optimization problems. In this paper, a novel surrogate model was proposed that could calculate the maximum electric field imposed on a ceramic insulator in a 120 kV line. The surrogate model was created based on the different scenarios of height, radius and inner radius of the Corona ring, as the inputs of the model, while the maximum electric field on the body of the insulator was considered as the output.

The proposed model was based on artificial intelligence techniques that have high accuracy and low computational time. Three methods were used here to develop the AI-based surrogate model, namely, Cascade forward neural network (CFNN), support vector regression and K-nearest neighbors regression. The results indicated that the CFNN has the highest accuracy among these methods with 99.81% R-squared and only 0.045468 root mean squared error while the testing time is less than 10 ms.

To the best of the authors’ knowledge, for the first time, a surrogate method is proposed for the prediction of the maximum electric field imposed on the high voltage insulators in the presence Corona ring which is faster than any conventional finite element method.

The purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.

Through analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.

The accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.

The application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

Gas metal arc-based directed energy deposition (GMA-DED) process experiences residual stress (RS) developed due to heat accumulation during successive layer deposition as a significant challenge. To address that, monitoring of transient temperature distribution concerning time is a critical input. Finite element analysis (FEA) is considered a decisive engineering tool in quantifying temperature and RS in all manufacturing processes. However, computational time and prediction accuracy has always been a matter of concern for FEA-based prediction of responses in the GMA-DED process. Therefore, this study aims to investigate the effect of finite element mesh variations on the developed RS in the GMA-DED process.

The variation in the element shape functions, i.e. linear- and quadratic-interpolation elements, has been used to model a single-track 10-layered thin-walled component in Ansys parametric design language. Two cases have been proposed in this study: Case 1 has been meshed with the linear-interpolation elements and Case 2 has been meshed with the combination of linear- and quadratic-interpolation elements. Furthermore, the modelled responses are authenticated with the experimental results measured through the data acquisition system for temperature and RS.

A good agreement of temperature and RS profile has been observed between predicted and experimental values. Considering similar parameters, Case 1 produced an average error of 4.13%, whereas Case 2 produced an average error of 23.45% in temperature prediction. Besides, comparing the longitudinal stress in the transverse direction for Cases 1 and 2 produced an error of 8.282% and 12.796%, respectively.

To avoid the costly and time-taking experimental approach, the experts have suggested the utilization of numerical methods in the design optimization of engineering problems. The FEA approach, however, is a subtle tool, still, it faces high computational cost and low accuracy based on the choice of selected element technology. This research can serve as a basis for the choice of element technology which can predict better responses in the thermo-mechanical modelling of the GMA-DED process.

This paper aims to investigate the performance of two novel numerical methods, the face-based smoothed finite element method (FS-FEM) and the edge-based smoothed finite element method (ES-FEM), which employ linear tetrahedral elements, for the purpose of strength assessment of a high-speed train hollow axle.

The calculation of stress for the wheelset, comprising an axle and two wheels, is facilitated through the application of the European axle strength design standard. This standard assists in the implementation of loading and boundary conditions and is exemplified by the typical CRH2 high-speed train wheelset. To evaluate the performance of these two methods, a hollow cylinder cantilever beam is first used as a benchmark to compare the present methods with other existing methods. Then, the strength analysis of a real wheelset model with a hollow axle is performed using different numerical methods.

The results of deflection and stress show that FS-FEM and ES-FEM offer higher accuracy and better convergence than FEM using linear tetrahedral elements. ES-FEM exhibits a superior performance to that of FS-FEM using linear tetrahedral elements, showing accuracy and convergence close to FEM using hexahedral elements.

This study channels the novel methods (FS-FEM and ES-FEM) in the static stress analysis of a railway wheelset. Based on the careful testing of FS-FEM and ES-FEM, both methods hold promise as more efficient tools for the strength analysis of complex railway structures.

Pores and shrink holes are unavoidable defects in the die-casting mass production process which may significantly influence the strength, fatigue and fracture behaviour as well as the life span of structures, especially if they are subjected to high static and dynamic loads. Such defects should be considered during the design process or after production, where the defects could be detected with the help of computed tomography (CT) measurements. However, this is usually not done in today's mass production environments. This paper deals with the stress analysis of die-cast structural parts with pores found from CT measurements or that are artificially placed within a structure.

