Applied Mathematical Modelling最新文献

{"title":"On the non-classical transfer matrix method for free vibration behaviour of multi-rigid-elastic unit microsystem","authors":"Guangyang Fu ,&nbsp;Kaikai Jin ,&nbsp;Wenjian Song ,&nbsp;Shenjie Zhou ,&nbsp;Hongyu Zheng","doi":"10.1016/j.apm.2025.116407","DOIUrl":"10.1016/j.apm.2025.116407","url":null,"abstract":"<div><div>The free vibration behaviour of multi-rigid-elastic unit microsystem is crucial for microminiaturization design. Classical transfer matrix method (CTMM) without material length-scale parameters fails to explain size-dependent free vibration response. In this paper, we revisit the theoretical framework for size effects, construct state vector, transfer matrix, transfer equation with material length-scale parameters, and develop isotropic non-classical transfer matrix method (NCTMM). Then, we derive the non-classical transfer matrix of typical microcomponent. The transfer matrix of torsion vibrating strain gradient microbar and transverse vibrating flexoelectric/flexomagnetic-elastic bilayer microbeam are developed based on the general flexomagnetic elasticity (GFME), respectively. Subsequently, we establish system transfer equation of multi-rigid-elastic unit chain microsystem. The microsystem free vibration problem is solved. It is found that the natural frequency of non-classical model increases gradually with decrease of the ratio of characteristic size and material length-scale parameter. When the ratio increases, the natural frequency of non-classical model is close to that of classical model. Moreover, the contribution from strain gradient elasticity, material length-scale parameter and slant edge crack type to electric/magnetic mode shape is further clarified. Compared with classical transfer matrix method (CTMM), the non-classical transfer matrix method (NCTMM) can perform system-level multi-body microscale analysis more appropriately.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"151 ","pages":"Article 116407"},"PeriodicalIF":4.4,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050726","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":"An adaptive policy iteration learning algorithm for optimal tracking control of nonlinear systems with state inequality constraints","authors":"Yuqi Zhang ,&nbsp;Bin Zhang ,&nbsp;Lutao Yan ,&nbsp;Lipo Mo ,&nbsp;Yingmin Jia","doi":"10.1016/j.apm.2025.116408","DOIUrl":"10.1016/j.apm.2025.116408","url":null,"abstract":"<div><div>This paper proposes a novel policy iteration algorithm to solve the optimal tracking control problem with state inequality constraints. The algorithm aims to optimize the cost function for general nonlinear systems over a specified time horizon. Firstly, the dynamics of the time-varying error system is transformed into an augmented system, thereby facilitating the learning of the system model. Subsequently, concurrent learning is employed to estimate the parameters of the augmented system via instantaneous and historical data. The adaptive policy iteration algorithm is then developed to learn the optimal control strategy. Convergence analysis shows that the algorithm effectively reduces the system's actual tracking cost. Finally, simulations have been conducted to validate the effectiveness of the proposed algorithm.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"151 ","pages":"Article 116408"},"PeriodicalIF":4.4,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050294","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":"Constraint-following vibration control for robot follow-up support system under force-stiffness interdependence","authors":"Zhao Liu ,&nbsp;Fangfang Dong ,&nbsp;Xiaomin Zhao ,&nbsp;Jiang Han ,&nbsp;Ye-Hwa Chen","doi":"10.1016/j.apm.2025.116415","DOIUrl":"10.1016/j.apm.2025.116415","url":null,"abstract":"<div><div>The robot follow-up support system provides a cost-effective and flexible support solution for machining thin-walled workpieces. In the past, however, the control design had been a challenge, mainly due to the difficulty in coping with the complex coupling and time-varying dynamic characteristics of the follow-up support system. This study proposes a novel heterogeneous hybrid stiffness model in a “parallel-serial-parallel” structure, along with a constraint-following control method for vibration suppression. First, a second-order vibration model of the follow-up support system was developed, capturing the primary stiffness characteristics of the system while simplifying the modeling through mass bundling. Second, time-varying stiffness analytical expressions are established for the main stiffness components, including the local workpiece region, gas springs at support modules, and the normal stiffness of the robot end-effector, facilitating real-time substitution in the control process. Third, the controllable air pressure term was separated from both sides of the vibration equation, yielding an equivalent underactuated system, and a constraint-following control algorithm was designed. The simulations demonstrate that the proposed control algorithm meets the servo requirements with high precision.