Latest open access articles published in Mathematical Modelling for Sustainable Engineering at https://www.acadlore.com/journals/MMSE https://www.acadlore.com/journals/MMSE Acadlore en Creative Commons Attribution(CC - BY) MMSE support@acadlore.com https://www.acadlore.com/article/MMSE/2026_2_2/mmse020201 Earthquakes can cause interconnected disruptions to the built environment, population health, emergency response systems, and community recovery, with consequences that may persist long after the initial seismic event. These post-earthquake dynamics are inherently time-dependent and may exhibit memory and hereditary effects that are not adequately represented by conventional integer-order differential equations. A physics-informed fractional framework was therefore developed to characterize the coupled evolution of post-earthquake disaster impacts and recovery processes. Five state variables were introduced to represent physical damage, population health burden, shelter demand, emergency response capacity, and community recovery. Their interactions were described through a coupled system of fractional-order differential equations. A physics-informed neural network was subsequently formulated by embedding the governing fractional-order equations and initial-condition constraints directly into the learning objective. Reference numerical trajectories were generated using the fractional Adams–Bashforth–Moulton method to assess the internal numerical consistency of the scenario-based simulations. Synthetic datasets informed by publicly available earthquake-related indicators were used to examine the computational behavior of the proposed framework under representative post-earthquake scenarios. The resulting formulation provides an integrated computational representation of the temporal dependencies among disaster impacts, public health burden, emergency response capacity, shelter demand, and community recovery while explicitly accounting for memory effects through fractional-order dynamics. The framework establishes a methodological basis for investigating post-earthquake system evolution and for examining how persistent disaster effects may influence recovery trajectories. Following validation against empirical observations from real earthquake events, the proposed approach could support scenario analysis, disaster preparedness, public health planning, emergency resource allocation, and quantitative assessment of post-earthquake recovery. 06-27-2026 <![CDATA[ Earthquakes can cause interconnected disruptions to the built environment, population health, emergency response systems, and community recovery, with consequences that may persist long after the initial seismic event. These post-earthquake dynamics are inherently time-dependent and may exhibit memory and hereditary effects that are not adequately represented by conventional integer-order differential equations. A physics-informed fractional framework was therefore developed to characterize the coupled evolution of post-earthquake disaster impacts and recovery processes. Five state variables were introduced to represent physical damage, population health burden, shelter demand, emergency response capacity, and community recovery. Their interactions were described through a coupled system of fractional-order differential equations. A physics-informed neural network was subsequently formulated by embedding the governing fractional-order equations and initial-condition constraints directly into the learning objective. Reference numerical trajectories were generated using the fractional Adams–Bashforth–Moulton method to assess the internal numerical consistency of the scenario-based simulations. Synthetic datasets informed by publicly available earthquake-related indicators were used to examine the computational behavior of the proposed framework under representative post-earthquake scenarios. The resulting formulation provides an integrated computational representation of the temporal dependencies among disaster impacts, public health burden, emergency response capacity, shelter demand, and community recovery while explicitly accounting for memory effects through fractional-order dynamics. The framework establishes a methodological basis for investigating post-earthquake system evolution and for examining how persistent disaster effects may influence recovery trajectories. Following validation against empirical observations from real earthquake events, the proposed approach could support scenario analysis, disaster preparedness, public health planning, emergency resource allocation, and quantitative assessment of post-earthquake recovery. ]]> A Physics-Informed Fractional Framework for Modeling Post-Earthquake Disaster Risk, Public Health Burden, and Recovery Dynamics ahmet yildirim nilufer yildirim suleyman enes aytac doi: 10.56578/mmse020201 Mathematical Modelling for Sustainable Engineering 06-27-2026 Mathematical Modelling for Sustainable Engineering 06-27-2026 2026 2 2 Article 65 10.56578/mmse020201 https://www.acadlore.com/article/MMSE/2026_2_2/mmse020201 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020105 This paper investigated homotopy analysis method (HAM) and Adomian decomposition method (ADM) to search an approximate-analytical solution for the susceptible–exposed–infected–recovered (SEIR) epidemic model. HAM controls convergence via the auxiliary parameter $\hbar$, whereas ADM decomposes nonlinear terms without linearization or perturbation. A comparative convergence analysis revealed that both methods produced accurate approximate-analytical solutions with few iterations; however, HAM demonstrated superior convergence speed and enhanced control over the solution region. Graphical illustrations were provided to compare the solution behavior and convergence characteristics of both methods. Furthermore, a comparative graphical assessment was conducted to evaluate the convergence rates of HAM and ADM, thereby identifying the method that exhibits faster convergence to the reference solution. 03-30-2026 <![CDATA[ This paper investigated homotopy analysis method (HAM) and Adomian decomposition method (ADM) to search an approximate-analytical solution for the susceptible–exposed–infected–recovered (SEIR) epidemic model. HAM controls convergence via the auxiliary parameter $\hbar$, whereas ADM decomposes nonlinear terms without linearization or perturbation. A comparative convergence analysis revealed that both methods produced accurate approximate-analytical solutions with few iterations; however, HAM demonstrated superior convergence speed and enhanced control over the solution region. Graphical illustrations were provided to compare the solution behavior and convergence characteristics of both methods. Furthermore, a comparative graphical assessment was conducted to evaluate the convergence rates of HAM and ADM, thereby identifying the method that exhibits faster convergence to the reference solution. ]]> A Comparative Study of HAM and ADM for the SEIR Epidemic Model nigar ali aziz ul islam mehmet yavuz gul zaman doi: 10.56578/mmse020105 Mathematical Modelling for Sustainable Engineering 03-30-2026 Mathematical Modelling for Sustainable Engineering 03-30-2026 2026 2 1 Article 49 10.56578/mmse020105 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020105 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020104 Light trapping in microcavities and non-homogeneous optical media has become increasingly important for the development of quantum information processing, slow-light devices, integrated photonic circuits, and bio-inspired optical systems. However, conventional optical trapping models based on fixed geometric configurations or standard nonlinear Schrödinger formulations are generally unable to accurately represent the combined effects of high-order dispersion, spatially varying material properties, and structural asymmetry encountered in realistic optical