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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.

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.

Based on the weak seismic performance and low ductility of coupled shear walls, engineered cementitious composites (ECC) is utilized to strengthen it to solve the deformation problem in tall buildings more effectively and study its mechanical properties more deeply.

The properties of reinforced concrete coupled shear wall (RCCSW) and reinforced ECC coupled shear wall (RECSW) have been studied by numerical simulation, which is in good agreement with the experimental results. The reliability of the finite element model is verified. On this basis, a detailed parameter study is carried out, including the strength and reinforcement ratio of longitudinal rebar, the placement height of ECC in the wall limb and the position of ECC connecting beams. The study indexes include failure mode and the skeleton curve.

The results suggest that the bearing capacity of RECSW is significantly affected by the ratio of longitudinal rebar. When the ratio of longitudinal rebar increases from 0.47% to 3.35%, the bearing capacity of RECSW increases from 250 kN to 303 kN, an increase of 21%. The strength of longitudinal rebar has little influence on the bearing capacity of RECSW. When the strength of the longitudinal rebar increases, the bearing capacity of RECSW increases little. The failure mode of RECSW can be improved by lowering the casting height of the ECC beam in a certain range.

In this paper, ECC is used to strengthen the coupled shear wall, and the accuracy of the finite element model is verified from the failure mode and skeleton curve. On this basis, the casting height of the ECC casting wall limb, the strength and reinforcement ratio of longitudinal rebar and the position of the ECC beam are studied in detail.

The aim of this study is to make a contribution towards reducing the deflections of silicon wafers. The deformation of silicon wafers used in the manufacture of electronic micro-components is one of the most common problems encountered by industrialists during manufacturing. Stack warping is typically produced during the process of depositing thin layers on a substrate. This is due to the thermal-mechanical stresses caused by the difference between the thermal expansion coefficients of the materials. Reducing wafer deformation is essential to increase reliability and improve quality. In this paper, the authors propose an approach based on minimal geometrical modifications to reduce the deformation of a silicon wafer coated with two thin layers. Numerical finite element models have been developed to evaluate the impact of geometrical modifications on warping amplitude. Finite element models have been validated compared with experimental models. The results obtained are encouraging and clearly show a considerable reduction in wafer deformation.

Reducing wafer deformation is essential to increase reliability and improve quality. In this paper, the authors propose an approach based on minimal geometrical modifications to reduce the deformation of a silicon wafer coated with two thin layers. Numerical finite element models have been developed to evaluate the impact of geometrical modifications on warping amplitude. Finite element models have been validated compared with experimental models.

The results obtained are encouraging and clearly show a considerable reduction in wafer deformation.

This paper describes the influence of geometric modification on wafer deformation. The work show also the cruciality of stress reduction in the purpose to obtain less wafer deformation.

This study establishes a method for predicting ground vibrations caused by railway tunnels in unsaturated soils with spatial variability.

First, an improved 2.5D finite-element-method-perfect-matching-layer (FEM-PML) model is proposed. The Galerkin method is used to derive the finite element expression in the ub-pl-pg format for unsaturated soil. Unlike the ub-v-w format, which has nine degrees of freedom per node, the ub-pl-pg format has only five degrees of freedom per node; this significantly enhances the calculation efficiency. The stretching function of the PML is adopted to handle the unlimited boundary domain. Additionally, the 2.5D FEM-PML model couples the tunnel, vehicle and track structures. Next, the spatial variability of the soil parameters is simulated by random fields using the Monte Carlo method. By incorporating random fields of soil parameters into the 2.5D FEM-PML model, the effect of soil spatial variability on ground vibrations is demonstrated using a case study.

The spatial variability of the soil parameters primarily affected the vibration acceleration amplitude but had a minor effect on its spatial distribution and attenuation over time. In addition, ground vibration acceleration was more affected by the spatial variability of the soil bulk modulus of compressibility than by that of saturation.

Using the 2.5D FEM-PML model in the ub-pl-pg format of unsaturated soil enhances the computational efficiency. On this basis, with the random fields established by Monte Carlo simulation, the model can calculate the reliability of soil dynamics, which was rarely considered by previous models.

Prefabricated columns connected by grouted sleeves are increasingly used in practical projects. However, seismic fragility analyses of such structures are rarely conducted. Seismic fragility analysis has an important role in seismic hazard evaluation. In this paper, the seismic fragility of sleeve connected prefabricated column is analyzed.

