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The long-span continuous rigid-frame bridges are commonly constructed by the section-by-section symmetrical balance suspension casting method. The deflection of these bridges is increasing over time. Wet joints are a typical construction feature of continuous rigid-frame bridges and will affect their integrity. To investigate the sensitivity of shear surface quality on the mechanical properties of long-span prestressed continuous rigid-frame bridges, a large serviced bridge is selected for analysis.

Its shear surface is examined and classified using the damage measuring method, and four levels are determined statistically based on the core sample integrity, cracking length and cracking depth. Based on the shear-friction theory of the shear surface, a 3D solid element-based finite element model of the selected bridge is established, taking into account factors such as damage location, damage number and damage of the shear surface. The simulated results on the stress distribution of the local segment, the shear surface opening and the beam deflection are extracted and analyzed.

The findings indicate that the main factors affecting the ultimate shear stress and shear strength of the shear surface are size, shear reinforcements, normal stress and friction performance of the shear surface. The connection strength of a single or a few shear surfaces decreases but with little effect on the local stress. Cracking and opening mainly occur at the 1/4 span. Compared with the rigid “Tie” connection, the mid-span deflection of the main span increases by 25.03% and the relative deflection of the section near the shear surface increases by 99.89%. However, when there are penetrating cracks and openings in the shear surface at the 1/2 span, compared with the 1/4 span position, the mid-span deflection of the main span and the relative deflection of the cross-section increase by 4.50%. The deflection of the main span increases with the failure of the shear surface.

These conclusions can guide the analysis of deflection development in long-span prestressed continuous rigid-frame bridges.

A novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.

First, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.

AAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.

AAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.

The authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

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.

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.

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.

This study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.

Based on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.

The findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.

The study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.

A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.

The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R²) is 0.93 for the validation set, and the R² for the test set A and test set B are 0.93 and 0.94, respectively.

This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

This study aims to enhance the understanding of fiber-reinforced polymer (FRP) applications in partially confined concrete, with a specific focus on improving economic value and load-bearing capacity. The research addresses the need for a more comprehensive analysis of non-uniform vertical strain responses and precise stress–strain models for FRP partially confined concrete.

DIC and strain gauges were employed to gather data during axial compression tests on FRP partially confined concrete specimens. Finite element analysis using ABAQUS was utilized to model partial confinement concrete with various constraint area ratios, ranging from 0 to 1. Experimental findings and simulation results were compared to refine and validate the stress–strain model.

The experimental results revealed that specimens exhibited strain responses characterized by either hardening or softening in both vertical and horizontal directions. The finite element analysis accurately reflected the relationship between surface constraint forces and axial strains in the x, y and z axes under different constraint area ratios. A proposed stress–strain model demonstrated high predictive accuracy for FRP partially confined concrete columns.

The stress–strain curves of partially confined concrete, based on Teng's foundation model for fully confined stress–strain behavior, exhibit a high level of predictive accuracy. These findings enhance the understanding of the mechanical behavior of partially confined concrete specimens, which is crucial for designing and assessing FRP confined concrete structures.

This research introduces innovative insights into the superior convenience and efficiency of partial wrapping strategies in the rehabilitation of beam-column joints, surpassing traditional full confinement methods. The study contributes methodological innovation by refining stress–strain models specifically for partially confined concrete, addressing the limitations of existing models. The combination of experimental and simulated assessments using DIC and FEM technologies provides robust empirical evidence, advancing the understanding and optimization of FRP-concrete structure performance. This work holds significance for the broader field of concrete structure reinforcement.

Hexahedral meshing is one of the most important steps in performing an accurate simulation using the finite element analysis (FEA). However, the current hexahedral meshing method in the industry is a nonautomatic and inefficient method, i.e. manually decomposing the model into suitable blocks and obtaining the hexahedral mesh from these blocks by mapping or sweeping algorithms. The purpose of this paper is to propose an almost automatic decomposition algorithm based on the 3D frame field and model features to replace the traditional time-consuming and laborious manual decomposition method.

The proposed algorithm is based on the 3D frame field and features, where features are used to construct feature-cutting surfaces and the 3D frame field is used to construct singular-cutting surfaces. The feature-cutting surfaces constructed from concave features first reduce the complexity of the model and decompose it into some coarse blocks. Then, an improved 3D frame field algorithm is performed on these coarse blocks to extract the singular structure and construct singular-cutting surfaces to further decompose the coarse blocks. In most modeling examples, the proposed algorithm uses both types of cutting surfaces to decompose models fully automatically. In a few examples with special requirements for hexahedral meshes, the algorithm requires manual input of some user-defined cutting surfaces and constructs different singular-cutting surfaces to ensure the effectiveness of the decomposition.

Benefiting from the feature decomposition and the 3D frame field algorithm, the output blocks of the proposed algorithm have no inner singular structure and are suitable for the mapping or sweeping algorithm. The introduction of internal constraints makes 3D frame field generation more robust in this paper, and it can automatically correct some invalid 3–5 singular structures. In a few examples with special requirements, the proposed algorithm successfully generates valid blocks even though the singular structure of the model is modified by user-defined cutting surfaces.

The proposed algorithm takes the advantage of feature decomposition and the 3D frame field to generate suitable blocks for a mapping or sweeping algorithm, which saves a lot of simulation time and requires less experience. The user-defined cutting surfaces enable the creation of special hexahedral meshes, which was difficult with previous algorithms. An improved 3D frame field generation method is proposed to correct some invalid singular structures and improve the robustness of the previous methods.

The assembly simulation in tolerance analysis is one of the most important steps for the tolerance design of mechanical products. However, most assembly simulation methods are based on the rigid body assumption, and those assembly simulation methods considering deformation have a poor efficiency. This paper aims to propose a novel efficient and precise tolerance analysis method based on stable contact to improve the efficiency and reliability of assembly deformation simulation.

The proposed method comprehensively considers the initial rigid assembly state, the assembly deformation and the stability examination of assembly simulation to improve the reliability of tolerance analysis results. The assembly deformation of mating surfaces was first calculated based on the boundary element method with optimal initial assembly state, then the stability of assembly simulation results was assessed by the density-based spatial clustering of applications with noise algorithm to improve the reliability of tolerance analysis. Finally, combining the small displacement torsor theory, the tolerance scheme was statistically analyzed based on sufficient samples.

A case study of a guide rail model demonstrated the efficiency and effectiveness of the proposed method.

The present study only considered the form error when generating the skin model shape, and the waviness and the roughness of the matching surface were not considered.

To the best of the authors’ knowledge, the proposed method is original in the assembly simulation considering stable contact, which can effectively ensure the reliability of the assembly simulation while taking into account the computational efficiency.