Applied Mathematical Modelling最新文献

{"title":"Vibration analysis of non-homogenous single-link flexible manipulator in uncertain environment","authors":"Priya Rao ,&nbsp;Dhabaleswar Mohapatra ,&nbsp;S. Chakraverty ,&nbsp;Debanik Roy","doi":"10.1016/j.apm.2025.115939","DOIUrl":"10.1016/j.apm.2025.115939","url":null,"abstract":"<div><div>This paper presents a novel dynamic model of a dual-cable-strapped single-link flexible manipulator under an uncertain workspace. The material of the link of the manipulator is considered to be non-homogeneous with inherent non-linearity, which is crucial in modelling. In this regard, linear and quadratic variations in the density of the material of the flexible link with space coordinates are considered. Uncertainty is introduced into its parameters in order to make the real-time dynamics of the flexible manipulator more challenging. Fuzzy parameters, in support of uncertainty, are invoked in the spring constants of the cables for modelling using Triangular Fuzzy Numbers (TFN). In particular, Interval Type-2 Triangular Fuzzy Numbers (IT2TFN) are considered in this investigation since higher-order fuzzy numbers can be beneficial, as the presence of uncertainty in the membership grade may also be unavoidable. The non-homogeneous flexible link is modelled as an Euler-Bernoulli beam, and the non-linear equations of motion are derived using Hamilton's principle and two boundary conditions. It may be difficult to obtain the exact solution of the governing differential equation because of the non-homogeneity in the parameters associated with the link. In this regard, the Adomian Decomposition Method (ADM) is implemented in the crisp as well as uncertain scenario to determine the natural frequencies of the single-link flexible manipulator. The existence and uniqueness of the solution is also illustrated. Tabular and graphical results are presented for validation and better visualisation.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115939"},"PeriodicalIF":4.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178389","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}

{"title":"Data-driven modeling for rapid prediction of aerodynamic noise directivity of flow over a cylinder","authors":"Yao Jin ,&nbsp;Fei Liao ,&nbsp;Jinsheng Cai","doi":"10.1016/j.apm.2025.115937","DOIUrl":"10.1016/j.apm.2025.115937","url":null,"abstract":"<div><div>Conventional high-fidelity simulations are prohibitively expensive for aerodynamic noise optimization and control applications. Developing surrogate models of minimal computational costs provide efficient alternatives in noise estimation for various numerical conditions. In the present work, three data-driven acoustic directivity modeling strategies are proposed, including a purely data-driven POD model and two semi-analytical data-driven models: force-model and dipole-model. All the three models significantly accelerate the prediction of noise directivity, which is attributed to their independence of conventional numerical approaches, despite with minor discrepancies in accuracy among each other. The POD-model is constructed based on the singular vector decomposition and an interpolation method, enabling high accuracy but requiring a large amount of training data. A sensitivity study is conducted on four parametric aspects, such as mode number, interpolation method, inherent flow nonlinearity in wake region, and the distribution of interpolation states in training datasets. The force-model, derived from the Ffowcs Williams-Hawkings equation, requires force fluctuations on the body surfaces. Also the dipole-model, leveraging the analytical formulation of dipole velocity potential, requires a careful specification of potential coefficient. These required information in force-model and dipole-model are directly approximated by data regression methods. Compared to POD-model, the notable merit of force-model and dipole-model is that rapid predictions can be implemented with reduced data requirements.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115937"},"PeriodicalIF":4.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989196","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}