environments. To address these limitations, a hybrid shifted Legendre–classical Laguerre operational matrix method was developed for the numerical solution of the variable-coefficient fifth-order Korteweg–de Vries (KdV) equation. The spatial domain, $x\in[0,L]$, is discretized using shifted Legendre polynomials to facilitate accurate enforcement of algebraic boundary conditions, whereas the semi-infinite temporal domain, $t\in[0,\infty)$, is represented by classical Laguerre polynomials that remain orthogonal with respect to the exponentially decaying weight function $w(t)=e^{-t}$. By combining spectral collocation with Chebyshev–Gauss–Lobatto nodes, the governing nonlinear partial differential equation was transformed into a square system of nonlinear algebraic equations, which was subsequently solved using a trust-region dogleg algorithm. Numerical results show that, under the variable coefficients, the pulse is not trapped: over $t\in[0,5]$, its peak drifts from $x\approx5$ toward $x\approx8.9$ and its amplitude decays from $\approx2.0$ to $\approx0.7$ as it sheds dispersive radiation, so the monitored $L^{2}$ quantity decreases to about 0.18 of its initial value; the proposed scheme resolves this drift-and-decay evolution stably. A controlled comparison against a fourth-order finite-difference scheme under identical time integration shows that the spectral discretization reaches a given accuracy with roughly an order of magnitude fewer unknowns and is several orders of magnitude more accurate at equal degrees of freedom. The fixed-point iteration is convergent, with the Jacobian spectral radius below one. The proposed framework provides an efficient and mathematically rigorous spectral methodology for modeling variable-coefficient higher-order soliton dynamics in non-homogeneous media, and establishes a unified computational framework for such problems. Although the Laguerre basis is defined on $[0,\infty)$, all reported simulations are evaluated on the finite window $t\in[0,5]$; the semi-infinite construction supplies a spectrally accurate temporal basis with the natural weight $e^{-t}$, and $[0,5]$ covers the dynamics of interest. 03-29-2026 <![CDATA[ <p>Light trapping in microcavities and non-homogeneous optical media has become increasingly important for the development of quantum information processing, slow-light devices, integrated photonic circuits, and bio-inspired optical systems. However, conventional optical trapping models based on fixed geometric configurations or standard nonlinear Schrödinger formulations are generally unable to accurately represent the combined effects of high-order dispersion, spatially varying material properties, and structural asymmetry encountered in realistic optical environments. To address these limitations, a hybrid shifted Legendre–classical Laguerre operational matrix method was developed for the numerical solution of the variable-coefficient fifth-order Korteweg–de Vries (KdV) equation. The spatial domain, $x\in[0,L]$, is discretized using shifted Legendre polynomials to facilitate accurate enforcement of algebraic boundary conditions, whereas the semi-infinite temporal domain, $t\in[0,\infty)$, is represented by classical Laguerre polynomials that remain orthogonal with respect to the exponentially decaying weight function $w(t)=e^{-t}$. By combining spectral collocation with Chebyshev–Gauss–Lobatto nodes, the governing nonlinear partial differential equation was transformed into a square system of nonlinear algebraic equations, which was subsequently solved using a trust-region dogleg algorithm. Numerical results show that, under the variable coefficients, the pulse is not trapped: over $t\in[0,5]$, its peak drifts from $x\approx5$ toward $x\approx8.9$ and its amplitude decays from $\approx2.0$ to $\approx0.7$ as it sheds dispersive radiation, so the monitored $L^{2}$ quantity decreases to about 0.18 of its initial value; the proposed scheme resolves this drift-and-decay evolution stably. A controlled comparison against a fourth-order finite-difference scheme under identical time integration shows that the spectral discretization reaches a given accuracy with roughly an order of magnitude fewer unknowns and is several orders of magnitude more accurate at equal degrees of freedom. The fixed-point iteration is convergent, with the Jacobian spectral radius below one. The proposed framework provides an efficient and mathematically rigorous spectral methodology for modeling variable-coefficient higher-order soliton dynamics in non-homogeneous media, and establishes a unified computational framework for such problems. Although the Laguerre basis is defined on $[0,\infty)$, all reported simulations are evaluated on the finite window $t\in[0,5]$; the semi-infinite construction supplies a spectrally accurate temporal basis with the natural weight $e^{-t}$, and $[0,5]$ covers the dynamics of interest.</p> ]]> A Hybrid Legendre–Laguerre Operational Matrix Method for the Variable-Coefficient Fifth-Order KdV Equation in Non-Homogeneous Optical Media cenk keşan doi: 10.56578/mmse020104 Mathematical Modelling for Sustainable Engineering 03-29-2026 Mathematical Modelling for Sustainable Engineering 03-29-2026 2026 2 1 Article 40 10.56578/mmse020104 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020104 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020103 Deep excavations constructed in densely built urban environments are frequently supported by prestressed anchor systems, whose performance can significantly influence the stability of adjacent soil and structures. In this study, a finite element model was developed in PLAXIS 2D to investigate the mechanical response of an anchored deep excavation subjected to both static and seismic conditions. The excavation was retained by diaphragm walls and supported by three levels of prestressed anchors, while a five-story building was located at a distance of 10 m from the excavation boundary. Four representative prestress distribution patterns were considered, including uniform, decreasing, increasing, and mid-level maximum distributions. The influence of these prestressing schemes was evaluated through a comprehensive analysis of anchor forces, diaphragm wall lateral displacements, building horizontal displacements, and foundation settlements. The results indicated that the initial prestress distribution exerted a pronounced influence on the system behavior under static conditions. Reductions in wall deformation and building settlement were found to be strongly dependent on the magnitude and distribution of the initial prestressing forces. Among the investigated strategies, the decreasing prestressing scheme provided the most favorable overall performance. In contrast, the mid-level maximum distribution scheme exhibited comparatively lower efficiency in limiting excavation-induced deformations. Under seismic loading, however, the differences among the prestress distribution patterns became negligible. These findings suggest that optimization of anchor prestress distribution is primarily beneficial for controlling excavation-induced deformation under static conditions, whereas its effectiveness becomes considerably less pronounced when seismic effects dominate system behavior. The study provides practical guidance for the design and optimization of prestressed anchoring systems for deep excavations located in seismically active urban areas. 