Forces in mechanics最新文献

{"title":"The Analytical Artificial Neural Networks Method","authors":"Ali Ahmadi Azar","doi":"10.1016/j.finmec.2026.100360","DOIUrl":"10.1016/j.finmec.2026.100360","url":null,"abstract":"<div><div>This study introduces the Analytical Artificial Neural Networks Method (AANNM), a groundbreaking framework that systematically converts the discrete, black-box outputs of neural network solvers into closed-form analytical solutions. The efficacy of AANNM is demonstrated by solving the differential equation governing the Kelvin-Voigt viscoelastic model. First, a high-fidelity numerical solution is obtained using a Physics-Informed Neural Network (PINN). The core innovation of AANNM is then deployed: the discrete PINN data is used to construct a system of algebraic equations, the solution of which yields the coefficients for a precise polynomial analytical expression. The derived AANNM solution is directly validated against the known exact analytical solution, demonstrating exceptional agreement and providing a more rigorous benchmark than comparisons with purely numerical methods. Crucially, while demonstrated with PINNs, the AANNM framework is solver-agnostic, designed to convert discrete solutions from any artificial neural network into analytical form. This inherent flexibility ensures the method's applicability to future ANN advancements, making it both timeless and adaptable. The proposed framework establishes AANNM as a transformative pipeline that bridges data-driven numerical models with rigorous analytical mathematics, significantly enhancing the interpretability, utility, and trustworthiness of machine learning in computational science.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"23 ","pages":"Article 100360"},"PeriodicalIF":3.5,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of weld profiling on the fatigue strength of thin-walled rectangular hollow section T-joints made of high strength steel","authors":"Benjamin Laher ,&nbsp;Christian Buzzi ,&nbsp;Peter Brunnhofer ,&nbsp;Martin Leitner","doi":"10.1016/j.finmec.2026.100359","DOIUrl":"10.1016/j.finmec.2026.100359","url":null,"abstract":"<div><div>In this study, a thin-walled high-strength S960 rectangular hollow section T-joint is cyclically tested at a stress ratio of R=0.1. The work focuses on the effect of weld profiling conducted as post-weld treatment by grinding of the weld seam. Numerical simulations using the real weld seam geometry are carried out and compared with strain gauge measurements. Thereby, it is shown that the stress states of both methods are in sound agreement and the crack initiation site can be assessed well by the numerical approach. The resulting nominal S/N curves reveal an increase of the fatigue strength by about 33% at two million load-cycles due to weld profiling, which represents a high potential for this post-weld treatment technique. Furthermore, the notch stress approach using the common procedure by modelling a reference radius of r_ref=1 mm at the weld toe as well as modelling the real weld toe geometry after weld profiling are applied. The results are compared to the recently published values in the Recommendations for Fatigue Design of Welded Joints and Components by the International Institute of Welding (IIW) and highlight that both different modelling methods lead to a sound notch stress fatigue assessment of the weld-profiled condition.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"23 ","pages":"Article 100359"},"PeriodicalIF":3.5,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparative numerical studies of the mechanical efficiency of sandwich-panels with different non-/auxetic prismatic and lattice cores subjected to ballistic loading","authors":"Marcel Walkowiak,&nbsp;Denis Anders,&nbsp;Ulf Reinicke","doi":"10.1016/j.finmec.2026.100354","DOIUrl":"10.1016/j.finmec.2026.100354","url":null,"abstract":"<div><div>Civil as well as military facilities, vehicles and applications must increasingly meet higher safety standards to ensure the highest possible protection against extraordinary stresses such as ballistic and/or air-blast loading. The use of lightweight sandwich constructions is considered an efficient and promising measure for enhancing passive safety and maintaining structural integrity. In addition to increased bending stiffness compared to monolithic plates of the same weight, they also exhibit a more favorable behavior under dynamic loading scenarios. The influence of open and closed auxetic core geometries on the relevant mechanical parameters under impact loads of spherical rigid projectiles (r_sph = 15 mm, m_sph = 10 g) with velocities of 200 ms⁻¹ will be analyzed in the present study in order to be able to draw principal conclusions on the auxetic mechanisms and their effectiveness. A new performance indicator is suggested in this context. Numerical studies were performed using the commercial finite element code ABAQUS/Explicit. This included a validated material model for the aluminum alloy EN AW-7108 T6, which considers strain-rate dependent plastic material behavior and typical failure criteria. A comparison with a monolithic reference plate of the same mass and conventional non-auxetic core topologies allows a final efficiency assessment of the sandwich designs with a modified internal structure. The displacements of the rear face surfaces as well as the resulting stresses on supporting structures can be reduced by up to 90 percent and the plastically dissipated energy can be increased by up to 15 percent for some core variants.