International Journal of Non-Linear Mechanics最新文献

{"title":"Structural partitioning for parallel construction of geometric nonlinear reduced-order models","authors":"Tuan Anh Bui ,&nbsp;Junyoung Park ,&nbsp;Jun-Sik Kim","doi":"10.1016/j.ijnonlinmec.2025.105092","DOIUrl":"10.1016/j.ijnonlinmec.2025.105092","url":null,"abstract":"<div><div>High-fidelity finite element models are widely used to predict the mechanical behavior of structures with complex geometries. While these models provide accurate results, they often require significant computational time, particularly when predicting nonlinear dynamic behavior. To address this, model order reduction techniques have been developed to reduce the computational time. However, constructing non-intrusive reduced-order models from high-fidelity finite element models still requires considerable computational time. This paper proposes a fully parallel process to accelerate the construction of geometrically nonlinear reduced-order models. In this approach, the structure is divided into multiple partitions, each assigned to a separate processor. The reduction basis for each partition ensures displacement consistency at partition interfaces without requiring additional modal coordinates at these interfaces. The parallel process operates without inter-processor communication, making it robust and straightforward to implement. It is compatible with various non-intrusive model order reduction techniques and achieves high computational efficiency. Notably, this approach introduces no additional errors, i.e., the reduced-order model constructed through the parallel process is identical to that obtained via traditional methods.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105092"},"PeriodicalIF":2.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust control design of nonlinear negative stiffness base isolators for MDOF systems","authors":"Sudip Chowdhury ,&nbsp;Sondipon Adhikari ,&nbsp;Arnab Banerjee","doi":"10.1016/j.ijnonlinmec.2025.105083","DOIUrl":"10.1016/j.ijnonlinmec.2025.105083","url":null,"abstract":"<div><div>Seismic isolation is crucial for protecting structures from earthquake-induced vibrations, yet traditional base isolators (TBI) often exhibit limitations in mitigating dynamic responses, particularly in multi-degree-of-freedom (MDOF) systems. This study introduces nonlinear negative stiffness base isolators (NNBI) as an advanced alternative, leveraging <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimisation to enhance vibration control. A mathematical framework was developed to derive closed-form expressions for optimal NNBI design parameters, followed by numerical validation through frequency and time-domain analyses, including harmonic excitations, random white noise, and near-field earthquake simulations. Results demonstrated that NNBI achieves at least 47.90 % greater dynamic response reduction compared to TBI, with a maximum improvement of 97.80 % for ten DOF systems, confirming its superior energy dissipation capabilities. These findings establish NNBI as a transformative solution for seismic resilience, with potential applications in tall buildings.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105083"},"PeriodicalIF":2.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Extended invariant cones as Nonlinear Normal Modes of inhomogeneous piecewise linear systems","authors":"A. Yassine Karoui,&nbsp;Remco I. Leine","doi":"10.1016/j.ijnonlinmec.2025.105072","DOIUrl":"10.1016/j.ijnonlinmec.2025.105072","url":null,"abstract":"<div><div>The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous piecewise linear systems, to a class of inhomogeneous continuous piecewise linear systems. The inhomogeneous terms can be constant and/or time-dependent, modeling nonsmooth mechanical systems with a clearance gap and external harmonic forcing, respectively. Using an augmented state vector, a modified invariant cone problem is formulated and solved to compute the nonlinear normal modes, understood as periodic solutions of the underlying conservative dynamics. An important contribution is that invariant cones of the underlying homogeneous system can be regarded as a singularity in the theory of nonlinear normal modes of continuous piecewise linear systems. In addition, we use a similar methodology to take external harmonic forcing into account. We illustrate our approach using numerical examples of mechanical oscillators with a unilateral elastic contact. The resulting backbone curves and frequency response diagrams are compared to the results obtained using the shooting method and brute force time integration.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105072"},"PeriodicalIF":2.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Static and dynamic nonlinear behavior and instabilities of a multistable system consisting of two shallow coupled arches","authors":"Carlos H.L. de Castro ,&nbsp;Diego Orlando ,&nbsp;Paulo B. Gonçalves","doi":"10.1016/j.ijnonlinmec.2025.105087","DOIUrl":"10.1016/j.ijnonlinmec.2025.105087","url":null,"abstract":"<div><div>Increased attention has been lately given to multistable systems that use the snap-through buckling of each unit to attain a desired hysteretic force-deformation response. Many of these systems consist of chains of bistable elements flexibly or rigidly connected and respond to an applied load or displacement in a progressive manner. However, little is known of their nonlinear static and dynamic nonlinear behavior and stability. This paper investigates the nonlinear response of multistable structure composed of two simply-supported or clamped buckled beams connected in series by a stiff frame. The resulting multistable system is subject to a transverse force applied at the top of the upper arch. The Lagrangian of the system is obtained and the nonlinear equilibrium equations and equations of motion are derived by the Ritz approach applying the energy stability criterion and Hamilton's principle respectively. Both local and global analyses are numerically conducted to clarify the nonlinear dynamics of the multistable model. Applying brute force and continuation techniques, the coexisting stable and unstable nonlinear equilibrium paths are obtained and the bifurcation points identified. This analysis is aided by the investigation of the potential energy landscape and the basins of attraction of the damped system. The influence of the rise-to-span ratio is clarified and the influence of different ratios on the energy required for switching from one stable state to another, escaping through a saddle channel, is discussed. When subjected to a harmonic excitation the multistable system exhibits coexisting bifurcation sequences starting at each potential well, which can merge leading to large amplitude cross-well motions. The diverse resonance regions are investigated using bifurcation diagrams, phase-space portraits, Poincaré maps and basins of attraction. This study can be used as a basis for the nonlinear analysis of more complex multistable structures constituted by several bistable units.