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Scholars mainly propose and establish theoretical models of cumulative fatigue damage for their research fields. This review aims to select the applicable model from many fatigue damage models according to the actual situation. However, relatively few models can be generally accepted and widely used.

This review introduces the development of cumulative damage theory. Then, several typical models are selected from linear and nonlinear cumulative damage models to perform data analyses and obtain the fatigue life for the metal.

Considering the energy law and strength degradation, the nonlinear fatigue cumulative damage model can better reflect the fatigue damage under constant and multi-stage variable amplitude loading. In the following research, the complex uncertainty of the model in the fatigue damage process can be considered, as well as the combination of advanced machine learning techniques to reduce the prediction error.

This review compares the advantages and disadvantages of various mainstream cumulative damage research methods. It provides a reference for further research into the theories of cumulative fatigue damage.

This paper aims to prepare third-order nonlinear optical (NLO) organic materials with large nonlinear optimization value, high damage threshold and ultrafast response time.

A series of novel symmetric and asymmetric compounds possessing third-order NLO properties were synthesized using 1,3,5-tribromobenzene as the basis. The photophysical and electrochemical properties, as well as the click reactions, were characterized by means of UV–VIS–NIR absorption spectroscopy and cyclic voltammetry.

The donor–acceptor chromophores were inserted into compound, making the molecule to have a broader absorption in the near-infrared regions and a narrower optical and electrochemical band gap. It also formed an electron-delocalized organic system, which has larger effects on achieving a third-order NLO response. The third-order NLO phenomenon of benzene ring complexes was experimentally studied at 532 nm using Z-scan technology, and some compounds showed the expected NLO properties.

The click products exhibit more NLO phenomena by performing different click combinations to the side groups, opening new perspectives on using the system in a variety of photoelectric applications.

The purpose of this paper is to develop surrogate models, using deep learning (DL), that can facilitate the application of EM analysis software. In the current status quo, electrical systems can be found in an ever-increasing range of products that are part of everyone’s daily live. With the advances in technology, industries such as the automotive, communications and medical devices have been disrupted with new electrical and electronic systems. The innovation and development of such systems with increasing complexity over time has been supported by the increased use of electromagnetic (EM) analysis software. Such software enables engineers to virtually design, analyze and optimize EM systems without the need for building physical prototypes, thus helping to shorten the development cycles and consequently cut costs.

The industry standard for simulating EM problems is using either the finite difference method or the finite element method (FEM). Optimization of the design process using such methods requires significant computational resources and time. With the emergence of artificial intelligence, along with specialized tools for automatic differentiation, the use of DL has become computationally much more efficient and cheaper. These advances in machine learning have ushered in a new era in EM simulations where engineers can compute results much faster while maintaining a certain level of accuracy.

This paper proposed two different models that can compute the magnetic field distribution in EM systems. The first model is based on a recurrent neural network, which is trained through a data-driven supervised learning method. The second model is an extension to the first with the incorporation of additional physics-based information to the authors’ model. Such a DL model, which is constrained by the laws of physics, is known as a physics-informed neural network. The solutions when compared with the ground truth, computed using FEM, show promising accuracy for the authors’ DL models while reducing the computation time and resources required, as compared to previous implementations in the literature.

The paper proposes a neural network architecture and is trained with two different learning methodologies, namely, supervised and physics-based. The working of the network along with the different learning methodologies is validated over several EM problems with varying levels of complexity. Furthermore, a comparative study is performed regarding performance accuracy and computational cost to establish the efficacy of different architectures and learning methodologies.

The multisource uncertainties, including material dispersion, load fluctuation and geometrical tolerance, have crucial effects on fatigue performance of turbine bladed disks. In view of the aim of this paper, it is essential to develop an advanced approach to efficiently quantify their influences and evaluate the fatigue life of turbine bladed disks.

In this study, a novel combined machine learning strategy is performed to fatigue assessment of turbine bladed disks. Proposed model consists of two modeling phases in terms of response surface method (RSM) and support vector regression (SVR), namely RSM-SVR. Two different input sets obtained from basic variables were used as the inputs of RSM, then the predicted results by RSM in first phase is used as inputs of SVR model by using a group data-handling strategy. By this way, the nonlinear flexibility of SVR inputs is improved and RSM-SVR model presents the high-tendency and efficiency characteristics.

