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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.

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 response of the Pine Flat dam–water–foundation rock system is studied by a new described approach (i.e. FE-(FE-TE)-FE). The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by the FE-(FE-HE)-FE approach (referred to as exact method which employs a rigorous fluid hyper-element). Subsequently, the transient analysis is carried out. In that part, it is only possible to compare the results for low and high normalized reservoir length cases. Therefore, the sensitivity of results is controlled due to normalized reservoir length values.

In the present study, dynamic analysis of a typical concrete gravity dam–water–foundation rock system is formulated by the FE-(FE-TE)-FE approach. In this technique, dam and foundation rock are discretized by plane solid finite elements while, water domain near-field region is discretized by plane fluid finite elements. Moreover, the H-W (i.e. Hagstrom–Warburton) high-order condition is imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.

High orders of H-W condition, such as O5-5 considered herein, generate highly accurate responses for both possible excitations under both types of full reflective and absorptive reservoir bottom conditions. It is such that transfer functions are hardly distinguishable from corresponding exact responses obtained through the FE-(FE-HE)-FE approach in time harmonic analyses. This is controlled for both low and high normalized reservoir length cases (L/H = 1 and 3). Moreover, it can be claimed that transient analysis leads practically to exact results (in numerical sense) when one is employing high order H-W truncation element. In other words, the results are not sensitive to reservoir normalized length under these circumstances.

Dynamic analysis of concrete gravity dam–water–foundation rock systems is formulated by a new method. The salient aspect of the technique is that it utilizes H-W high-order condition at the truncation boundary. The method is discussed for all types of excitation and reservoir bottom conditions.

In the analysis of structures in a fire situation by simplified and analytical methods, one assumption is that the fire resistance time is greater than or equal to the required fire resistance time. Among the methodologies involving the fire resistance time, the most used is the tabular method, which associates fire resistance time values to structural elements based on minimum dimensions of the cross section. The tabular method is widely accepted by the technical-scientific community due to the fact that it is safe and practical. However, its main criticism is that it results in lower fire resistance times than advanced thermal and thermostructural analysis methods. The objective of this study was to evaluate the fire resistance time of reinforced concrete beams and compare it with the required fire resistance time recommended by the tabular method of NBR 15200 (ABNT, 2012).

The fire resistance time and required fire resistance time of reinforced concrete beams were evaluated using, respectively, numerical models developed based on the finite element method and the tabular method of NBR 15200 (ABNT, 2012). The influence of the following parameters was investigated: longitudinal reinforcement cover, characteristic compressive strength of concrete, beam height, longitudinal reinforcement area and arrangement of steel bars.

Among the evaluated parameters, the covering of the longitudinal reinforcement proved to be more relevant for the fire resistance time, justifying that the tabular method of NBR 15200 (ABNT, 2012) being strongly and directly influenced by this parameter. In turn, more resistant concretes, higher beams and higher steel grades have lower fire resistance time values. This is because beams in these conditions have greater resistance capacity at room temperature and, consequently, are subject to external stresses of greater magnitude. In some cases, the fire resistance time was even lower than the required fire resistance time prescribed by NBR 15200 (ABNT, 2012). Both the fire resistance time and the required fire resistance time were not influenced by the arrangement of the longitudinal reinforcements.

The present paper innovates by demonstrating the influence of other important design variables on the required fire resistance time of the NBR 15200 (ABNT, 2012). Among several conclusions, it was found that the load level to which the structural elements are subjected considerably affects their fire resistance time. For this reason, it was recommended that the methods for calculating the required fire resistance time consider the load level. In addition, the article quantifies the security degree of the tabular method and exposes some situations for which the tabular method proved to be unsafe. Moreover, in all the models analyzed, the relationship between the span and the vertical deflection associated with the failure of the beams in a fire situation was determined. With this, a span over average deflection relationship was presented in which beams in fire situations fail.

The main objective of this paper is to investigate the response of human skin to an intense temperature drop at the surface. In addition, this paper aims to evaluate the efficiency of finite difference and finite volume methods in solving the highly nonlinear form of Pennes’ bioheat equation.