A model for predicting the seismic demand on sleeve connected prefabricated columns has been created by incorporating engineering demand parameters (EDP) and probabilities of seismic failure. The incremental dynamics analysis (IDA) curve clusters of this type of column were obtained using finite element analysis. The seismic fragility curve is obtained by regression of Exponential and Logical Function Model.

The IDA curve cluster gradually increased the dispersion after a peak ground acceleration (PGA) of 0.3 g was reached. For both columns, the relative displacement of the top of the column significantly changed after reaching 50 mm. The seismic fragility of the prefabricated column with the sleeve placed in the cap (SPCA) was inadequate.

The sleeve was placed in the column to overcome the seismic fragility of prefabricated columns effectively. In practical engineering, it is advisable to utilize these columns in regions susceptible to earthquakes and characterized by high seismic intensity levels in order to mitigate the risk of structural damage resulting from ground motion.

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.

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.

The purpose of this study is to propose a simplifying approach for modelling a reliability test. Modelling the reliability tests of printed circuit board (PCB)/microelectronic component assemblies requires the adoption of several simplifying assumptions. This study introduces and validates simplified assumptions for modeling a four-point bend test on a PCB/wafer-level chip scale packaging assembly.

In this study, simplifying assumptions were used. These involved substituting dynamic imposed displacement loading with an equivalent static loading, replacing the spherical shape of the interconnections with simplified shapes (cylindrical and cubic) and transitioning from a three-dimensional modelling approach to an equivalent two-dimensional model. The validity of these simplifications was confirmed through both quantitative and qualitative comparisons of the numerical results obtained. The maximum principal plastic strain in the solder balls and copper pads served as the criteria for comparison.

The simplified hypotheses were validated through quantitative and qualitative comparisons of the results from various models. Consequently, it was determined that the replacement of dynamic loading with equivalent static loading had no significant impact on the results. Similarly, substituting the spherical shape of interconnections with an equivalent shape and transitioning from a three-dimensional approach to a two-dimensional one did not substantially affect the precision of the obtained results.

This study serves as a valuable resource for researchers seeking to model accelerated reliability tests, particularly in the context of four-point bending tests. The results obtained in this study will assist other researchers in streamlining their numerical models, thereby reducing calculation costs through the utilization of the simplified hypotheses introduced and validated herein.

The combination of an Engineered Cementitious Composite (ECC) layer and steel plate to reinforce RC beams (ESRB) is a new strengthening method. The ESRB was proposed based on the steel plate at the bottom of RC beams, aiming to solve the problem of over-reinforced RC beams and improve the bearing capacity of RC beams without affecting their ductility.

In this paper, the finite element model of ESRB was established by ABAQUS. The results were compared with the experimental results of ESRB in previous studies and the reliability of the finite element model was verified. On this basis, parameters such as the width of the steel plate, thickness of the ECC layer, damage degree of the original beam and cross-sectional area of longitudinal tensile rebar were analyzed by the verified finite element model. Based on the load–deflection curve of ESRB, ESRB was discussed in terms of ultimate bearing capacity and ductility.

The results demonstrate that when the width of the steel plate increases, the ultimate load of ESRB increases to 133.22 kN by 11.58% as well as the ductility index increases to 2.39. With the increase of the damage degree of the original beam, the ultimate load of ESRB decreases by 23.7%–91.09 kN and the ductility index decreases to 1.90. With the enhancement of the cross-sectional area of longitudinal tensile rebar, the ultimate bearing capacity of ESRB increases to 126.75 kN by 6.2% and the ductility index elevates to 2.30. Finally, a calculation model for predicting the flexural capacity of ESRB is proposed. The calculated results of the model are in line with the experimental results.

Based on the comparative analysis of the test results and numerical simulation results of 11 test beams, this investigation verified the accuracy and reliability of the finite element simulation from the aspects of load–deflection curve, characteristic load and failure mode. Furthermore, based on load–deflection curve, the effects of steel plate width, ECC layer thickness, damage degree of the original beam and cross-sectional area of longitudinal tensile rebar on the ultimate bearing capacity and ductility of ESRB were discussed. Finally, a simplified method was put forward to further verify the effectiveness of ESRB through analytical calculation.