{"title":"Phase-field simulation for the mechanical and fracture properties of NdFeB under quasi-static loading conditions","authors":"Xinyu Zheng,&nbsp;Liqun Wang,&nbsp;Guolai Yang,&nbsp;Jianli Ge","doi":"10.1016/j.apm.2025.115944","DOIUrl":"10.1016/j.apm.2025.115944","url":null,"abstract":"<div><div>NdFeB has been widely used in various fields due to its excellent magnetic properties. However, as a brittle material, its mechanical properties limit its application, and research into these properties remains inadequate. This study employs the phase field method to investigate the mechanical response and fracture mechanism of NdFeB. The phase field method, a numerical approach that has garnered significant attention in recent years, is a highly effective crack regularization variational method for simulating crack initiation and propagation. A phase field model for the fracture surface of NdFeB was established, with the software implementation method provided. The accuracy of the model was validated through comparisons with several typical experimental results. Finally, an analysis was conducted on the impact of structural dimensions, positional tolerances, and pre-existing cracks on the mechanical properties of NdFeB specimens, with a detailed examination of the crack propagation process.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115944"},"PeriodicalIF":4.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178388","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}

{"title":"Mathematical modelling for large-aperture mirror systems: enabling optical-mechanical performance analysis and support structure optimization","authors":"Pengwei Liang ,&nbsp;Xueguan Song ,&nbsp;Yong Xiang ,&nbsp;Zhaoyang Li ,&nbsp;Tao Zhang ,&nbsp;Junwei Zhang","doi":"10.1016/j.apm.2025.115938","DOIUrl":"10.1016/j.apm.2025.115938","url":null,"abstract":"<div><div>Large-aperture mirror systems (LAMS) are widely used in fields such as electro-optical countermeasures, spaceborne remote sensing, and laser communication. Accurate modeling and analysis of LAMS are crucial for its design and optimization. To transition from one-off simulation models to a generalized theoretical mathematical model, this paper presents a theoretical modeling method that combines the Reciprocal Theorem of Work and the Perturbation Method. First, based on the Kirchhoff plate theory, a variable-coefficient deflection governing equations for LAMS is derived. Then, using the principles of the Perturbation Method, an analytical solution for the governing equations within the framework of the Reciprocal Theorem of Work is obtained. Additionally, the proposed governing equations are validated for convergence, and it is found that the solution converges when <em>m</em> ≥ 3. By comparing with FEM results, the accuracy of the proposed model is confirmed, with the root mean square error (RMSE) below 9.918 × 10^-4 and R² exceeding 0.875. Furthermore, the influence of higher-order perturbation terms and computational efficiency are analyzed. The results show that the first-order perturbation solution satisfies the accuracy requirements, and the proposed method offers significant computational efficiency advantages over FEM. Finally, for a specific LAMS model, the proposed governing equations are applied to optimize its support scheme. The results indicate that, for 9 support points, the optimal radius of the inner supports is 0.267<em>a</em>, while the outer supports have an optimal radius of 0.775<em>a</em>. For 18 support points, the optimal radius of the inner supports is 0.343<em>a</em>, with the outer supports having an optimal radius of 0.811<em>a</em>. Overall, the proposed method establishes a theoretical foundation for designing and optimizing the support structures of LAMS, significantly facilitating engineers in optimizing its optomechanical performance.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115938"},"PeriodicalIF":4.4,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989198","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}