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100354"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146173507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vibration analysis of a rotating FGM cracked beam under a tangent follower force","authors":"Ayaa H. Fadhel ,&nbsp;Talib EH. Elaikh ,&nbsp;Ali Hasan Ali ,&nbsp;Husam A. Neamah","doi":"10.1016/j.finmec.2026.100355","DOIUrl":"10.1016/j.finmec.2026.100355","url":null,"abstract":"<div><div>In the current study, we investigate the dynamic response of cracked rotating FG-beams with two variable boundary conditions. The crack is considered to be simulated by a massless torsional spring model. The beam motion equation is obtained based on Hamilton’s concept. In this study, a power-law exponent describes graded beam materials as they vary through the beam's thickness. The beam's natural frequencies are established by solving the vibration equations with the Galerkin method. The study investigates the effect of geometrical and material properties, rotating speed, distributed force, hub length, and crack parameters on these frequencies. The analysis shows that the power index decreases the dimensionless natural frequencies for all end conditions, with or without a crack. In the absence of cracks, the ratio of the reduction in frequency of the double-simply supported FG beam is 17.58%, and the ratio of the reduction in frequency of the clamped-free end conditions is 15.95%. The frequency decreases by 22.75% and 19.60% in S-S and C-F, respectively, with a crack.</div><div>Also, the dimensionless vibration frequency decreases with increasing tangent follower force, by 14.97% in S-S and 10.65% in C-F. Also, the results exhibit that crack depth lowers the dimensionless vibration frequencies. Moreover, the analysis shows that the hub radius ratio raises the dimensionless vibration frequencies, irrespective of the presence of a crack, across all end conditions. The findings provide useful insight for the vibration analysis and design of rotating FG structures in practical applications.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100355"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic load localization and time history identification using blind source separation and structural modal shape matching","authors":"Kun Li ,&nbsp;Zhuo Fu ,&nbsp;Xianfeng Man ,&nbsp;Shuai Wang ,&nbsp;Yixiang Chen ,&nbsp;Nuo Chen","doi":"10.1016/j.finmec.2026.100350","DOIUrl":"10.1016/j.finmec.2026.100350","url":null,"abstract":"<div><div>Accurate knowledge of dynamic load locations and time histories is a critical input for structural design but is often infeasible to measure directly. While numerous load identification methods exist, they predominantly address the localization and time-history reconstruction separately, relying on the prior assumption that one of the two is known. This paper introduces a novel and efficient integrated approach that combines Blind Source Separation (BSS) with Structural Modal Shape Matching (SMSM) to concurrently identify both the spatial location and temporal profile of dynamic loads. The proposed methodology is founded on the principle that modal loads and physical loads are mutually convertible. Initially, truncated modal loads are stably reconstructed in the modal space using a shape function method with Tikhonov regularization. These recovered modal loads are then interpreted as blind mixtures of the unknown physical load source signals, with the structural modal shape coefficients acting as the mixing matrix. BSS is subsequently employed to separate the equivalent load time histories and estimate the mixing matrix. Since the mixing coefficient vector is linearly related to the structural mode shape vector at the load application point, SMSM is implemented by quantifying the intersection angles between the estimated mixing vectors and candidate modal shape vectors to pinpoint the most probable load locations. Finally, the actual load time histories are accurately retrieved using the reconstructed modal loads and the identified modal shape matrix. The efficacy of the proposed method is rigorously demonstrated through two numerical examples involving a complex ropeway tower and a rectangular plate.