In this paper the authors illustrate two general methodologies to take into account the porosity of die-cast components in the stress analysis. The detailed geometry of a die-cast part including all discontinuities such as pores and shrink holes can be included via STL data provided by CT measurements. The first approach is a combination of the finite element method (FEM) and the finite cell method (FCM), which extends the FEM if the real geometry cuts finite elements. The FCM is only applied in regions with pores. This procedure has the advantage that all simulations with different pore distributions, real or artificial, can be calculated without changing the base finite element mesh. The second approach includes the pore information as STL data into the original CAD model and creates a new adapted finite element mesh for the simulation. Both methods are compared and evaluated for an industrial problem.

The STL data of defects which the authors received from CT measurements could not be directly applied without repairing them. Therefore, for FEM applications an appropriate repair procedure is proposed. The first approach, which combines the FEM with the FCM, the authors have realized within the commercial software tool Abaqus. This combination performs well, which is demonstrated for test examples, and is also applied for a complex industrial project. The developed in-house code still has some limitations which restrict broader application in industry. The second pure FEM-based approach works well without limitations but requires increasing computational effort if many different pore distributions are to be investigated.

A new simulation approach which combines the FEM with the FCM has been developed and implemented into the commercial Abaqus FEM software. This approach the authors have applied to simulate a real engineering die-cast structure with pores. This approach could become a preferred way to consider pores in practical applications, where the porosity can be derived either from CT measurements or are artificially adopted for design purposes. The authors have also shown how pores can be considered in the standard FEM analysis as well.

Natural gas hydrate (NGH) has been regarded as one of the most important resources due to NGH's large amounts of reserve. However, NGH development still faces many technical challenges, such as low production rate and reservoir instability resulting from NGH decomposition. Therefore, developing a fully coupled THMC model for simulating the hydrate decomposition and studying its mechanical behavior is very important and necessary. The purpose of this article is to develop and solve a multi-phase, strong nonlinearity and large-scale fully coupled thermal-hydro-mechanical–chemical (THMC) model for simulating the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and rock deformation during NGH decomposition.

In this paper, a multi-phase, strong nonlinearity and large-scale fully coupled THMC model is developed for simulating the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and rock deformation during NGH dissociation. The fully coupled THMC model is solved by using a fully implicit finite element method, in which the gas pressure, water pressure, temperature and displacement are taken as basic unknown variables. The proposed model is validated against with the experimental data, showing high accuracy and reliability.

A multi-phase, strong nonlinearity and large-scale fully coupled THMC model is developed for simulating the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and rock deformation during NGH decomposition. The proposed model is validated against with the experimental data, showing high accuracy and reliability.

Some assumptions are made to make the model tractable, including (1) the composition gas of hydrate is pure methane; (2) the gas-liquid multi-phase flow in the pore obeys Darcy's law; (3) hydrate occurs on the surface of soil particles, both of them form the composite consolidation material; (4) the small-strain assumption is applied to composite solid materials, which are treated as skeletons and cannot be moved; (5) momentum change caused by phase change is not considered.

NGH has been regarded as one of the most important resources due to its large amounts of reserve. However, NGH development still faces many technical challenges, such as low production rate and reservoir instability resulting from NGH decomposition. Most of the existing studies decouple the process with solid deformation and seepage behavior, but the accuracy of the numerical results will be sacrificed to certain extent. Therefore, it is very important and necessary to develop a fully coupled THMC model for simulating the hydrate decomposition and studying its mechanical behavior.

NGH, widely distributed in shallow seabed or permanent frozen region, has the characteristics of high energy density and high combustion efficiency (Yan et al., 2020). A total of around 7.5 × 1,018 m³ has been proved to exist around the world and 1 m³ of NGH can release about 160–180 m³ of natural gas (Kvenvolden and Lorenson) under normal conditions. Safely and sustainably extracting NGH commercially can effectively relieve global energy pressure and contribute to achieving carbon reduction goals.

The novelty of the present work lies in mainly two aspects. First, a fully coupled THMC model is developed for studying the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and solid deformation during NGH dissociation. Second, the numerical solution is obtained by using a fully implicit finite element method (FEM) and is validated against experimental data.