Pub Date : 2026-01-19DOI: 10.1016/j.apm.2026.116773
Wenqi Wu , Xiaochao Xia
Quantile regression has widespread applications in various fields because it can flexibly model conditional quantile, rather than conditional mean, of a response variable given some covariates, offering robustness to outliers, heavy-tailed responses, and heteroskedasticity. While, composite quantile regression can gain more efficiency and robustness by addressing multiple conditional quantiles of the response variable simultaneously. However, when massive data are encountered, fitting a composite quantile regression model could be computationally challenging and even infeasible. To address this issue, this paper proposes a random perturbation subsampling approach under composite quantile regression, where the number of parameters is allowed to diverge to infinity with the subsample size. Particularly, the proposed algorithm can be directly adaptive to quantile regression. In contrast to optimal subsampling methods, our procedure has the significant merit of avoiding the need of computing the sampling probabilities that are often complex, data dependent and time-consuming. Theoretically, the convergence rate and asymptotic normality for our proposed estimators are rigorously established. Extensive simulations numerically demonstrate the effectiveness of the proposed methods. Finally, we apply our methods to two real-world applications from physicochemical properties and superconductivity datasets, further empirically showcasing the advantages of our methods in computation.
{"title":"Random perturbation subsampling estimation under composite quantile regression with diverging dimensions","authors":"Wenqi Wu , Xiaochao Xia","doi":"10.1016/j.apm.2026.116773","DOIUrl":"10.1016/j.apm.2026.116773","url":null,"abstract":"<div><div>Quantile regression has widespread applications in various fields because it can flexibly model conditional quantile, rather than conditional mean, of a response variable given some covariates, offering robustness to outliers, heavy-tailed responses, and heteroskedasticity. While, composite quantile regression can gain more efficiency and robustness by addressing multiple conditional quantiles of the response variable simultaneously. However, when massive data are encountered, fitting a composite quantile regression model could be computationally challenging and even infeasible. To address this issue, this paper proposes a random perturbation subsampling approach under composite quantile regression, where the number of parameters is allowed to diverge to infinity with the subsample size. Particularly, the proposed algorithm can be directly adaptive to quantile regression. In contrast to optimal subsampling methods, our procedure has the significant merit of avoiding the need of computing the sampling probabilities that are often complex, data dependent and time-consuming. Theoretically, the convergence rate and asymptotic normality for our proposed estimators are rigorously established. Extensive simulations numerically demonstrate the effectiveness of the proposed methods. Finally, we apply our methods to two real-world applications from physicochemical properties and superconductivity datasets, further empirically showcasing the advantages of our methods in computation.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116773"},"PeriodicalIF":4.4,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-18DOI: 10.1016/j.apm.2026.116769
Jiajun Zhang , Jialu Guo , Chencheng Feng , Jing Wang , Yang Zhang , A.S. Ademiloye
Due to their superior tensile properties, fiber-reinforced composite (FRC) structures have been widely applied in modern industries. This study employs phase field modeling to simulate the process of elastic-plastic fracture in FRC structures. In this study, we first establish a constitutive model for elastoplastic solids and a phase field model for fracture in solid materials. By employing the Newton-Raphson iterative method, the displacement field and phase field are solved separately based on an alternating iterative scheme. Subsequently, we presented three numerical examples to demonstrate the robustness and accuracy of the proposed model. First, we simulated the elastoplastic fracture response of isotropic materials and validate the accuracy of the elastoplastic fracture phase field model. Next, we examined the tensile and fracture behaviors of unidirectional fiber reinforced composite plate with a central circular hole and varying fiber angles. Finally, the influence of curved fiber on the unilateral tensile fracture of FRC plates was investigated. Considering the pronounced heterogeneity between fibers and matrix materials, this study assumes that the fibers remain in the linear elastic regime and introduces a yield function to describe the matrix behavior. Our computational results demonstrate the accuracy and robustness of the proposed model for predicting the elastoplastic fracture response of FRC structures. Furthermore, we observed that in comparison to the elastic phase field fracture model, the occurrence of fracture is delayed when an elasto-plastic phase model is employed due to the complex interactions between the plastic dissipation energy and the fracture energy.