03-28-2026 <![CDATA[ Deep excavations constructed in densely built urban environments are frequently supported by prestressed anchor systems, whose performance can significantly influence the stability of adjacent soil and structures. In this study, a finite element model was developed in PLAXIS 2D to investigate the mechanical response of an anchored deep excavation subjected to both static and seismic conditions. The excavation was retained by diaphragm walls and supported by three levels of prestressed anchors, while a five-story building was located at a distance of 10 m from the excavation boundary. Four representative prestress distribution patterns were considered, including uniform, decreasing, increasing, and mid-level maximum distributions. The influence of these prestressing schemes was evaluated through a comprehensive analysis of anchor forces, diaphragm wall lateral displacements, building horizontal displacements, and foundation settlements. The results indicated that the initial prestress distribution exerted a pronounced influence on the system behavior under static conditions. Reductions in wall deformation and building settlement were found to be strongly dependent on the magnitude and distribution of the initial prestressing forces. Among the investigated strategies, the decreasing prestressing scheme provided the most favorable overall performance. In contrast, the mid-level maximum distribution scheme exhibited comparatively lower efficiency in limiting excavation-induced deformations. Under seismic loading, however, the differences among the prestress distribution patterns became negligible. These findings suggest that optimization of anchor prestress distribution is primarily beneficial for controlling excavation-induced deformation under static conditions, whereas its effectiveness becomes considerably less pronounced when seismic effects dominate system behavior. The study provides practical guidance for the design and optimization of prestressed anchoring systems for deep excavations located in seismically active urban areas. ]]> Influence of Anchor Prestress Distribution on the Response of an Anchored Deep Excavation-Soil-Building System under Seismic Loading sabira aktureyeva mohsen seyedi doi: 10.56578/mmse020103 Mathematical Modelling for Sustainable Engineering 03-28-2026 Mathematical Modelling for Sustainable Engineering 03-28-2026 2026 2 1 Article 26 10.56578/mmse020103 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020103 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020102 Understanding the mechanisms governing mutualistic interactions is essential for maintaining ecological stability and ensuring the sustainable management of natural ecosystems. To capture the nonlinear benefits inherent in such interactions, this study developed a mathematical model incorporating a Holling Type II functional response, which accounted for handling time and saturation effects. We established the ecological feasibility of the model by proving the non-negativity and boundedness of its solutions and conducted a rigorous qualitative analysis to investigate the existence and stability of equilibrium points. Numerical simulations across a range of ecological conditions supported the analytical results, while sensitivity analysis identified key pathways influencing population dynamics. Furthermore, an optimal control framework employing time-dependent control strategies was introduced to promote species coexistence. The model was solved numerically to evaluate the effectiveness of these interventions. Overall, the findings provide valuable insights for ecological planning and highlight the important role of mathematical modeling in advancing sustainable ecosystem management. 03-26-2026 <![CDATA[ Understanding the mechanisms governing mutualistic interactions is essential for maintaining ecological stability and ensuring the sustainable management of natural ecosystems. To capture the nonlinear benefits inherent in such interactions, this study developed a mathematical model incorporating a Holling Type II functional response, which accounted for handling time and saturation effects. We established the ecological feasibility of the model by proving the non-negativity and boundedness of its solutions and conducted a rigorous qualitative analysis to investigate the existence and stability of equilibrium points. Numerical simulations across a range of ecological conditions supported the analytical results, while sensitivity analysis identified key pathways influencing population dynamics. Furthermore, an optimal control framework employing time-dependent control strategies was introduced to promote species coexistence. The model was solved numerically to evaluate the effectiveness of these interventions. Overall, the findings provide valuable insights for ecological planning and highlight the important role of mathematical modeling in advancing sustainable ecosystem management. ]]> Optimal Control of Two-Species Mutualistic Interaction under Holling Type II Functional Response m. rakib akun m. humayun kabir doi: 10.56578/mmse020102 Mathematical Modelling for Sustainable Engineering 03-26-2026 Mathematical Modelling for Sustainable Engineering 03-26-2026 2026 2 1 Article 12 10.56578/mmse020102 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020102 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020101 A sustainable solid waste-based cementitious system was developed using refining slag, steel slag, desulfurized gypsum, and granulated blast furnace slag (GBFS), and its low-temperature hydration behavior was investigated through a combined experimental and modelling approach. The strength development and microstructural evolution of the quaternary system under different curing temperatures were systematically analyzed. A temperature-dependent hydration kinetics interpretation was introduced to explain the variation in mechanical performance. The hydration characteristics were examined using X-ray diffraction (XRD), thermogravimetric–differential scanning calorimetry (TG–DSC), and scanning electron microscopy (SEM). The results indicate that curing temperature plays a dominant role in governing hydration kinetics and strength evolution. The compressive strength shows a clear positive correlation with temperature, which can be attributed to the accelerated formation of hydration products, mainly ettringite (AFt) and calcium silicate hydrate (C–S–H) gel. Under low-temperature conditions, the hydration process is significantly retarded due to reduced ion mobility and suppressed dissolution of solid waste components. The proposed mechanism suggests that refining slag contributes to the activation of the quaternary system by enhancing early-stage hydration reactions and improving structural densification. From a sustainability perspective, the developed system provides an effective pathway for large-scale utilization of industrial solid wastes while reducing dependence on conventional cement. The findings offer both experimental insights and a modelling-oriented interpretation of low-temperature hydration processes, providing a useful reference for the design and optimization of sustainable cementitious systems in cold-region engineering applications. 