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105087"},"PeriodicalIF":2.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of constrained mechanical systems around an equilibrium position","authors":"S. Natsiavas,&nbsp;C. Georgiadis,&nbsp;L. Papapostolou","doi":"10.1016/j.ijnonlinmec.2025.105088","DOIUrl":"10.1016/j.ijnonlinmec.2025.105088","url":null,"abstract":"<div><div>This study focuses on a special class of multibody dynamic systems, involving bilateral motion constraints. Specifically, both the equations of motion and the equations of the motion constraints appear in a linear equality form. First, following an appropriate Analytical Dynamics approach, the dominant dynamics of the systems examined is eventually represented by a coupled set of second order linear ordinary differential equations for both the system coordinates and the Lagrange multipliers corresponding to the motion constraints. This allows a thorough investigation of the dynamics, based on classical linear procedures. For this, the structure of the corresponding undamped eigenvalue problem is revealed first in a complete form. This opens the way to determine the response of the undamped system by applying an appropriate modal analysis technique. Next, damping terms leading to classical modes of vibration are also included in the governing equations and their effects are studied in detail. Finally, the analytical results are complemented and illustrated further by considering a typical set of mechanical examples. Besides predicting the dynamics of linear constrained systems, the new methodology provides a strong basis for investigating in depth several related theoretical and technical issues, like the stability properties of equilibrium solutions of mechanical systems or of numerical schemes applied to the solution of multibody systems with nonlinear characteristics.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105088"},"PeriodicalIF":2.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid piezoelectric-electromagnetic energy harvesting from limit cycle oscillation of the wing","authors":"Yun Cheng ,&nbsp;Daochun Li ,&nbsp;Tiejun Zhang","doi":"10.1016/j.ijnonlinmec.2025.105082","DOIUrl":"10.1016/j.ijnonlinmec.2025.105082","url":null,"abstract":"<div><div>As a nonlinear aeroelastic phenomenon, limit cycle oscillation (LCO) of the wing has the potential to supply continuous electrical power output through energy harvesting. In this paper, a basic wing-store structure with hybrid piezoelectric-electromagnetic energy harvesters is proposed to harvest the mechanical energy from bending-torsional coupling LCO response. The nonlinear structure model, the unsteady aerodynamic model and the hybrid energy harvesting model are built and form a piezoelectric-electromagnetic-aeroelastic state-space model. Results show that the extra store at the wingtip can alter the flutter speed and the frequency of the wing. It means that the wing store can lead to LCO response with a higher flutter frequency at lower wind speed. Changing the parameters of the structure and energy harvesting systems can change the intensities and the wind speed range that result in LCO response of the wing. The above features can impact the applicability and electrical power output of the energy harvesting systems. The additional electromagnetic energy harvester can further improve the overall energy conversion efficiency. The details of these effects are demonstrated and the methods for optimizing electric outputs are discussed.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105082"},"PeriodicalIF":2.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Responses of any arbitrary initially stressed reference and the stress-free reference","authors":"Soumya Mukherjee","doi":"10.1016/j.ijnonlinmec.2025.105070","DOIUrl":"10.1016/j.ijnonlinmec.2025.105070","url":null,"abstract":"<div><div>The constitutive relation for an initially stressed reference is often determined by using the response of a virtual stress-free reference. However, identifying the constitutive relation of the original stress-free body can be challenging without conducting destructive tests. This paper presents three approaches for determining the response of a stress-free reference—or any arbitrary initially stressed reference—when the response of a particular initially stressed reference is known. Unlike standard practice, these approaches of changing reference configurations do not begin with a known stress-free state. The first and third approaches directly derive the constitutive relations of one stressed reference from another. The first approach is applicable to a specific constitutive relation of the known initially stressed state, while the third approach extends the first and is applicable to any constitutive form. The second approach uses any general response of a given stressed reference to identify the stress-free material. The response of the stress-free material is further analyzed and processed to determine the response of any stressed reference. We observe that even when the known initially stressed state is Green elastic, the arbitrarily stressed or stress-free references may exhibit implicit elasticity. Several explicit constitutive relations are also exemplified. One of the examples utilizes the invariants of Seth’s generalized strain measures. For experimental validation of this model, we transform the Treloar data to various initially stressed references. Model parameters corresponding to a specific stressed state are optimized by corroborating the model against the Treloar data associated with that reference. These optimized parameters are then used to determine the constitutive relations for the stress-free and other stressed reference configurations. The resulting constitutive relations for various references show identical alignment with the corresponding Treloar data, thereby validating the present approaches for changing the reference configuration. It is demonstrated that the developed models satisfy all restrictions related to the change of references. Furthermore, we develop universal relations for stress-free isotropic implicit elastic materials.