{"title":"Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites","authors":"Jiajun Zhang , Jialu Guo , Chencheng Feng , Jing Wang , Yang Zhang , A.S. Ademiloye","doi":"10.1016/j.apm.2026.116769","DOIUrl":"10.1016/j.apm.2026.116769","url":null,"abstract":"<div><div>Due to their superior tensile properties, fiber-reinforced composite (FRC) structures have been widely applied in modern industries. This study employs phase field modeling to simulate the process of elastic-plastic fracture in FRC structures. In this study, we first establish a constitutive model for elastoplastic solids and a phase field model for fracture in solid materials. By employing the Newton-Raphson iterative method, the displacement field and phase field are solved separately based on an alternating iterative scheme. Subsequently, we presented three numerical examples to demonstrate the robustness and accuracy of the proposed model. First, we simulated the elastoplastic fracture response of isotropic materials and validate the accuracy of the elastoplastic fracture phase field model. Next, we examined the tensile and fracture behaviors of unidirectional fiber reinforced composite plate with a central circular hole and varying fiber angles. Finally, the influence of curved fiber on the unilateral tensile fracture of FRC plates was investigated. Considering the pronounced heterogeneity between fibers and matrix materials, this study assumes that the fibers remain in the linear elastic regime and introduces a yield function to describe the matrix behavior. Our computational results demonstrate the accuracy and robustness of the proposed model for predicting the elastoplastic fracture response of FRC structures. Furthermore, we observed that in comparison to the elastic phase field fracture model, the occurrence of fracture is delayed when an elasto-plastic phase model is employed due to the complex interactions between the plastic dissipation energy and the fracture energy.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116769"},"PeriodicalIF":4.4,"publicationDate":"2026-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-17DOI: 10.1016/j.apm.2026.116775
Sjoerd De Jong , Andrea Brugnoli , Ramy Rashad , Yi Zhang , Stefano Stramigioli
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element exterior calculus and domain decomposition to interconnect two systems with dual input-output behavior. The spatial domain is split into two parts by introducing an arbitrary interface. Each subdomain is discretized with a mixed finite element formulation that introduces a uniform boundary condition in a natural way as the input. In each subdomain the finite element spaces are selected from a finite element subcomplex to obtain a stable discretization. The two systems are then interconnected together by making use of a feedback interconnection. This is achieved by discretizing the boundary inputs using appropriate spaces that couple the two formulations. The final systems include all boundary conditions explicitly and do not contain any Lagrange multiplier. Time integration is performed using the implicit midpoint or Störmer-Verlet scheme. The method can also be applied to semilinear systems containing algebraic nonlinearities. The proposed strategy is tested on different examples: geometrically exact intrinsic beam model, the wave equation, membrane elastodynamics and the Mindlin plate. Numerical tests assess the conservation properties of the scheme, the effectiveness of the methodology and its robustness against shear locking phenomena.
{"title":"A domain decomposition strategy for natural imposition of mixed boundary conditions in port-Hamiltonian systems","authors":"Sjoerd De Jong , Andrea Brugnoli , Ramy Rashad , Yi Zhang , Stefano Stramigioli","doi":"10.1016/j.apm.2026.116775","DOIUrl":"10.1016/j.apm.2026.116775","url":null,"abstract":"<div><div>In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element exterior calculus and domain decomposition to interconnect two systems with dual input-output behavior. The spatial domain is split into two parts by introducing an arbitrary interface. Each subdomain is discretized with a mixed finite element formulation that introduces a uniform boundary condition in a natural way as the input. In each subdomain the finite element spaces are selected from a finite element subcomplex to obtain a stable discretization. The two systems are then interconnected together by making use of a feedback interconnection. This is achieved by discretizing the boundary inputs using appropriate spaces that couple the two formulations. The final systems include all boundary conditions explicitly and do not contain any Lagrange multiplier. Time integration is performed using the implicit midpoint or Störmer-Verlet scheme. The method can also be applied to semilinear systems containing algebraic nonlinearities. The proposed strategy is tested on different examples: geometrically exact intrinsic beam model, the wave equation, membrane elastodynamics and the Mindlin plate. Numerical tests assess the conservation properties of the scheme, the effectiveness of the methodology and its robustness against shear locking phenomena.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116775"},"PeriodicalIF":4.4,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.1016/j.apm.2026.116770
Vasileios E. Papageorgiou , Irene Votsi , George Tsaklidis
Accurate assessment of epidemic severity requires stochastic indicators that quantify outbreak size and timing under uncertainty. Numerous studies have introduced different stochastic models and associated epidemic descriptors, providing explicit formulas and algorithms that enable their estimation. Most of the studies consider constant epidemic dynamics, which limit the accuracy and the possibility of providing online estimates. In this paper, we introduce a SPIR (Susceptible, Presymptomatic, Infectious, Removed) model based on a 3-dimensional Markov chain. In the framework of this model, stochastic descriptors are introduced including the total number of infections, the occurrence time of a specific number of deaths and the number of infections generated from an index presymptomatic or an infectious case. The paper then integrates an augmented state-space formulation with particle filtering to estimate time-varying epidemiological parameters from surveillance data. Using mpox data from Ghana (2022), the time-varying approach improves predictive accuracy compared with a standard constant parameter method. The root mean squared error (RMSE) decreases from 12.497 to 5.480 for the expected total infections until extinction and from 2.082 to 1.588 for the expected time to the first death. In summary, incorporating time-varying parameter estimates through the filtering process enhances the precision of descriptors, allowing for more realistic epidemic scenarios. Overall, incorporating dynamically updated parameters improves the precision of stochastic descriptor estimation and supports data-driven online assessment of emerging outbreaks.