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100350"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental investigation of mechanical properties of hybrid sisal fiber and sheep wool reinforced epoxy composite material","authors":"Zewditu Aschalew Tarekgne ,&nbsp;Teshome Mulatie Bogale ,&nbsp;Velmurugan Paramasivam","doi":"10.1016/j.finmec.2026.100353","DOIUrl":"10.1016/j.finmec.2026.100353","url":null,"abstract":"<div><div>Hybrid two or more fiber-reinforced composites are generally prepared to enhance different properties as compared to single-fiber reinforced composites. Sheep wool and sisal fibers are natural fibers that can be obtained from animal and plant sources respectively. After extracted and treated the fibers, the woven yarn fiber mat was prepared. The woven hybrid composite was fabricated with a 20% weight fraction of fiber by using hand layup fabrication techniques. Composites samples were prepared under five different weight percentage ratios of sheep wool to sisal fiber 0:20, 5:15, 10:10, 15:5, and 20:0. And each weight percentage of a sample was fabricated with two different angles (0°-90° and ±45°) of orientations. From the experimental test results, it was observed that the tensile, compressive, flexural strengths increase directly with increase sisal fiber weight percentage of composite samples in both 0-90° and ±45°angle of orientations. However, between the two angles of orientation, the tensile and flexural strengths of the hybrid sheep wool and sisal fiber epoxy composite samples were highest in 0-90°angle orientations composite samples. On other hand, the compressive and impact strengths were highest in ±45°angle orientation of the composite samples. Overall, the composite sample with a 15:5 sisal fiber-sheep wool ratio (SA4 and SB4) demonstrated the best mechanical performance. The maximum tensile and flexural strengths of 95.73 MPa and 358.80 MPa, respectively, were obtained for the 0°–90° oriented composite, whereas the highest compressive strength of 95.73 MPa and impact strength is 746.77 kJ/m² were observed in the ±45° oriented composite. The experimental test result shows that the hybrid sheep wool and sisal fiber epoxy composite are alternative materials for the interior part of automotive applications like interior roof and door panels.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100353"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146022760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chemomechanical modeling of lithiation-induced failure based on strain gradient plasticity theory","authors":"Zengsheng Ma","doi":"10.1016/j.finmec.2025.100343","DOIUrl":"10.1016/j.finmec.2025.100343","url":null,"abstract":"<div><div>Porous silicon (Si) anodes in lithium-ion batteries (LIBs) experience significant diffusion-induced stress gradients during electrochemical cycling, leading to crack propagation and active material pulverization. To systematically predict such failure behaviors, this study proposes a chemo-mechanical coupling framework by integrating strain gradient plasticity (SGP) theory with damage mechanics. The theoretical model explicitly resolves the interplay among lithiation kinetics, dislocation-mediated plasticity, and progressive damage accumulation in porous Si structures. Finite element method (FEM) simulations reveal the spatiotemporal evolution of lithium concentration fields, stress-strain distributions, and microcrack patterns. Parametric analyses identify critical structural parameters (e.g., pore radius, porosity) governing stress localization and interfacial delamination. Additionally, this work constructs a quantitative failure mechanism diagram that correlates state-of-charge (SOC), porosity, and pore geometry with fracture thresholds. The diagram offers actionable guidance for optimizing electrode architectures to mitigate stress-induced degradation in high-capacity LIB anodes.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100343"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improved Bayesian model updating framework using an enriched spring-based finite element model for structural health monitoring","authors":"Masoomeh Farrokhtar,&nbsp;Reza Saleh Jalali,&nbsp;Morteza Sohrabi Gilani","doi":"10.1016/j.finmec.2026.100357","DOIUrl":"10.1016/j.finmec.2026.100357","url":null,"abstract":"<div><div>Classical finite‐element model updating (FEMU) requires iterative updates of the structural model. Alternative approaches are often computationally expensive or oversimplify the actual physical behavior of the structures. This paper introduces a novel approach, an enriched spring-based Bayesian finite element model updating (ES-BFEMU) method, which reduces computational cost while preserving high fidelity. In the proposed model, each structural element is divided into two beam-like sub-elements and a rotational spring. The stiffness matrix is derived by enriching the strain energy of both the sub-elements and the spring. This formulation enhances the physical interpretability of local stiffness degradation by explicitly representing rotational flexibility in potential damage zones. The enriched stiffness matrix is updated to provide a more realistic finite element model by detecting stiffness reductions within a Bayesian FEMU framework that considers the uncertainties. The computational efficiency is improved by adopting an adaptive transitional Markov chain Monte Carlo (TMCMC) algorithm to obtain the posterior probability of parameters. The proposed model is applied