The accuracy and tendency of the RSM-SVR model, applied to the fatigue life estimation of turbine bladed disks, are validated. The results indicate that the proposed model is capable of accurately simulating the nonlinear response of turbine bladed disks under multisource uncertainties, and SVR-RSM model provides an accurate prediction strategy compared to RSM and SVR for fatigue analysis of complex structures.

The results indicate that the proposed model is capable of accurately simulate the nonlinear response of turbine bladed disks under multisource uncertainties, and SVR-RSM model provides an accurate prediction compared to RSM and SVRE for fatigue analysis of turbine bladed disk.

The ultimate capacity and ductility behavior of a reinforced concrete (RC) beam generally depends on its constituent material properties. This study aims to use ANSYS to accentuate the nonlinear parametric finite element (FE) simulations of RC sections under monotonic loading.

The concrete matrix and steel reinforcement are the primary constituent materials of RC beams. The material properties such as tensile reinforcement area, tensile bars yield strength, concrete compressive strength and strain rate in tensile reinforcement at nominal strength have significantly influenced the ultimate response of RC beams. Therefore, these intensive parameters are considered in this study to ascertain their effect on the RC beam's ultimate behavior. The nonlinear response up to the ultimate load capacity and the crack evolutions of RC beams are predicted efficiently.

The parametric study reveals that increasing the tensile steel reinforcements (from Ast = 213–857 mm2) significantly improves the ultimate load capacity by 229% and yield deflections by 20%. However, it declines the ultimate deflection by 47% and ductility by 56% substantially. Varying the strain limit (?tn = 0.010–0.0015) of tensile reinforcement has proficiently increased the ultimate load-resisting capacity by 20%, whereas the ductility declined by 62%. When the concrete strength increases (from fck = 25–65 MPa), the cracking load increases profoundly by 51%, whereas the ultimate capacity has found an insignificant effect.

The load-deflection response plots extracted from the proposed numerical model exhibit satisfactory accuracy (less than 9% deviation) against the experimental curves available in the literature, which emphasizes the proficiency of the proposed FE model.

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.

The partially prestressed concrete beam with unbonded tendon is still an active field of research because of the difficulty in analyzing and understanding its behavior. The finite-element (FE) simulation of such beams using numerical software is very scarce in the literature and therefore this study is taken to demonstrate the modeling aspects of unbonded partially prestressed concrete (UPPSC) beams. This study aims to present the three-dimensional (3-D) nonlinear FE simulations of UPPSC beams subjected to monotonic static loadings using the numerical analysis package ANSYS.

The sensitivity study is carried out with three different mesh densities to obtain the optimum elements that reflect on the load–deflection behavior of numerical models, and the model with optimum element density is used further to model all the UPPSC beams in this study. Three half-symmetry FE model is constructed in ANSYS parametric design language domain with proper boundary conditions at the symmetry plane and support to achieve the same response as that of the full-scale experimental beam available in the literature. The linear and nonlinear material behavior of prestressing tendon and conventional steel reinforcements, concrete and anchorage and loading plates are modeled using link180, solid65 and solid185 elements, respectively. The Newton–Raphson iteration method is used to solve the nonlinear solution of the FE models.

The evolution of concrete cracking at critical loadings, yielding of nonprestressed steel reinforcements, stress increment in the prestressing tendon, stresses in concrete elements and the complete load–deflection behavior of the UPPSC beams are well predicted by the proposed FE model. The maximum discrepancy of ultimate moments and deflections of the validated FE models exhibit 13% and −5%, respectively, in comparison with the experimental results.

The FE analysis of UPPSC beams is done using ANSYS software, which is a versatile tool in contrast to the experimental testing to study the stress increments in the unbonded tendons and assess the complete nonlinear response of partially prestressed concrete beams. The validated numerical model and the techniques presented in this study can be readily used to explore the parametric analysis of UPPSC beams.

The developed model is capable of predicting the strength and nonlinear behavior of UPPSC beams with reasonable accuracy. The load–deflection plot captured by the FE model is corroborated with the experimental data existing in the literature and the FE results exhibit good agreement against the experimentally tested beams, which expresses the practicability of using FE analysis for the nonlinear response of UPPSC beams using ANSYS software.