{"title":"Dynamic estimation of stochastic descriptors in the SPIR model using particle filtering","authors":"Vasileios E. Papageorgiou , Irene Votsi , George Tsaklidis","doi":"10.1016/j.apm.2026.116770","DOIUrl":"10.1016/j.apm.2026.116770","url":null,"abstract":"<div><div>Accurate assessment of epidemic severity requires stochastic indicators that quantify outbreak size and timing under uncertainty. Numerous studies have introduced different stochastic models and associated epidemic descriptors, providing explicit formulas and algorithms that enable their estimation. Most of the studies consider constant epidemic dynamics, which limit the accuracy and the possibility of providing online estimates. In this paper, we introduce a SPIR (Susceptible, Presymptomatic, Infectious, Removed) model based on a 3-dimensional Markov chain. In the framework of this model, stochastic descriptors are introduced including the total number of infections, the occurrence time of a specific number of deaths and the number of infections generated from an index presymptomatic or an infectious case. The paper then integrates an augmented state-space formulation with particle filtering to estimate time-varying epidemiological parameters from surveillance data. Using mpox data from Ghana (2022), the time-varying approach improves predictive accuracy compared with a standard constant parameter method. The root mean squared error (RMSE) decreases from 12.497 to 5.480 for the expected total infections until extinction and from 2.082 to 1.588 for the expected time to the first death. In summary, incorporating time-varying parameter estimates through the filtering process enhances the precision of descriptors, allowing for more realistic epidemic scenarios. Overall, incorporating dynamically updated parameters improves the precision of stochastic descriptor estimation and supports data-driven online assessment of emerging outbreaks.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116770"},"PeriodicalIF":4.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guideway assembly accuracy is the key factor affecting the geometric accuracy of the movement axis of high-precision CNC machine tools. However, the current guideway assembly method relies on repetitive assembly, measurement, and repair. This results in a cumbersome process that lacks both efficiency and precision. To fill this research gap, this study proposes a prediction and optimization method of guideway assembly error based on the elastic interaction effect. The study constructs a multi-parameter optimization model of the guideway base surface by establishing its profile equation. The optimal datum surface is determined using a genetic algorithm. Based on this, a new guideway assembly process is presented. The assembly datum optimization method is then verified with the guideway-bed assembly platform as an example. The experimental results show that the mean value of the assembly error is reduced by 68%, and the maximum value is reduced by 76%. At the same time, the assembly efficiency is also improved.