{"title":"Random walk models of advection-diffusion in layered media","authors":"Elliot J. Carr","doi":"10.1016/j.apm.2025.115942","DOIUrl":"10.1016/j.apm.2025.115942","url":null,"abstract":"<div><div>Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such transport processes are well established, they fail to account for randomness inherent in many problems and are valid only for a large number of particles. To address this, this paper derives a suite of equivalent random walk (discrete-time discrete-space) models for several standard continuum (partial differential equation) models of diffusion and advection-diffusion across a fully- or semi-permeable interface. Our approach involves discretising the continuum model in space and time to yield a Markov chain, which governs the transition probabilities between spatial lattice sites during each time step. Discretisation in space is carried out using a standard finite volume method while two options are considered for discretisation in time. A simple forward Euler discretisation yields a local (nearest-neighbour) random walk with simple analytical expressions for the transition probabilities while an exact exponential discretisation yields a non-local random walk with transition probabilities defined numerically via a matrix exponential. Constraints on the size of the spatial and/or temporal steps are provided for each option to ensure the transition probabilities are in <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. MATLAB code comparing the random walk and continuum models is available on GitHub (<span><span>https://github.com/elliotcarr/Carr2024c</span><svg><path></path></svg></span>) with simulation results demonstrating good agreement for several example problems.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115942"},"PeriodicalIF":4.4,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling of CNT alignment state on the strain sensing characteristics of MWCNT-based nanocomposites","authors":"Xiaodong Xia ,&nbsp;Junhua Xiao ,&nbsp;Weidong Yang ,&nbsp;George J. Weng","doi":"10.1016/j.apm.2025.115946","DOIUrl":"10.1016/j.apm.2025.115946","url":null,"abstract":"<div><div>The strain sensing characteristics of MWCNT-based nanocomposite sensors are highly dependent on the orientation and distribution of CNTs. Most CNT sensors are neither perfectly aligned nor randomly oriented; they are just the two limiting state of partially aligned sensors. To cover this wider distribution, an anisotropic homogenization model is established to study the axial and transverse multi-field coupled performances of MWCNT-based nanocomposite strain sensors from perfectly aligned to randomly oriented state. The transversely isotropic conductivity and mechanical moduli are utilized as the dual homogenization parameters in the present anisotropic analysis. The effective mechanical moduli are evaluated via the Mori-Tanaka method, while the electrical conductivities are calculated by the effective-medium approximation. The loading-dependent tunneling distance among the partially aligned MWCNTs is established under the axial or transverse loading to assess the contribution of electron tunneling. The predicted axial and transverse strain sensing capacities, including the resistance change ratios and strain sensitivity factors, of partially aligned MWCNT-based nanocomposite sensors are demonstrated and shown to agree with experiments. The axial sensing characteristics of a partially aligned strain sensor is higher than that of a randomly oriented one due to the alignment of MWCNTs. The optimal MWCNT volume fraction of high strain sensing characteristics is determined to be near the percolation threshold. The revealed anisotropic electromechanically coupled behaviors can provide guidance to tailor the axial and transverse sensing characteristics for the general class of partially aligned nanocomposite strain sensors.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115946"},"PeriodicalIF":4.4,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multivariate grey prediction model with fractional time-lag parameter and its application","authors":"Bo Zeng,&nbsp;Yibo Tuo","doi":"10.1016/j.apm.2025.115940","DOIUrl":"10.1016/j.apm.2025.115940","url":null,"abstract":"<div><div>The time-lag parameter captures the asynchronous relationship between dependent and independent variables. However, traditional time-lag parameters have two limitations: they are restricted to positive integers, and their identification relies on subjective methods, reducing model adaptability and performance. To address these issues, a new multivariate grey prediction model, NSGM(1,N,<em>τ</em>), is proposed. Built upon the classic NSGM(1,N) framework, the proposed model incorporates the cubic spline interpolation method to extend the time-lag parameter from positive integers to fractions, effectively eliminating the aforementioned limitations. Applied to simulate and predict Jiangsu Province's port cargo throughput (PCT), the NSGM(1,N,<em>τ</em>) model achieved a mean absolute percentage error (MAPE) of just 0.7382 %, outperforming two similar models with MAPEs of 7.5897 <em>%</em> and 1.3097 %. This advancement enhances the predictive capabilities of the multivariate grey prediction model and offers a robust method for forecasting PCT with high precision.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115940"},"PeriodicalIF":4.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179382","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}