One-dimensional linear and nonlinear forms of Pennes’ bioheat equation with uniform grids were used to study the behavior of human skin. The specific heat capacity, thermal conductivity and blood perfusion rate were assumed to be linear functions of temperature. The nonlinear form of the bioheat equation was solved using the Newton linearization method for the finite difference method and the Picard linearization method for the finite volume method. The algorithms were validated by comparing the results from both methods.

The study demonstrated the capacity of both finite difference and finite volume methods to solve the one-dimensional and highly nonlinear form of the bioheat equation. The investigation of human skin’s thermal behavior indicated that thermal conductivity and blood perfusion rate are the most effective properties in mitigating a surface temperature drop, while specific heat capacity has a lesser impact and can be considered constant.

This paper modeled the transient heat distribution within human skin in a one-dimensional manner, using temperate-dependent physical properties. The nonlinear equation was solved with two numerical methods to ensure the validity of the results, despite the complexity of the formulation. The findings of this study can help in understanding the behavior of human skin under extreme temperature conditions, which can be beneficial in various fields, including medical and engineering.

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.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

Realistic composite vehicles with 2, 3, 5 and 9 axles, consisting of a truck with one or two trailers, are addressed in this paper by computational models for vehicle–bridge interaction analysis.

The vehicle–bridge interaction (VBI) models are formed by sets of 2-D rigid blocks interconnected by mass, damping and stiffness elements to simulate their suspension system. The passage of the vehicles is performed at different speeds. Several rolling surface profiles are admitted, considering the maintenance grade of the pavement. The spectral density functions are generated from an experimental database to form the longitudinal surface irregularity profiles. A computational code written in Phyton based on the finite element method was developed considering the Euler–Bernoulli beam model.

Several models of composite heavy vehicles are presented as manufactured and currently travel on major roads. Dynamic amplification factors are presented for each type of composite vehicle.

The VBI models for compound heavy vehicles are 2-D.

This work contributes to improving the safety and lifetime of the bridges, as well as the stability and comfort of the vehicles when passing over a bridge.

The structural response of the bridge is affected by the type and size of the compound vehicles, their speed and the conservative grade of the pavement. Moreover, one axle produces vibrations that can be superposed by the vibrations of the other axles. This effect can generate not usual dynamic responses.

This paper aims to estimate the bearing capacity of a surface strip and circular footings lying on layered sand using numerical limit analysis.

Lower and upper bound limit analysis, as well as finite elements and second-order conic programming (SOCP), are used in this analysis. The yield criterion of Mohr-Coulomb is used to model soil behavior. Using this technique, stringent lower and upper bounds on ultimate bearing capacity can be achieved by assuming an associated flow law.

The obtained results indicate that the exact collapse load is typically being bracketed to within 6% about a mean of both the bounds. The obtained results are compared with the existing literature wherever applicable.

To the best of the authors’ knowledge, no study has used lower and upper bound limit analysis, as well as finite elements and SOCP, to estimate the bearing capacity of a surface strip and circular footings lying on layered sand.

Fiber reinforced additive manufacturing (FRAM) is an emerging technology that combines additive manufacturing and composite materials. As a result, design freedom offered by the manufacturing process can be leveraged in design optimization. The purpose of the study is to propose a novel method that improves structural performance by optimizing 3D print orientation of FRAM components.

This work proposes a two-part design optimization method that optimizes 3D global print orientation and topology of a component to improve a structural objective function. The method considers two classes of design variables: (1) print orientation design variables and (2) density-based topology design variables. Print orientation design variables determine a unique 3D print orientation to influence anisotropic material properties. Topology optimization determines an optimal distribution of material within the optimized print orientation.

Two academic examples are used to demonstrate basic behavior of the method in tension and shear. Print orientation and sequential topology optimization improve structural compliance by 90% and 58%, respectively. An industry-level example, an aerospace component, is optimized. The proposed method is used to achieve an 11% and 15% reduction of structural compliance compared to alternative FRAM designs. In addition, compliance is reduced by 43% compared to an equal-mass aluminum design.

Current research surrounding FRAM focuses on the manufacturing process and neglects opportunities to leverage design freedom provided by FRAM. Previous FRAM optimization methods only optimize fiber orientation within a 2D plane and do not establish an optimized 3D print orientation, neglecting exploration of the entire orientation design space.