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"150 ","pages":"Article 116415"},"PeriodicalIF":4.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019234","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":"An efficient iterative method to find the Moore-Penrose inverse of tensors: Applications in image processing and data mining","authors":"Raziyeh Erfanifar,&nbsp;Masoud Hajarian","doi":"10.1016/j.apm.2025.116426","DOIUrl":"10.1016/j.apm.2025.116426","url":null,"abstract":"<div><div>Matrices and tensors serve as fundamental tools in mathematical modelling, enabling applications such as linear transformations, systems of equations, and multivariate data analysis. This work introduces a computational framework for determining the Moore-Penrose (MP) inverse of tensors using the Einstein product (EP), along with a detailed theoretical analysis. The proposed method builds on an iterative method designed for solving nonlinear equations. Numerical comparisons with existing methods demonstrate that the proposed method requires fewer iterations, performs fewer EPs, and consumes significantly less CPU time. To highlight practical applications, we consider partial and fractional differential equations, particularly those resulting in sparse matrices, as representative cases. The iterates generated by the proposed method are utilized as pre-conditioners in tensor form to solve multilinear systems of the form:<span><span><span><math><mrow><mi>B</mi><mo>*</mo><mi>X</mi><mo>=</mo><mi>C</mi><mo>.</mo></mrow></math></span></span></span>Finally, we present various practical numerical examples to demonstrate the efficiency and accuracy of the proposed method. The results highlight the robustness and effectiveness of the method in computing the MP inverse of tensors. This method provides significant computational advantages and proves highly applicable across diverse domains, including mathematics, physics, image processing, and data mining.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"151 ","pages":"Article 116426"},"PeriodicalIF":4.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050293","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":"Design and analysis of a spherical wheel-legged hybrid robot with leg adjustment modules for enhanced locomotion performance","authors":"Li Liu ,&nbsp;Youhao Ke ,&nbsp;Yao Huang ,&nbsp;Jun Cao ,&nbsp;Junqiang Lou ,&nbsp;Luhai Ye","doi":"10.1016/j.apm.2025.116424","DOIUrl":"10.1016/j.apm.2025.116424","url":null,"abstract":"<div><div>The motion performance of spherical wheel-legged hybrid robots in quadruped mode is constrained by their spherical shell structure, resulting in limited strides. This paper proposes a novel spherical wheel-legged hybrid robot equipped with leg adjustment modules, drawing inspiration from the motion mechanism of spinal joints in reptiles. These modules facilitate the movement of the leg modules through gear mechanisms, enabling them to function as eccentric pendulums in spherical mode and to replicate the function of spinal joints in quadruped mode. A kinematic analysis of the leg mechanism was conducted using the vector method. Further analyses addressed the linear and turning motion characteristics of the quadruped mode, influenced by the leg adjustment module, leading to the planning of the corresponding gait. Simulations were performed in Adams, along with a series of analyses, to validate the accuracy of the theoretical model. A prototype was developed and tested for its mode conversion, linear motion, and turning performance. The experimental results demonstrate that the robot can smoothly switch between spherical and quadruped modes. In quadruped mode, its turning radius decreased significantly. With a spherical diameter of 300 mm, the stride length increases from 158mm to 201mm, and the linear speed rises by 27.2% as the initial adjustment angles increase from 0° to 19°. These improvements collectively enhance the locomotion performance of the robot, as intended.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"150 ","pages":"Article 116424"},"PeriodicalIF":4.