{"title":"Error analysis model and optimization method for guideway assembly based on elastic interaction effects","authors":"Zhuangzhu Guo , Qiang Cheng , Hongyi Zhang , Peng Niu , Caixia Zhang , Zhifeng Liu","doi":"10.1016/j.apm.2026.116774","DOIUrl":"10.1016/j.apm.2026.116774","url":null,"abstract":"<div><div>Guideway assembly accuracy is the key factor affecting the geometric accuracy of the movement axis of high-precision CNC machine tools. However, the current guideway assembly method relies on repetitive assembly, measurement, and repair. This results in a cumbersome process that lacks both efficiency and precision. To fill this research gap, this study proposes a prediction and optimization method of guideway assembly error based on the elastic interaction effect. The study constructs a multi-parameter optimization model of the guideway base surface by establishing its profile equation. The optimal datum surface is determined using a genetic algorithm. Based on this, a new guideway assembly process is presented. The assembly datum optimization method is then verified with the guideway-bed assembly platform as an example. The experimental results show that the mean value of the assembly error is reduced by 68%, and the maximum value is reduced by 76%. At the same time, the assembly efficiency is also improved.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116774"},"PeriodicalIF":4.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.1016/j.apm.2026.116768
Han Du , Cheng Gao , Xiaodong Xia , George J. Weng
Carbon nanotube (CNT)-based nanocomposites exhibit exceptional electrical tunability under external electric fields, while the dynamics of field-driven CNT alignment and its impact on transverse isotropy of the overall composite remain underexplored. This study establishes a unified micro-mesoscale framework to decode the electro-structural evolution of CNT-polymer composites. We integrate an overdamped rotational kinetics model for CNT reorientation with an effective-medium homogenization scheme, incorporating interfacial electron tunneling, electron hopping, and dielectric relaxation. Our theory quantifies how electric field parameters (strength, frequency, and duration) govern CNT alignment-characterized by a maximum distribution angle-and subsequently modulate the composite’s effective electrical conductivity and dielectric permittivity. Validated against three independent experiments, this work provides insights into the alignment dynamics of CNTs, the evolution of percolation thresholds, and the field-tuned electrical behaviors of composites. The modeling and theory are crucial for the design and optimization of CNT nanocomposites for flexible electronics, energy storage, and field-responsive smart materials.
{"title":"Field-tuned CNT alignment and frequency dependence of electrical properties of CNT based nanocomposites","authors":"Han Du , Cheng Gao , Xiaodong Xia , George J. Weng","doi":"10.1016/j.apm.2026.116768","DOIUrl":"10.1016/j.apm.2026.116768","url":null,"abstract":"<div><div>Carbon nanotube (CNT)-based nanocomposites exhibit exceptional electrical tunability under external electric fields, while the dynamics of field-driven CNT alignment and its impact on transverse isotropy of the overall composite remain underexplored. This study establishes a unified micro-mesoscale framework to decode the electro-structural evolution of CNT-polymer composites. We integrate an overdamped rotational kinetics model for CNT reorientation with an effective-medium homogenization scheme, incorporating interfacial electron tunneling, electron hopping, and dielectric relaxation. Our theory quantifies how electric field parameters (strength, frequency, and duration) govern CNT alignment-characterized by a maximum distribution angle-and subsequently modulate the composite’s effective electrical conductivity and dielectric permittivity. Validated against three independent experiments, this work provides insights into the alignment dynamics of CNTs, the evolution of percolation thresholds, and the field-tuned electrical behaviors of composites. The modeling and theory are crucial for the design and optimization of CNT nanocomposites for flexible electronics, energy storage, and field-responsive smart materials.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116768"},"PeriodicalIF":4.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.apm.2026.116744
Pengpeng He , Yintang Wen , Xi Liang , Xiaoli Du , Yankai Feng , Yue Di , Yuyan Zhang
Micro-/nanolattice under service conditions exhibit pronounced size effects and time-dependent behavior; however, existing analytical models struggle to provide a unified description of the coupling mechanisms among these effects and unit-cell parameters, which severely limits the application of micro-/nanolattice in advanced devices. This study proposes a unified and extensible analytical modeling framework to systematically elucidate the coupled influences of size effects, viscoelasticity, geometric features, and substrate parameters on the macroscopic response of micro-/nanolattice. To achieve this, the modified couple stress theory is rigorously coupled with the Kelvin–Voigt viscoelastic model within the framework of Hamilton’s principle. For the first time, closed-form analytical solutions are derived for the time-dependent macroscopic response of body-centered cubic (BCC) lattice unit cells under quasi-static loading, while explicitly incorporating geometric deformation and boundary constraints. The proposed model is then validated against experimental data obtained from additively manufactured lattice specimens, demonstrating good applicability and reliability. The results reveal a clear time-scale dominant mechanism. At the early stage of loading, size effects dominate the mechanical response: curvature-related couple stress terms significantly enhance the global initial stiffness and induce strong nonlinear modulation of the unit cell Poisson’s ratio, whereas viscous effects remain secondary. As the loading time increases, microstructural energy dissipation progressively accumulates, leading to a continuous strengthening of viscous effects, which act synergistically with size effects and ultimately govern the long-term response evolution of the unit cell. Meanwhile, the regulation mechanisms related to unit-cell parameters and size effects are systematically clarified. Notably, under strong size effects and high relative density, the unit cell response may even exhibit auxetic behavior. By overcoming the limitations of numerical approaches in resolving multi-parameter coupling mechanisms in micro-/nanolattice, the analytical framework proposed in this study provides a robust theoretical foundation for multiscale analysis, response prediction, and design optimization of micro-/nanolattice, offering valuable guidance for the development of advanced micro-/nanolattice devices and architected metamaterials.