{"title":"A thermodynamic constitutive model based on uncoupled physical mechanisms for polymer-based shape memory composites and its application in 4D printing","authors":"Hao Duan ,&nbsp;Jianping Gu ,&nbsp;Huiyu Sun ,&nbsp;Hao Zeng ,&nbsp;Jesus A. Rodriguez-Morales","doi":"10.1016/j.apm.2025.115926","DOIUrl":"10.1016/j.apm.2025.115926","url":null,"abstract":"<div><div>Four-dimensional (4D) printing is a new interdisciplinary research field that integrates sophisticated manufacturing, smart materials and mechanics. Shape memory polymer (SMP) and their composites (SMPCs) have been widely used in the field of 4D printing due to their smart and rapid response. Thus, we develop a novel thermodynamic constitutive model for SMP and SMPC, and investigate its application in 4D printing. Structure relaxation and stress relaxation are considered to follow different physical mechanisms but are related by an internal thermodynamic state variable that can represent the non-equilibrium structure. Founded on the thermodynamic variable, a physics-based fictive temperature theory is constructed for structure relaxation, and also a new stress relaxation model is proposed to characterize the time-dependent behaviors related to mechanical changes. It is shown that the influences of temperatures, strain rates, pre-strains, reinforcing fillers, and recovery conditions on stress-strain and shape memory responses are well predicted by the thermodynamic constitutive model.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115926"},"PeriodicalIF":4.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989199","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}

{"title":"Innovative data-driven algorithm for defect parameter identification in large-scale structures","authors":"Shouyan Jiang ,&nbsp;Wangtao Deng ,&nbsp;Peng Zhang ,&nbsp;Guofu Hu ,&nbsp;Chengbin Du","doi":"10.1016/j.apm.2025.115935","DOIUrl":"10.1016/j.apm.2025.115935","url":null,"abstract":"<div><div>This study proposes an innovative data-driven algorithm that combines the scaled boundary finite element method with an autoencoder and a causal dilated convolutional neural network for defect identification in large-scale structures. The scaled boundary finite element method simulates the propagation of waves in large-scale structures containing various types of defects. Conveniently, the scaled boundary finite element method can simulate different types of defects within structures and, by discretizing only the boundaries of structures, efficiently generate sufficient training data. To simulate wave propagation in large-scale structures, an absorbing boundary model based on Rayleigh damping is established, avoiding computations across the entire structural domain. The affinity propagation clustering algorithm is employed to optimize the number and layout of sensors, and the optimized multi-sensor data serve as the original training samples for autoencoder feature extraction. Autoencoder exhibits strong nonlinear feature extraction capabilities, mapping the high-dimensional original input feature vector space to a low-dimensional latent feature vector space to obtain low-dimensional latent features for network model training. This effectively improves the learning efficiency of the network model. The constructed causal dilated convolutional neural network model ensures orderliness of temporal data and achieves a larger receptive field without increasing neural network complexity, thereby capturing more historical information. Numerical examples demonstrate that the proposed model can accurately identify the quantified information of defects in large-scale structures. Compared with the previous model, the proposed model exhibits improved robustness.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115935"},"PeriodicalIF":4.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989200","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}

{"title":"Pharmaceutical logistics network planning considering low-carbon policy and demand uncertainty","authors":"Hao Zou,&nbsp;Jiehui Jiang","doi":"10.1016/j.apm.2025.115933","DOIUrl":"10.1016/j.apm.2025.115933","url":null,"abstract":"<div><div>Reducing carbon emissions has become a critical priority in the global effort to combat climate change. This study examined a pharmaceutical logistics network planning problem under drug demand uncertainty within the framework of a carbon cap-and-trade policy. An ambiguity set for medical demand is constructed using historical pharmaceutical order data to account for uncertainty. The problem is then formulated as a two-stage distributionally robust optimization model, with the first stage addressing facility location decisions and the second stage focusing on transportation strategies. A decomposition-based method was developed to solve this model by leveraging the structure of the proposed formulation. Numerical experiments demonstrated the practicality and effectiveness of the proposed models and solution approach. The results show that redesigning the logistics network and leveraging rail transit can achieve reductions of 14.71 % in total costs and 40.75 % in carbon emissions compared to the current case. The analysis also revealed that logistics network configurations and transportation strategies are highly sensitive to carbon pricing. Therefore, governments should enhance carbon emission oversight and stabilize carbon market prices to ensure the effective implementation of carbon cap-and-trade policies.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115933"},"PeriodicalIF":4.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989201","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}