The calculation and design of the structures are carried out with the aim of obtaining a sufficiently ductile behavior to allow the structure to undergo displacements, without risk of sudden breaks or loss of stability. The purpose of this study is to develop and validate a computer program (Thin beam2), allowing the modeling and simulation of the nonlinear behavior of reinforced concrete elements, on the other part, it is estimating the local and global ductility of the sections or elements constituting these structures.

The authors present two nonlinear analysis methods to carry out a parametric study of the factors influencing the local and global ductility of reinforced concrete structures. The first consists in evaluating the nonlinear behavior at the level of the cross-section of the reinforced concrete elements used in the elaborate Sectenol 1 program, it allows us to have the local ductility. The second, allows us to evaluate the nonlinear behavior of the element used in the modified thin beam 2 program, it allows us to estimate the overall ductility of the element.

The validation results of the Thin beam2 program are very satisfactory, by conferring the analytic and experimental results obtained by various researchers and the parametric study shows that each factor such as the compressive strength of the concrete has a favorable effect on ductility. Conversely, the normal compression force and the high resistance of tensioned reinforcements adversely affect ductility.

The reliability of the two programs lies in obtaining the local and global ductility of reinforced concrete structures because the calculation and design of the structures are carried out with the aim of obtaining ductile behavior without risk of breakage and instability.

This paper aims to present nonlinear numerical simulations using the versatile finite element (FE) analysis tool ANSYS and theoretical analysis based on code provisions to assess the load-carrying capacity of reinforced concrete (RC) beams under two-point monotonic static loadings.

Four quarter-size FE models with load and geometry symmetry conditions were constructed, the load-bearing capacity and associated mid-span deflections at critical points are verified against the full-scale experimental RC beams available in the literature. These developed FE models incorporated the tension stiffening effects and bond–slip behaviour. Theoretical analyses based on Indian standard code IS: 456–2000 and ACI 318–19 were also carried to verify the experimental and numerical predicted moments at critical loading points.

The load-deflection curves predicted through FE models exhibit closer corroboration with the experimental curves throughout the loading history. The contour plots for deflections, concrete principal stresses, reinforcement yield stresses are satisfactorily predicted by the FE models, which reveal the complete information of nonlinear behaviour of RC beams. The developed model well captured the initial and progressive crack patterns at each load increments.

The FE modelling is an efficient, valid and economical tool that is an alternative to the expensive experimental program and can be used to explore, analyse and fully understand the nonlinear response of RC beams under static loadings.

The ultimate moment capacity evaluated based on ACI 318–19 code provision show a better correlation with the experimental data as compared to the IS: 456–2000 code provision. The ultimate loads and associated centre-span deflections predicted by RN-2, RN-3, RB-12 and RB-16 FE model show a discrepancy of 1.66 and –0.49%, –4.68 and –0.60%, –9.38 and –14.53% and –4.37 and 4.21%, respectively, against the experimental results, which reveals that the developed ANSYS FE models predict consistent results and achieved a reasonable agreement with the experimental data.

Tapered steel sections are widely used in house building design due to their structural efficiency and aesthetic appearance. Due to the practical usage of web tapering specifications in the metal building industry, fabrication and material expenses are analyzed to achieve geometric and economic productivity. The purpose of this study is to investigate the effectiveness of utilizing web profiles with openings in reducing the weight of steel beams.

In this paper, the nonlinear analysis of the bending behavior of a tapered steel section with an opening was studied by finite element analysis. The results were then compared with those of the tapered steel section without an opening in terms of displacement and yield moment.

The bending capacity of a tapered steel section was analyzed using finite element analysis. Results showed that the tapered steel section without openings had a higher bending capacity compared to the section with various sizes of web openings. The results also showed that decreasing the number of openings would increase the bending capacity, whereas increasing the size of the opening would decrease it. The difference in the yield moment between the tapered steel section with and without openings was only 15.818%. A total of 60 nonlinear analyses were conducted to investigate the effect of the number and size of web openings, flange thickness and web thickness on the bending behavior. However, this study showed that web opening with octagon shape and 0.6D size of web opening, where D is the depth of section, showed the best section in terms of yield moment and volume reduction compared to other opening size and shape.

It is also found that tapered steel section has better moment resistance in thicker flange and web. The study is valuable for engineers and designers who work with steel structures and need to optimize the performance of tapered steel sections with web openings.