03-23-2026 <![CDATA[ A sustainable solid waste-based cementitious system was developed using refining slag, steel slag, desulfurized gypsum, and granulated blast furnace slag (GBFS), and its low-temperature hydration behavior was investigated through a combined experimental and modelling approach. The strength development and microstructural evolution of the quaternary system under different curing temperatures were systematically analyzed. A temperature-dependent hydration kinetics interpretation was introduced to explain the variation in mechanical performance. The hydration characteristics were examined using X-ray diffraction (XRD), thermogravimetric–differential scanning calorimetry (TG–DSC), and scanning electron microscopy (SEM). The results indicate that curing temperature plays a dominant role in governing hydration kinetics and strength evolution. The compressive strength shows a clear positive correlation with temperature, which can be attributed to the accelerated formation of hydration products, mainly ettringite (AFt) and calcium silicate hydrate (C–S–H) gel. Under low-temperature conditions, the hydration process is significantly retarded due to reduced ion mobility and suppressed dissolution of solid waste components. The proposed mechanism suggests that refining slag contributes to the activation of the quaternary system by enhancing early-stage hydration reactions and improving structural densification. From a sustainability perspective, the developed system provides an effective pathway for large-scale utilization of industrial solid wastes while reducing dependence on conventional cement. The findings offer both experimental insights and a modelling-oriented interpretation of low-temperature hydration processes, providing a useful reference for the design and optimization of sustainable cementitious systems in cold-region engineering applications. ]]> Integrated Modelling and Experimental Analysis of Low-Temperature Hydration Mechanisms in Sustainable Fully Solid Waste Cementitious Materials chao ren hui zhang yanhui xi lianyang sun houbin jiao yibin liu doi: 10.56578/mmse020101 Mathematical Modelling for Sustainable Engineering 03-23-2026 Mathematical Modelling for Sustainable Engineering 03-23-2026 2026 2 1 Article 1 10.56578/mmse020101 https://www.acadlore.com/article/MMSE/2026_2_1/mmse020101 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010205 This study examines Turkey’s electricity production and consumption values following the devastating earthquakes (7.7 and 7.6 MW) that occurred on February 6, 2023, affecting 14 million people in 11 provinces, and proposes solutions for system continuity in the face of natural disasters. The earthquakes severely disrupted electricity distribution systems, with average daily production falling from 859,820.94 MWh in January to 851,221.52 MWh in February, and consumption decreasing from 881,208.74 MWh to 863,619.86 MWh. This research analyses Turkey’s existing electricity infrastructure, focusing on the integration of photovoltaic (PV) systems and battery energy storage systems (BESS) as a suitable solution for maintaining electricity supply during and after natural disasters. With Turkey’s installed solar power capacity reaching 9.79% of total electricity production as of December 2022 and the rapid growth of unlicensed distributed generation systems, this study highlights how PV-BESS technology can support critical services such as communication, search and rescue, healthcare, heating, and lighting in emergencies. The findings demonstrate that strategically deploying distributed solar power systems combined with BESS can significantly increase energy resilience during emergencies and normal use, reduce reliance on fossil fuels, and ensure the continuity of essential services. 12-30-2025 <![CDATA[ <p><span style="color: rgb(0, 0, 0); font-family: Times New Roman, sans-serif">This study examines Turkey’s electricity production and consumption values following the devastating earthquakes (7.7 and 7.6 MW) that occurred on February 6, 2023, affecting 14 million people in 11 provinces, and proposes solutions for system continuity in the face of natural disasters. The earthquakes severely disrupted electricity distribution systems, with average daily production falling from 859,820.94 MWh in January to 851,221.52 MWh in February, and consumption decreasing from 881,208.74 MWh to 863,619.86 MWh. This research analyses Turkey’s existing electricity infrastructure, focusing on the integration of photovoltaic (PV) systems and battery energy storage systems (BESS) as a suitable solution for maintaining electricity supply during and after natural disasters. With Turkey’s installed solar power capacity reaching 9.79% of total electricity production as of December 2022 and the rapid growth of unlicensed distributed generation systems, this study highlights how PV-BESS technology can support critical services such as communication, search and rescue, healthcare, heating, and lighting in emergencies. The findings demonstrate that strategically deploying distributed solar power systems combined with BESS can significantly increase energy resilience during emergencies and normal use, reduce reliance on fossil fuels, and ensure the continuity of essential services.</span></p> ]]> Analysis of Electricity Production and Consumption to Ensure Continuity After February 6, 2023 Earthquake: PV-BESS Solutions mehmet çeçen doi: 10.56578/mmse010205 Mathematical Modelling for Sustainable Engineering 12-30-2025 Mathematical Modelling for Sustainable Engineering 12-30-2025 2025 1 2 Article 115 10.56578/mmse010205 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010205 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010204 Thermal ablation has been widely adopted for the treatment of liver tumors; however, treatment efficacy can be substantially compromised by vascular heat-sink effects arising from adjacent blood vessels. In this study, a comprehensive investigation was conducted to quantitatively compare radiofrequency ablation and microwave ablation with specific emphasis on vessel-induced thermal dissipation. A coupled multiphysics finite element framework was developed in COMSOL Multiphysics. For radiofrequency ablation, quasi-static electric currents were coupled with the bioheat transfer equation to model Joule heating, whereas for microwave ablation, electromagnetic wave propagation was coupled with bioheat transfer to represent dielectric heating. Thermal tissue injury was evaluated using an Arrhenius damage formulation, and treatment outcome was quantified in terms of necrotic volume fraction after a simulated ablation duration of 600 s. Two configurations were examined: a baseline liver tissue domain without vascular structures and a vascularized domain incorporating a representative 5 mm-diameter blood vessel positioned in proximity to the ablation applicator. In addition, a verification scenario was implemented by reproducing reported operating conditions from the literature to confirm the predicted magnitude of vessel-related lesion attenuation under a consistent necrosis definition. The results demonstrate that the presence of a blood vessel leads to a markedly greater reduction in predicted necrotic volume for radiofrequency ablation (34.08%) than for microwave ablation (18.96%). Furthermore, the simulated ablation morphology was found to be more spherical in radiofrequency ablation and more axially elongated in microwave ablation. These findings indicate that vascular heat-sink effects differentially influence ablation modalities and should be explicitly considered during modality selection and parameter optimization, particularly for tumors located adjacent to major hepatic vessels. The proposed computational framework provides a robust and extensible platform for pre-procedural planning and comparative evaluation of thermal ablation strategies in vascularized hepatic tissue. 12-30-2025 <![CDATA[ <p>Thermal ablation has been widely adopted for the treatment of liver tumors; however, treatment efficacy can be substantially compromised by vascular heat-sink effects arising from adjacent blood vessels. In this study, a comprehensive investigation was conducted to quantitatively compare radiofrequency ablation and microwave ablation with specific emphasis on vessel-induced thermal dissipation. A coupled multiphysics finite element framework was developed in COMSOL Multiphysics. For radiofrequency ablation, quasi-static electric currents were coupled with the bioheat transfer equation to model Joule heating, whereas for microwave ablation, electromagnetic wave propagation was coupled with bioheat transfer to represent dielectric heating. Thermal tissue injury was evaluated using an Arrhenius damage formulation, and treatment outcome was quantified in terms of necrotic volume fraction after a simulated ablation duration of 600 s. Two configurations were examined: a baseline liver tissue domain without vascular structures and a vascularized domain incorporating a representative 5 mm-diameter blood vessel positioned in proximity to the ablation applicator. In addition, a verification scenario was implemented by reproducing reported operating conditions from the literature to confirm the predicted magnitude of vessel-related lesion attenuation under a consistent necrosis definition. The results demonstrate that the presence of a blood vessel leads to a markedly greater reduction in predicted necrotic volume for radiofrequency ablation (34.08%) than for microwave ablation (18.96%). Furthermore, the simulated ablation morphology was found to be more spherical in radiofrequency ablation and more axially elongated in microwave ablation. These findings indicate that vascular heat-sink effects differentially influence ablation modalities and should be explicitly considered during modality selection and parameter optimization, particularly for tumors located adjacent to major hepatic vessels. The proposed computational framework provides a robust and extensible platform for pre-procedural planning and comparative evaluation of thermal ablation strategies in vascularized hepatic tissue.