{"title":"Analytical modeling of the coupled viscoelastic and microstructure-dependent behaviors in micro-/nanolattices","authors":"Pengpeng He , Yintang Wen , Xi Liang , Xiaoli Du , Yankai Feng , Yue Di , Yuyan Zhang","doi":"10.1016/j.apm.2026.116744","DOIUrl":"10.1016/j.apm.2026.116744","url":null,"abstract":"<div><div>Micro-/nanolattice under service conditions exhibit pronounced size effects and time-dependent behavior; however, existing analytical models struggle to provide a unified description of the coupling mechanisms among these effects and unit-cell parameters, which severely limits the application of micro-/nanolattice in advanced devices. This study proposes a unified and extensible analytical modeling framework to systematically elucidate the coupled influences of size effects, viscoelasticity, geometric features, and substrate parameters on the macroscopic response of micro-/nanolattice. To achieve this, the modified couple stress theory is rigorously coupled with the Kelvin–Voigt viscoelastic model within the framework of Hamilton’s principle. For the first time, closed-form analytical solutions are derived for the time-dependent macroscopic response of body-centered cubic (BCC) lattice unit cells under quasi-static loading, while explicitly incorporating geometric deformation and boundary constraints. The proposed model is then validated against experimental data obtained from additively manufactured lattice specimens, demonstrating good applicability and reliability. The results reveal a clear time-scale dominant mechanism. At the early stage of loading, size effects dominate the mechanical response: curvature-related couple stress terms significantly enhance the global initial stiffness and induce strong nonlinear modulation of the unit cell Poisson’s ratio, whereas viscous effects remain secondary. As the loading time increases, microstructural energy dissipation progressively accumulates, leading to a continuous strengthening of viscous effects, which act synergistically with size effects and ultimately govern the long-term response evolution of the unit cell. Meanwhile, the regulation mechanisms related to unit-cell parameters and size effects are systematically clarified. Notably, under strong size effects and high relative density, the unit cell response may even exhibit auxetic behavior. By overcoming the limitations of numerical approaches in resolving multi-parameter coupling mechanisms in micro-/nanolattice, the analytical framework proposed in this study provides a robust theoretical foundation for multiscale analysis, response prediction, and design optimization of micro-/nanolattice, offering valuable guidance for the development of advanced micro-/nanolattice devices and architected metamaterials.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116744"},"PeriodicalIF":4.4,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.apm.2026.116765
Nannan Zhao , Jiacheng Luo , Su Qin , Zhushan Shao , Kui Wu
The application of circumferential yielding lining proposes a good solution to the problem of overstress and failure of preliminary support in squeezing large deformation tunnels. Establishing a practical theoretical model to predict the mechanical response of tunnels using circumferential yielding lining can provide meaningful guidance for the initial design of support. This study suggests that the surrounding rock exhibits viscoelastic-plastic behaviour, and also shows plastic softening and residual characteristics after reaching a plastic state; the deformation process of circumferential yielding lining is divided into elastic, yielding and compaction stages, according to the mechanical properties of special elements. A simplified two-dimensional mechanical model is established to capture the interaction between the surrounding rock and circumferential yielding lining, taking into account the effects of tunnel face advancement and stress path. Based on the engineering reality (stress state of the surrounding rock at the time of lining installation), the interaction between the surrounding rock and lining is discussed in various cases; corresponding analytical solutions for the tunnel displacement and support pressure are proposed for each case. Furthermore, a numerical simulation is conducted using an actual tunnel, and a comprehensive comparison is performed between the theoretical prediction results, numerical simulation data, and monitored tunnel displacement. Finally, parametric sensitivity analysis is completed based on the proposed theoretical model, and the impacts of geological parameters and support parameters are discussed. By using this theoretical model, the design rationality of the circumferential yielding lining can be quickly evaluated and some design recommendations can be easily obtained.