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048419","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 spectral-fast Voronoi framework based on multivariate Karhunen–Loève expansion for simulation of two-dimensional random fields","authors":"Zeju Yin,&nbsp;Weidong Pan,&nbsp;Xin Zheng","doi":"10.1016/j.apm.2025.116422","DOIUrl":"10.1016/j.apm.2025.116422","url":null,"abstract":"<div><div>This study proposes a high-precision, high-efficiency, and widely applicable algorithm for simulating two-dimensional random fields, capable of handling irregular, non-stationary, multivariate-correlated, and spatiotemporally-correlated random fields, as well as random fields with Lagrangian displacement. The primary innovations of this study are as follows: (1) By employing triangular spectral element methods (TSEM) and the Fast Multipole Method (FMM), the proposed algorithm significantly enhances the accuracy and efficiency of traditional Karhunen–Loève expansion (KLE) for spatiotemporally correlated random fields. It improves the computation of multivariate cross-covariance integrals while avoiding the costly eigenvalue decomposition of the full spatiotemporal covariance matrix; (2) To enable simulations in irregular domains, a global backtracking algorithm is proposed to address singular edge mismatches arising from quasi-interpolation in TSEM, and a hybrid binary–quadtree partitioning strategy is introduced to prevent malformed or sparse elements in FMM tree decomposition; (3) By leveraging the linear transformation property of KLE, a low-bias sampling strategy is employed to extract pointwise occurrence probabilities within each simulated sample. The algorithm is validated through three representative cases: a non-stationary multivariate slope field, a spatiotemporally correlated atmospheric field, and a spatially random material property field for a NACA airfoil. The results confirm the accuracy, efficiency, and broad applicability of the proposed method in modeling complex random fields.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"150 ","pages":"Article 116422"},"PeriodicalIF":4.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048420","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":"Steady laminar fluid flow through spiral ducts based on circle involutes","authors":"Brendan Harding","doi":"10.1016/j.apm.2025.116414","DOIUrl":"10.1016/j.apm.2025.116414","url":null,"abstract":"<div><div>We revisit the analysis of steady laminar incompressible Newtonian fluid flow through (planar) spiral duct geometries. Spiral ducts are utilised in a number of fluid flow applications, largely due to their ability to incorporate a large flow distance into a relatively small volume. Archimedean spirals are an attractive design choice in many application areas, including microfluidic devices, due to the simplicity of their description and a constant spacing between turns. Herein we examine fluid flow through a spiral duct geometry based on the involute of a circle. These involute based spiral duct geometries retain some key features of Archimedean spirals while possessing several desirable design properties. Moreover, a curvilinear coordinate system constructed around an involute spiral naturally leads to a straightforward orthogonal coordinate system which facilitates a detailed analysis of fluid flow through the spiral duct geometry. We derive the Navier–Stokes equations using this coordinate system and analyse the fluid flow through the spiral duct geometries with a focus on making detailed comparisons with the flow through axis-symmetric curved ducts. Our analysis ultimately provides an efficient means for estimating spiral duct flow, a robust justification for the use of curved duct flow as an approximation for spiral duct flow in certain regimes and reveals some of the specific differences between the spiral and axis-symmetric curved ducts without being obfuscated by a curvature parameter perturbation. Our methodology is readily applied to study spiral duct of any cross-section shape, including the rectangular cross-sections which are common in a variety of applications.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"150 ","pages":"Article 116414"},"PeriodicalIF":4.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019235","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":"Self-triggering evolutionary optimal control of multi-modular robot manipulators","authors":"Hucheng Jiang,&nbsp;Tianjiao An,&nbsp;Bo Dong,&nbsp;Bing Ma,&nbsp;Yuanchun Li","doi":"10.1016/j.apm.2025.116427","DOIUrl":"10.1016/j.apm.2025.116427","url":null,"abstract":"<div><div>Leveraging the unique flexibility, modular robot manipulators are typically suitable for complex operational tasks in extreme environments, which frequently require the cooperative operation of multi-modular robot manipulator. Herein, the load distribution policy for the heterogeneous cooperative operation tasks of multi-modular robot manipulator is proposed in this article, which allocates appropriate wrenches to multi-modular robot manipulator to achieve the desired motion of the manipulated object. Subsequently, a novel self-triggering optimal control method via evolution computing is proposed to address the optimal regulation problems of multi-modular robot manipulator. The evolution computing algorithm can search for a superior policy during policy improvement when calculating gradient information becomes infeasible or system dynamic is not differentiable, overcoming the limitations of gradient-dependent adaptive dynamic programming. The