</p> ]]> Computational Assessment of Vascular Heat-Sink Effects in Radiofrequency and Microwave Ablation of Liver Tumors muhammet kaan yeşilyurt mansur mustafaoğlu doi: 10.56578/mmse010204 Mathematical Modelling for Sustainable Engineering 12-30-2025 Mathematical Modelling for Sustainable Engineering 12-30-2025 2025 1 2 Article 102 10.56578/mmse010204 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010204 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010203 The application of fiber-reinforced polymer (FRP) for shear strengthening of concrete structures has become increasingly popular. However, the inherent scatter in shear test makes accurate prediction of the shear capacity a significant challenge, as traditional design code often struggle to capture the complex nonlinear interactions among multiple factors. To address this limitation, this study introduces a machine learning (ML) approach to develop a high-accuracy predictive model. A database comprising 552 experimental tests on FRP-strengthened concrete beams in shear was assembled. Three ensemble learning algorithms—Random Forest (RF), Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost)—were systematically compared and evaluated against predictions from three existing design codes: ACI 440.2-23, FIB Bulletin 14, and GB 50608-2020. Results indicate that all ML models significantly outperform the existing code-based calculations. Among them, the XGBoost model demonstrated the best performance, achieving a coefficient of determination ($\mathrm{R}^2$) of 0.94 and a mean absolute percentage error (MAPE) as low as 12.81% on the test set. Interpretability analysis based on shapely additive explanations (SHAP) values further identified and elucidated the physical significance of key influencing features, such as FRP bonded height ($h_f$), beam width ($b$), and stirrup reinforcement ratio ($\rho_{s v}$), and elucidated their physical significance on the shear capacity. This study confirms the superiority and engineering application potential of data-driven approaches for predicting the shear performance of FRP-strengthened members. Moreover, high-accuracy capacity prediction enables more economical and environmentally friendly strengthening designs. This contributes to reducing material overuse, lowering construction energy consumption and carbon emissions, thereby supporting the sustainability goals of structural engineering. 12-30-2025 <![CDATA[ <p>The application of fiber-reinforced polymer (FRP) for shear strengthening of concrete structures has become increasingly popular. However, the inherent scatter in shear test makes accurate prediction of the shear capacity a significant challenge, as traditional design code often struggle to capture the complex nonlinear interactions among multiple factors. To address this limitation, this study introduces a machine learning (ML) approach to develop a high-accuracy predictive model. A database comprising 552 experimental tests on FRP-strengthened concrete beams in shear was assembled. Three ensemble learning algorithms—Random Forest (RF), Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost)—were systematically compared and evaluated against predictions from three existing design codes: ACI 440.2-23, FIB Bulletin 14, and GB 50608-2020. Results indicate that all ML models significantly outperform the existing code-based calculations. Among them, the XGBoost model demonstrated the best performance, achieving a coefficient of determination ($\mathrm{R}^2$) of 0.94 and a mean absolute percentage error (MAPE) as low as 12.81% on the test set. Interpretability analysis based on shapely additive explanations (SHAP) values further identified and elucidated the physical significance of key influencing features, such as FRP bonded height ($h_f$), beam width ($b$), and stirrup reinforcement ratio ($\rho_{s v}$), and elucidated their physical significance on the shear capacity. This study confirms the superiority and engineering application potential of data-driven approaches for predicting the shear performance of FRP-strengthened members. Moreover, high-accuracy capacity prediction enables more economical and environmentally friendly strengthening designs. This contributes to reducing material overuse, lowering construction energy consumption and carbon emissions, thereby supporting the sustainability goals of structural engineering.</p> ]]> A Decision-Oriented Modelling Framework for Sustainable Strengthening of Reinforced Concrete Structures Using Data-Driven Capacity Prediction ming wang yifeng zheng doi: 10.56578/mmse010203 Mathematical Modelling for Sustainable Engineering 12-30-2025 Mathematical Modelling for Sustainable Engineering 12-30-2025 2025 1 2 Article 94 10.56578/mmse010203 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010203 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010202 Reservoir drawdown is a critical loading condition that alters seepage and stress distributions in earth dams, potentially inducing instability and excessive deformation. Understanding the coupled hydraulic-mechanical response during drawdown is therefore essential for ensuring long-term dam safety and performance. The stability and deformation response of earth dams during reservoir drawdown were systematically investigated, with particular emphasis placed on the coupled effects of drawdown rate, core geometry, core permeability, core strength, and shell strength. Two-dimensional finite element analyses were performed using PLAXIS 2D to evaluate the factor of safety against instability and the associated crest settlement under a range of representative conditions. The numerical results indicate that an increase in the reservoir drawdown rate leads to a noticeable increase in the factor of safety against horizontal instability, whereas the corresponding influence on crest settlement is negligible. Variations in core geometry were found to exert a pronounced effect on dam performance: an increase in undrained core width results in larger crest settlement while simultaneously reducing the factor of safety. In contrast, higher core permeability slightly improves the factor of safety, although its influence on crest settlement remains marginal. The mechanical properties of dam materials were shown to play a dominant role in both stability and deformation behavior. In particular, increases in core and shell strength parameters significantly enhance the factor of safety while substantially reducing crest settlement. These results provide valuable insight for the design, assessment, and risk-informed management of earth dams subjected to rapid or controlled reservoir drawdown conditions. 