to the Salar Bridge, a six-span structure instrumented with accelerometers, displacement transducers, and strain gauges. Structural damage is simulated by introducing stiffness reduction coefficients into the elastic modulus of selected elements, with scenarios defined at reduction levels of 2%, 5%, 10%, and 15%. The introduced damages were successfully detected with a deviation of &lt;2%. The proposed ES-BFEMU was also compared with surrogate and reduced-order FEMU approaches, demonstrating improved computational efficiency and higher accuracy in damage identification. The proposed model serves as a bridge between the surrogate and reduced-order FEMU. It reduces the computational cost associated with the reduced-order FEMU by a factor of 3.57 and enhances the accuracy of the surrogate method by 33%. The stress-time results of ES-BFEMU show a prediction error of &lt;6.15% when compared to experimental results. These results demonstrate that ES-BFEMU provides a computationally efficient, physically interpretable, and reliable framework for structural health monitoring and damage identification.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100357"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental and numerical damage assessment of PLA based on young’s modulus reduction using the bonora damage model","authors":"Mohammad Ali Kazemi ,&nbsp;Seyedsajad Jafari ,&nbsp;Mostafa akbari","doi":"10.1016/j.finmec.2025.100345","DOIUrl":"10.1016/j.finmec.2025.100345","url":null,"abstract":"<div><div>The goal of this paper is to experimentally and numerically investigate damage evolution in PLA+ materials, based on the reduction of Young’s modulus during cyclic loading–unloading tests. Standard tensile specimens were fabricated via FDM 3D printing and tested under displacement-controlled cyclic loading, while strain was measured using both extensometer and digital image correlation. The Bonora damage model was calibrated for PLA+ by fitting the damage parameter to experimental plastic strain data. The obtained constants (D_cr=0.20, ε_th=0.012, ε_f=0.042, α=0.76) were implemented in a custom VUSDFLD subroutine in ABAQUS. The finite element simulations successfully predicted final failure, showing good agreement with the experimental damage parameter evolution. The numerical predictions deviated &lt;5 % from experimental results, confirming the high accuracy of the Bonora-based model implementation. This combined experimental–numerical framework provides a reliable basis for predicting progressive damage in PLA+ components under quasi-static loading. The novelty of this work lies in the calibration of the Bonora model for PLA+, which shows enhanced ductility compared to conventional PLA, and in demonstrating its potential for reliable application in both engineering load-bearing structures and biodegradable biomedical devices.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100345"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical investigation of nonlinear response of single-walled carbon nanotube resting on elastic foundation subjected to casimir-electrostatic-van der waals forces","authors":"E.H. Abubakar ,&nbsp;A.A. Yinusa ,&nbsp;M.G. Sobamowo ,&nbsp;O.M. Sadiq","doi":"10.1016/j.finmec.2025.100344","DOIUrl":"10.1016/j.finmec.2025.100344","url":null,"abstract":"<div><div>This paper presents analytical investigation into the nonlinear dynamic response of single-walled carbon nanotube (SWCNT) resting on elastic foundation and subjected to magneto-thermal and electrostatic environment under the influence of Casimir and intermolecular forces. The Euler-Bernoulli beam theory, the nonlocal elasticity theory and Hamilton’s principle of nonlinear mechanistic motion are applied in the theoretical formulation of the governing differential equation and the Galerkin decomposition technique is used to decompose the formulated equation of motion into spatial and temporal parts. The duffing equation which describes the temporal part of the equation of motion of the SWCNT is then solved analytically. Subsequently, the frequency ratios of the nanotube for end conditions including simple-simple, clamped-clamped, clamped-simple, and clamped-free are obtained. Furthermore, parametric study is carried out to show the influences of Casimir force, intermolecular force, electrostatic force, magnetic term, elastic foundation and thermal term on the nanotube’s stability. The stability response solution obtained from the parametric study reveals that an increase in Casimir force enables CNTs to experience an additional attractive pressure that decreases their stability and may result in buckling or collapse. Meanwhile, increase in Van der Waals force reduces critical buckling load. Additionally, increasing the electrostatic force results in an increased frequency ratio and vibration amplitude. These parameters need to be carefully monitored or controlled to prevent instabilities due to their sensitivities.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"22 ","pages":"Article 100344"},"PeriodicalIF":3.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}