proof of convergence for the evolution computing algorithm further enhances the rigorousness of the evolution computing-based self-triggering optimal control method. Additionally, to reduce communication bandwidth, energy consumption, and computational load, a self-triggering control scheme is introduced into the controller, and an appropriate self-triggering condition is designed, which solely utilizes the current state of the system to determine the next triggering moment for the modular robot manipulators. Compared with traditional event-triggering control, self-triggering control does not require dedicated hardware to monitor whether triggering rules are violated. Hence, the introduction of self-triggering control significantly broadens the application scenarios for modular robot manipulators. Ultimately, the modular robot manipulator system is proven to be uniformly ultimately bounded with the Lyapunov theory. The visualization data of experimental results verifies the superiority of the evolution computing-based self-triggering optimal control method.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"150 ","pages":"Article 116427"},"PeriodicalIF":4.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026302","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 second Piola-Kirchhoff stress-driven homogenization scheme for nonlinear elasticity","authors":"Sourav Kumar,&nbsp;Navin Kumar,&nbsp;Manish Agrawal","doi":"10.1016/j.apm.2025.116409","DOIUrl":"10.1016/j.apm.2025.116409","url":null,"abstract":"<div><div>This paper presents a novel stress-driven computational homogenization framework for imposing the second Piola-Kirchhoff (IIPK) stress tensor in the context of finite deformation. Unlike the commonly used first Piola-Kirchhoff stress (IPK), which is asymmetric and lacks frame and rotation invariance, the IIPK stress is frame-invariant and independent of rigid body rotations. In this study, we develop a variational framework integrated with finite element method to impose the IIPK stress on the representative volume element (RVE). For a prescribed IIPK stress tensor, the framework yields the corresponding equivalent Green-Lagrange strain tensor and the associated linearized elasticity tensor. The proposed formulation is analytically and numerically shown to satisfy the Hill-Mandel condition ensuring consistent micro-macro transitions. To facilitate the finite element implementation, an easy-to-implement linear constraint is derived to enforce the periodic boundary condition while eliminating rigid body modes and preventing the singularity of the global stiffness matrix. The effectiveness of this approach is validated through various numerical examples involving material and geometric nonlinearities, showcasing the framework’s robustness and accuracy.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"151 ","pages":"Article 116409"},"PeriodicalIF":4.4,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050305","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 port-Hamiltonian framework for the modeling and FEM discretization of hyperelastic systems","authors":"Cristobal Ponce ,&nbsp;Yongxin Wu ,&nbsp;Yann Le Gorrec ,&nbsp;Hector Ramirez","doi":"10.1016/j.apm.2025.116403","DOIUrl":"10.1016/j.apm.2025.116403","url":null,"abstract":"<div><div>This article presents a systematic modeling methodology for deriving the infinite-dimensional port-Hamiltonian representation of geometrically nonlinear and hyperelastic systems, and a structure-preserving mixed FEM approach. The proposed methods provide a rigorous framework for obtaining the dynamic nonlinear partial differential equations governing these systems, ensuring that they are consistent with a Stokes–Dirac geometric structure. This structure is fundamental for modular multiphysics modeling and nonlinear passivity-based control. The modeling methodology is rooted in a total Lagrangian formulation, incorporating Green–Lagrange strains and second Piola–Kirchhoff stresses, where generalized displacements and strains define the interconnection structure. Using the generalized Hamilton's principle, infinite-dimensional port-Hamiltonian systems are systematically derived. To preserve the structure upon spatial discretization, a three-field mixed finite element approach is proposed, in which displacements, strains, and stresses are explicitly treated as independent variables to retain the port-Hamiltonian structure. The effectiveness of the framework is demonstrated through model derivation and simulations, using a geometrically nonlinear planar beam with Saint Venant–Kirchhoff material, and a compressible nonlinear 2D elasticity problem with a Neo-Hookean material model, as illustrative examples.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"150 ","pages":"Article 116403"},"PeriodicalIF":4.4,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987921","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}