12-12-2025 <![CDATA[ Reservoir drawdown is a critical loading condition that alters seepage and stress distributions in earth dams, potentially inducing instability and excessive deformation. Understanding the coupled hydraulic-mechanical response during drawdown is therefore essential for ensuring long-term dam safety and performance. The stability and deformation response of earth dams during reservoir drawdown were systematically investigated, with particular emphasis placed on the coupled effects of drawdown rate, core geometry, core permeability, core strength, and shell strength. Two-dimensional finite element analyses were performed using PLAXIS 2D to evaluate the factor of safety against instability and the associated crest settlement under a range of representative conditions. The numerical results indicate that an increase in the reservoir drawdown rate leads to a noticeable increase in the factor of safety against horizontal instability, whereas the corresponding influence on crest settlement is negligible. Variations in core geometry were found to exert a pronounced effect on dam performance: an increase in undrained core width results in larger crest settlement while simultaneously reducing the factor of safety. In contrast, higher core permeability slightly improves the factor of safety, although its influence on crest settlement remains marginal. The mechanical properties of dam materials were shown to play a dominant role in both stability and deformation behavior. In particular, increases in core and shell strength parameters significantly enhance the factor of safety while substantially reducing crest settlement. These results provide valuable insight for the design, assessment, and risk-informed management of earth dams subjected to rapid or controlled reservoir drawdown conditions. ]]> Stability and Deformation Behavior of Earth Dams under Variable Reservoir Drawdown Rates and Material Properties ali abraheem ramadhan alqilfat mohsen seyedi doi: 10.56578/mmse010202 Mathematical Modelling for Sustainable Engineering 12-12-2025 Mathematical Modelling for Sustainable Engineering 12-12-2025 2025 1 2 Article 82 10.56578/mmse010202 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010202 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010201 Tower crane structural systems are widely used in large-scale construction projects, where foundation performance is critical to structural safety under ultimate loading conditions. In addition to satisfying ultimate bearing capacity, serviceability requirements—particularly total and differential settlements—must be rigorously addressed in foundation design. In this study, the performance of a tower crane foundation subjected to ultimate loads was evaluated using an integrated approach combining field testing, in situ monitoring, and finite element analysis. A tower crane foundation constructed for an industrial project was examined as a representative case. The subsurface profile comprised an uncontrolled fill layer overlying medium-dense sand, very stiff clay, and hard clay. Due to the high uncertainty associated with the fill material, plate load tests were conducted to characterize its deformation behavior. The test results were subsequently used in a back analysis with PLAXIS 2D to determine representative deformation parameters. The analysis indicated that the foundation dimensions recommended in the manufacturer’s technical catalog were inadequate when settlement criteria were explicitly considered. Consequently, revised foundation dimensions of 8 m × 8 m were proposed. Finite element simulations were performed to evaluate the deformation response of the redesigned foundation under ultimate loading conditions. Field settlement measurements obtained at two monitoring points during operation exhibited close agreement with the numerical predictions. The study underscores the importance of integrating experimentally calibrated numerical analysis and field monitoring in the safety assessment of tower crane foundation systems, particularly for foundations resting on heterogeneous or uncontrolled soil deposits. 12-03-2025 <![CDATA[ Tower crane structural systems are widely used in large-scale construction projects, where foundation performance is critical to structural safety under ultimate loading conditions. In addition to satisfying ultimate bearing capacity, serviceability requirements—particularly total and differential settlements—must be rigorously addressed in foundation design. In this study, the performance of a tower crane foundation subjected to ultimate loads was evaluated using an integrated approach combining field testing, in situ monitoring, and finite element analysis. A tower crane foundation constructed for an industrial project was examined as a representative case. The subsurface profile comprised an uncontrolled fill layer overlying medium-dense sand, very stiff clay, and hard clay. Due to the high uncertainty associated with the fill material, plate load tests were conducted to characterize its deformation behavior. The test results were subsequently used in a back analysis with PLAXIS 2D to determine representative deformation parameters. The analysis indicated that the foundation dimensions recommended in the manufacturer’s technical catalog were inadequate when settlement criteria were explicitly considered. Consequently, revised foundation dimensions of 8 m × 8 m were proposed. Finite element simulations were performed to evaluate the deformation response of the redesigned foundation under ultimate loading conditions. Field settlement measurements obtained at two monitoring points during operation exhibited close agreement with the numerical predictions. The study underscores the importance of integrating experimentally calibrated numerical analysis and field monitoring in the safety assessment of tower crane foundation systems, particularly for foundations resting on heterogeneous or uncontrolled soil deposits. ]]> Performance Assessment of Tower Crane Foundation Systems under Ultimate Loading Conditions muhammet karabulut safa çevik doi: 10.56578/mmse010201 Mathematical Modelling for Sustainable Engineering 12-03-2025 Mathematical Modelling for Sustainable Engineering 12-03-2025 2025 1 2 Article 73 10.56578/mmse010201 https://www.acadlore.com/article/MMSE/2025_1_2/mmse010201 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010105 The long-term performance and safety of high-speed railway infrastructure are strongly governed by the dynamic interaction between trains and the rail–track system, particularly in the presence of structural irregularities. In this study, the influence of rail and sleeper irregularities on train-induced vertical ballast settlement was systematically investigated using advanced three-dimensional finite element simulations implemented in PLAXIS 3D. Nine representative track configurations were established, encompassing ideal conditions as well as isolated and combined rail and sleeper irregularities. Dynamic train loading was simulated at operating speeds of 100, 200, and 300 km/h, while nonlinear constitutive behavior of ballast and substructure materials, together with realistic contact interactions between track components, was explicitly considered. The numerical results indicate that even minor geometric or support irregularities significantly disrupt load transfer mechanisms, leading to localized stress concentrations and accelerated ballast settlement. With increasing train speed, the sensitivity of the rail–track system to such irregularities was markedly amplified, resulting in pronounced dynamic displacements. Track configurations involving concurrent rail and sleeper irregularities exhibited the most severe settlement responses. These findings demonstrate that ballast degradation is governed not only by train speed but also by the interaction and superposition of track irregularities, which can substantially shorten maintenance cycles if left unaddressed. The study underscores the critical importance of early defect identification, preventive maintenance strategies, and high-fidelity numerical modeling in enhancing the resilience, serviceability, and long-term reliability of modern high-speed railway networks. 