{"title":"Mathematical analytical model for interaction between tunnel viscoelastic-plastic surrounding rock and circumferential yielding lining considering stress path effect","authors":"Nannan Zhao , Jiacheng Luo , Su Qin , Zhushan Shao , Kui Wu","doi":"10.1016/j.apm.2026.116765","DOIUrl":"10.1016/j.apm.2026.116765","url":null,"abstract":"<div><div>The application of circumferential yielding lining proposes a good solution to the problem of overstress and failure of preliminary support in squeezing large deformation tunnels. Establishing a practical theoretical model to predict the mechanical response of tunnels using circumferential yielding lining can provide meaningful guidance for the initial design of support. This study suggests that the surrounding rock exhibits viscoelastic-plastic behaviour, and also shows plastic softening and residual characteristics after reaching a plastic state; the deformation process of circumferential yielding lining is divided into elastic, yielding and compaction stages, according to the mechanical properties of special elements. A simplified two-dimensional mechanical model is established to capture the interaction between the surrounding rock and circumferential yielding lining, taking into account the effects of tunnel face advancement and stress path. Based on the engineering reality (stress state of the surrounding rock at the time of lining installation), the interaction between the surrounding rock and lining is discussed in various cases; corresponding analytical solutions for the tunnel displacement and support pressure are proposed for each case. Furthermore, a numerical simulation is conducted using an actual tunnel, and a comprehensive comparison is performed between the theoretical prediction results, numerical simulation data, and monitored tunnel displacement. Finally, parametric sensitivity analysis is completed based on the proposed theoretical model, and the impacts of geological parameters and support parameters are discussed. By using this theoretical model, the design rationality of the circumferential yielding lining can be quickly evaluated and some design recommendations can be easily obtained.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116765"},"PeriodicalIF":4.4,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.apm.2026.116764
Feng Li , Wei Zhang , Shaoqian Li , Sheng Gao , YiFei Han , Zhong Li
The recursive Newton-Euler algorithm is a method for implicitly formulating system dynamics models. This paper focuses on space robots, overcoming the limitations inherent in conventional recursive frameworks to derive an explicit matrix mapping formulation. Additionally, the matrix construction process is enhanced through Neumann series expansion and sparse matrix techniques. This approach effectively circumvents the surge in memory consumption that would otherwise arise from abandoning the recursive framework. Profile data on computation time and memory usage were collected through the modelling of a space robot system equipped with a six degree-of-freedom manipulator on the MATLAB platform. The modelling utilized both the recursive Newton-Euler algorithm and the proposed global closed-form matrix dynamics formulation. Experimental results indicate that the model errors across all time points of the output components remain at the order of, with maximum errors not exceeding. Regarding computational efficiency, the proposed formulation exhibits lower complexity than the recursive Newton-Euler algorithm when the manipulator's degrees of freedom exceed 7. This paper further derives closed-form expressions for the time derivative of the inertia submatrix and its partial derivatives with respect to joint angles, thereby underscoring the broader research potential of the proposed formulation. These findings establish a foundation for integrating geometric properties into future dynamics formulations.
{"title":"A global closed-form matrix reconstruction approach for recursive dynamics of space robots within the lie algebra framework","authors":"Feng Li , Wei Zhang , Shaoqian Li , Sheng Gao , YiFei Han , Zhong Li","doi":"10.1016/j.apm.2026.116764","DOIUrl":"10.1016/j.apm.2026.116764","url":null,"abstract":"<div><div>The recursive Newton-Euler algorithm is a method for implicitly formulating system dynamics models. This paper focuses on space robots, overcoming the limitations inherent in conventional recursive frameworks to derive an explicit matrix mapping formulation. Additionally, the matrix construction process is enhanced through Neumann series expansion and sparse matrix techniques. This approach effectively circumvents the surge in memory consumption that would otherwise arise from abandoning the recursive framework. Profile data on computation time and memory usage were collected through the modelling of a space robot system equipped with a six degree-of-freedom manipulator on the MATLAB platform. The modelling utilized both the recursive Newton-Euler algorithm and the proposed global closed-form matrix dynamics formulation. Experimental results indicate that the model errors across all time points of the output components remain at the order of<span><math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>15</mn></mrow></msup></math></span>, with maximum errors not exceeding<span><math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>14.5</mn></mrow></msup></math></span>. Regarding computational efficiency, the proposed formulation exhibits lower complexity than the recursive Newton-Euler algorithm when the manipulator's degrees of freedom exceed 7. This paper further derives closed-form expressions for the time derivative of the inertia submatrix and its partial derivatives with respect to joint angles, thereby underscoring the broader research potential of the proposed formulation. These findings establish a foundation for integrating geometric properties into future dynamics formulations.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116764"},"PeriodicalIF":4.4,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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