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105070"},"PeriodicalIF":2.8,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 improved constitutive model for the rate-dependent mechanical behaviour of rubbery materials","authors":"Bijuan Yan ,&nbsp;Guansen Qiao ,&nbsp;Yihang Geng ,&nbsp;Zhangda Zhao ,&nbsp;Tao Yang","doi":"10.1016/j.ijnonlinmec.2025.105077","DOIUrl":"10.1016/j.ijnonlinmec.2025.105077","url":null,"abstract":"<div><div>In order to accurately predict the mechanical behaviour of fluororubber and silicone rubber under different strain rates, an improved model based on the existing strain rate-dependent viscoelastic constitutive models is proposed in this article. Firstly, a strain rate-dependent variable-order fractional model is established. Then, the method of combining theory and experiment is adopted to explore the influence of the key parameters on prediction accuracy. Following this, the relaxation time is found to be the key factor affecting the accuracy of the predicted results of the mechanical properties through the analyses. Finally, the model is improved by replacing the relaxation time with the viscoelastic coefficient. The results show that the relative errors of the stress prediction results are within 3% for silicone rubber and reduced by 1.7%–4.5% for fluororubber. These findings can provide theoretical references and support for the analysis of the mechanical properties of the similar types of viscoelastic materials.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105077"},"PeriodicalIF":2.8,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical study of the elastoplastic buckling of conical shells under external pressure","authors":"Gwladys Belone ,&nbsp;Van Dong Do ,&nbsp;Philippe Le Grognec ,&nbsp;Philippe Rohart ,&nbsp;Samir Assaf","doi":"10.1016/j.ijnonlinmec.2025.105069","DOIUrl":"10.1016/j.ijnonlinmec.2025.105069","url":null,"abstract":"<div><div>Pressure vessels are traditionally made up of cylindrical shells and hemispherical or ellipsoidal ends, but in some cases, conical sections are also present so as to ensure the transition between cylindrical sections of different radii. The buckling phenomenon is one of the main failure mode of such pressure equipments, due to the thinness of the components and the compressive stresses commonly undergone throughout standard loads like external pressure, and thus an essential dimensioning factor. If the buckling behavior of cylindrical and spherical shells has been widely investigated in the literature, the specific case of conical shells has received much less attention, all the more so in plasticity. Therefore, the present paper aims to address the problem of elastoplastic buckling of a conical shell under external pressure in an analytical way. This study is based on the plastic bifurcation theory and relies on the simplest possible hypotheses in terms of kinematics, constitutive law and boundary conditions. However, in absence of closed-form expressions, approximate solutions for the critical pressure are sought, based on the choice of appropriate shape functions in the framework of the Rayleigh–Ritz method. Unlike the case of cylindrical or spherical shells under external pressure which display uniform pre-critical stress states, the stress field appears to be heterogeneous in the length direction of a conical shell, so that three scenarios may occur. A conical shell may buckle elastically, entirely in the plastic range, or in an intermediate situation where the shell is partially elastic and plastic at the critical time. The present analytical solution is validated against reference numerical results obtained through finite element computations, considering a wide range of geometric and material parameters so as to cover all three scenarios.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105069"},"PeriodicalIF":2.8,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unveiling the dynamics of particle-reinforced electro-magneto-active circular membrane","authors":"Ankush Agrawal,&nbsp;Aman Khurana","doi":"10.1016/j.ijnonlinmec.2025.105064","DOIUrl":"10.1016/j.ijnonlinmec.2025.105064","url":null,"abstract":"<div><div>Electro-magneto-active (EMA) membranes are materials that integrate electromagnetic and active properties to form flexible, responsive surfaces. These membranes typically consist of a soft, elastic matrix embedded with magnetic or electromagnetic particles, which can be manipulated by external magnetic fields or electrical currents. This paper investigates the nonlinear dynamics of an electro-magneto-active circular membrane, a sophisticated smart actuator. Specifically, a continuum physics-based model is implemented to predict the membrane’s dynamic response to applied electro-magneto-mechanical loads. The obtained results offer valuable preliminary insights into the influence of both DC and AC dynamic actuation modes on the membrane’s nonlinear behavior. Notably, we find that increased particle reinforcement, as indicated by the filler content, significantly enhances polymer strength and reduces deformation. Also, an increase in shear modulus ratio results in a reduction in oscillation intensity and an enhancement in excitation frequency. Additionally, time–history response, Poincaré maps, and phase diagrams are utilized to evaluate the membrane’s stability, periodicity, beating phenomena, and resonant behavior. These findings are pivotal for advancing the design and functionality of smart membranes in various biomedical applications.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105064"},"PeriodicalIF":2.8,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}