09-29-2025 <![CDATA[ The long-term performance and safety of high-speed railway infrastructure are strongly governed by the dynamic interaction between trains and the rail–track system, particularly in the presence of structural irregularities. In this study, the influence of rail and sleeper irregularities on train-induced vertical ballast settlement was systematically investigated using advanced three-dimensional finite element simulations implemented in PLAXIS 3D. Nine representative track configurations were established, encompassing ideal conditions as well as isolated and combined rail and sleeper irregularities. Dynamic train loading was simulated at operating speeds of 100, 200, and 300 km/h, while nonlinear constitutive behavior of ballast and substructure materials, together with realistic contact interactions between track components, was explicitly considered. The numerical results indicate that even minor geometric or support irregularities significantly disrupt load transfer mechanisms, leading to localized stress concentrations and accelerated ballast settlement. With increasing train speed, the sensitivity of the rail–track system to such irregularities was markedly amplified, resulting in pronounced dynamic displacements. Track configurations involving concurrent rail and sleeper irregularities exhibited the most severe settlement responses. These findings demonstrate that ballast degradation is governed not only by train speed but also by the interaction and superposition of track irregularities, which can substantially shorten maintenance cycles if left unaddressed. The study underscores the critical importance of early defect identification, preventive maintenance strategies, and high-fidelity numerical modeling in enhancing the resilience, serviceability, and long-term reliability of modern high-speed railway networks. ]]> Influence of Rail–Track Structural Irregularities on Train-Induced Ballast Settlement ahmed mohamed h. algadi mohsen seyedi doi: 10.56578/mmse010105 Mathematical Modelling for Sustainable Engineering 09-29-2025 Mathematical Modelling for Sustainable Engineering 09-29-2025 2025 1 1 Article 63 10.56578/mmse010105 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010105 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010104 Efficient management of airflow and heat dissipation in data centers is becoming increasingly critical as computing densities increase and thermal loads grow. To address these challenges, this study numerically examines the thermo-fluid behavior of a medium-sized data center containing twelve heat-generating server racks under multiple ventilation strategies. A three-dimensional CFD model was developed using the RANS equations with the SST $k$–$\omega$ turbulence formulation and the Boussinesq approximation to account for buoyancy-driven flow. Eight ventilated configurations were evaluated by combining two louver orientations (20$^{\circ}$ and 50$^{\circ}$), two inlet heights (top or bottom), and two inlet velocity modes (constant or pulsatile), in addition to a no-ventilation control scenario. Both steady and transient simulations were performed to capture the interactions between inlet momentum, recirculation patterns, and thermal stratification over a one-hour operational period. The control case exhibited strong thermal stratification and a stable hot layer beneath the ceiling, demonstrating the inadequacy of natural convection alone. Introducing ventilation significantly modified the airflow topology and improved cooling performance, though with considerable sensitivity to inlet design. Shallower-angle louvers (20$^{\circ}$) enhanced horizontal jet penetration and reduced recirculation pockets, whereas steeper louvers (50$^{\circ}$) generated stronger impingement and more localized hot spots. Inlet height further shaped vertical temperature distribution: bottom inlets effectively cooled lower and mid-rack levels, while top inlets reduced ceiling-layer temperatures by disrupting buoyant plumes. Pulsatile ventilation outperformed constant inflow by periodically increasing momentum, enhancing mixing, and weakening plume formation during peak phases. Mass-flow analysis similarly showed that extraction capacity strongly correlated with inlet velocity amplitude. Overall, the results highlight the importance of coordinated selection of inlet position, louver angle, and temporal forcing. The combined use of shallow-angle louvers and pulsatile ventilation presents a promising pathway for improving cooling uniformity and thermal management in high-density data centers. 09-25-2025 <![CDATA[ <p>Efficient management of airflow and heat dissipation in data centers is becoming increasingly critical as computing densities increase and thermal loads grow. To address these challenges, this study numerically examines the thermo-fluid behavior of a medium-sized data center containing twelve heat-generating server racks under multiple ventilation strategies. A three-dimensional CFD model was developed using the RANS equations with the SST $k$–$\omega$ turbulence formulation and the Boussinesq approximation to account for buoyancy-driven flow. Eight ventilated configurations were evaluated by combining two louver orientations (20$^{\circ}$ and 50$^{\circ}$), two inlet heights (top or bottom), and two inlet velocity modes (constant or pulsatile), in addition to a no-ventilation control scenario. Both steady and transient simulations were performed to capture the interactions between inlet momentum, recirculation patterns, and thermal stratification over a one-hour operational period. The control case exhibited strong thermal stratification and a stable hot layer beneath the ceiling, demonstrating the inadequacy of natural convection alone. Introducing ventilation significantly modified the airflow topology and improved cooling performance, though with considerable sensitivity to inlet design. Shallower-angle louvers (20$^{\circ}$) enhanced horizontal jet penetration and reduced recirculation pockets, whereas steeper louvers (50$^{\circ}$) generated stronger impingement and more localized hot spots. Inlet height further shaped vertical temperature distribution: bottom inlets effectively cooled lower and mid-rack levels, while top inlets reduced ceiling-layer temperatures by disrupting buoyant plumes. Pulsatile ventilation outperformed constant inflow by periodically increasing momentum, enhancing mixing, and weakening plume formation during peak phases. Mass-flow analysis similarly showed that extraction capacity strongly correlated with inlet velocity amplitude. Overall, the results highlight the importance of coordinated selection of inlet position, louver angle, and temporal forcing. The combined use of shallow-angle louvers and pulsatile ventilation presents a promising pathway for improving cooling uniformity and thermal management in high-density data centers.</p> ]]> Analysis of Ventilation Architectures for Data Center Cooling Using Steady and Transient Computational Fluid Dynamics Simulations leila riahinezhad melika mohammadkhah ahmad nooraeen doi: 10.56578/mmse010104 Mathematical Modelling for Sustainable Engineering 09-25-2025 Mathematical Modelling for Sustainable Engineering 09-25-2025 2025 1 1 Article 48 10.56578/mmse010104 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010104 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010103 With the rapid development of solar power generation technology, the hotspot effect of photovoltaic (PV) arrays poses a key challenge to the efficiency and stability of the system. Conventional PV array models have significant limitations in dealing with complex shadow shading and multi-peak output characteristics, especially when confronted with complex topologies such as the complex-total-cross-tied (CTCT) structures. To address this issue, this paper proposed a mathematical model for PV arrays based on multipoint parabolic motion, which could accurately simulate the output characteristics of PV arrays under localized shading conditions. The model decomposed the current-voltage ($I-V$) characteristic curve of the PV arrays into multiple parabolic trajectories. A shadow shading model for complex structures was successfully constructed by combining with a kinematic model. MATLAB/Simulink simulations and experimental validation showed that the proposed model guaranteed computational accuracy with error less than 5%, while computational efficiency was greatly improved. The proposed model could accurately capture the multi-peak characteristics when compared with the traditional engineering model. Results from the experiment further verified the robustness of the model in dynamic shading scenarios, hence providing an efficient and reliable tool for maximum power tracking and hotspot localization in the PV system. 09-14-2025 <![CDATA[ <p>With the rapid development of solar power generation technology, the hotspot effect of photovoltaic (PV) arrays poses a key challenge to the efficiency and stability of the system. Conventional PV array models have significant limitations in dealing with complex shadow shading and multi-peak output characteristics, especially when confronted with complex topologies such as the complex-total-cross-tied (CTCT) structures. To address this issue, this paper proposed a mathematical model for PV arrays based on multipoint parabolic motion, which could accurately simulate the output characteristics of PV arrays under localized shading conditions. The model decomposed the current-voltage ($I-V$) characteristic curve of the PV arrays into multiple parabolic trajectories. A shadow shading model for complex structures was successfully constructed by combining with a kinematic model. MATLAB/Simulink simulations and experimental validation showed that the proposed model guaranteed computational accuracy with error less than 5%, while computational efficiency was greatly improved. The proposed model could accurately capture the multi-peak characteristics when compared with the traditional engineering model. Results from the experiment further verified the robustness of the model in dynamic shading scenarios, hence providing an efficient and reliable tool for maximum power tracking and hotspot localization in the PV system.</p> ]]> Hotspots in Photovoltaic Arrays Based on Multipoint Parabolic Motion zhikai dai gong chen zhiqi chen chang lu yao zheng xinyi wang jinqiu wang rui min xinyang wu wei wei zhengpeng yang deyi li huachao zhang ziyu yang yeshuai shao doi: 10.56578/mmse010103 Mathematical Modelling for Sustainable Engineering 09-14-2025 Mathematical Modelling for Sustainable Engineering 09-14-2025 2025 1 1 Article 35 10.56578/mmse010103 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010103 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010102 The new generation composite materials are widely used in Engineering due to their light weight, high strength, and resistance to corrosion and wear. Two main modeling strategies, the piecewise layered approach and the continuously graded approach were employed in the literature, with the latter offering a more realistic representation. Recent studies have highlighted the importance of analyzing the stability and vibration behavior of exponentially graded cylindrical shells, particularly when embedded in elastic media. Nevertheless, most works were limited to simply supporting boundary conditions and so neglected the foundation effects. To fill this notable gap in the literature, the present study focused on the buckling behavior of exponentially graded cylindrical shells (EGCSs) with clamped edges under external pressure within an elastic medium. A theoretical framework was then established for future design applications in advanced Engineering fields. 09-11-2025 <![CDATA[ The new generation composite materials are widely used in Engineering due to their light weight, high strength, and resistance to corrosion and wear. Two main modeling strategies, the piecewise layered approach and the continuously graded approach were employed in the literature, with the latter offering a more realistic representation. Recent studies have highlighted the importance of analyzing the stability and vibration behavior of exponentially graded cylindrical shells, particularly when embedded in elastic media. Nevertheless, most works were limited to simply supporting boundary conditions and so neglected the foundation effects. To fill this notable gap in the literature, the present study focused on the buckling behavior of exponentially graded cylindrical shells (EGCSs) with clamped edges under external pressure within an elastic medium. A theoretical framework was then established for future design applications in advanced Engineering fields. ]]> Buckling Characteristics of Exponentially Graded Cylindrical Shells with Clamped Edges Supported by Elastic Eedium a. h. sofiyev a. a. memmedov e. schnack doi: 10.56578/mmse010102 Mathematical Modelling for Sustainable Engineering 09-11-2025 Mathematical Modelling for Sustainable Engineering 09-11-2025 2025 1 1 Article 26 10.56578/mmse010102 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010102 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010101 This study investigated the static bending behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microbeams supported on an elastic foundation. The proposed model was formulated by coupling higher-order shear deformation beam theories (HoSDBTs) with the modified couple stress theory (MCST). Four distinct CNT distribution patterns within the polymer matrix were considered. Using Hamilton’s principle, governing equations and boundary conditions for simply-supported microbeams were derived and solved analytically. This comprehensive parametric study explored the effects of the material length scale, CNT volume fraction, aspect ratio, foundation stiffness (Winkler and Pasternak models), and CNT gradation on bending stiffness. Results revealed that all parameters notably influenced the mechanical response, with key roles played by size-dependent effects and elastic foundation interactions. The proposed MCST-enhanced HoSDBT model effectively captures size-dependent behaviors, rendering it suitable for the design and optimization of FG-CNTRC micro-devices. 09-02-2025 <![CDATA[ This study investigated the static bending behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microbeams supported on an elastic foundation. The proposed model was formulated by coupling higher-order shear deformation beam theories (HoSDBTs) with the modified couple stress theory (MCST). Four distinct CNT distribution patterns within the polymer matrix were considered. Using Hamilton’s principle, governing equations and boundary conditions for simply-supported microbeams were derived and solved analytically. This comprehensive parametric study explored the effects of the material length scale, CNT volume fraction, aspect ratio, foundation stiffness (Winkler and Pasternak models), and CNT gradation on bending stiffness. Results revealed that all parameters notably influenced the mechanical response, with key roles played by size-dependent effects and elastic foundation interactions. The proposed MCST-enhanced HoSDBT model effectively captures size-dependent behaviors, rendering it suitable for the design and optimization of FG-CNTRC micro-devices. ]]> Static Bending Behaviour of FG-CNTRC Microbeams Resting on Elastic Foundation Using Higher-Order Shear Deformation Beam Theories and Modified Couple Stress Theory van-hieu dang doi: 10.56578/mmse010101 Mathematical Modelling for Sustainable Engineering 09-02-2025 Mathematical Modelling for Sustainable Engineering 09-02-2025 2025 1 1 Article 1 10.56578/mmse010101 https://www.acadlore.com/article/MMSE/2025_1_1/mmse010101