International Journal of Non-Linear Mechanics最新文献

{"title":"Modeling of residual stiffness phenomenon in modified Iwan model of bolted joints and its application","authors":"Hao Chen ,&nbsp;Zhiming Hao ,&nbsp;Jinxin Kuang ,&nbsp;Yongjian Mao","doi":"10.1016/j.ijnonlinmec.2024.104909","DOIUrl":"10.1016/j.ijnonlinmec.2024.104909","url":null,"abstract":"<div><div>Bolted joints have been widely used in various mechanical structures. Due to the presence of contact interfaces, the joints exhibit complex nonlinear behavior under dynamic loading. Effective prediction of the dynamic response of bolted structures requires the construction of appropriate dynamic models. This paper proposes a modified Iwan model which gives a more comprehensive description of joints than the previous Iwan models, especially for the phenomenon of residual stiffness in macro slip. The equations of the model's backbone curve, hysteresis curve, and energy dissipation are derived. The parameter identification procedure is also provided. Subsequently, connection elements based on the modified Iwan model are integrated into a single bolted joint and a thin-walled cylinder containing multiple bolted joints, the responses under quasi-static unidirectional loading, quasi-static cyclic loading and constant-frequency excitation are investigated. The physical interpretation of the parameters in the model is discussed, thus explaining the relationship between the bolted joint's physical parameters and some important variables. The results indicate that the model can effectively characterize the nonlinear mechanical behavior of the bolted joint for both micro and macro slip regime, with significant improvement in computational efficiency.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104909"},"PeriodicalIF":2.8,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312497","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":"Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation","authors":"Dilara Siraeva","doi":"10.1016/j.ijnonlinmec.2024.104904","DOIUrl":"10.1016/j.ijnonlinmec.2024.104904","url":null,"abstract":"<div><div>We applied a method of symmetry reduction to the gas dynamics equations with a special form of the equation of state. This equation of state is a pressure represented as the sum of a density and an entropy functions. The symmetry Lie algebra of the system is 12-dimensional. One, two and three-dimensional subalgebras were considered. In this article, four-dimensional subalgebras are considered for the first time. Specifically, invariants are calculated for 50 four-dimensional subalgebras. Using invariants of one of the subalgebras, a symmetry reduction of the original system is calculated. The reduced system is a partially invariant submodel because one gas-dynamic function cannot be expressed in terms of the invariants. The submodel leads to two families of exact solutions, one of which describes the isochoric motion of the media, and the other solution specifies an arbitrary blow-up surface. For the first family of solutions, the particle trajectories are parabolas or rays; for the second family of solutions, the particles move along cubic parabolas or straight lines. From each point of the blow-up surface, particles fly out at different speeds and end up on a straight line at any other fixed moment in time. A description of the motion of particles for each family of solutions is given.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104904"},"PeriodicalIF":2.8,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323368","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":"Impact of compliant electrodes on the dynamics of electromagnetoactive membranes","authors":"Asesh Kumar Patra ,&nbsp;Aman Khurana ,&nbsp;Deepak Kumar ,&nbsp;Prashant Saxena","doi":"10.1016/j.ijnonlinmec.2024.104906","DOIUrl":"10.1016/j.ijnonlinmec.2024.104906","url":null,"abstract":"<div><div>The dynamics of electromagnetoactive polymer (EMAP) membranes have attracted much attention recently because of their wide range of modern robotic applications. Such applications majorly centered on how the dynamics of this novel class of membranes are affected by the mechanical behavior of the compliant electrode. This article presents the dynamic modeling and analysis of EMAP membranes, examining how the inertia of the electrode, coupled with its inherent viscoelastic properties, impacts its dynamic performance. Both the compression and suspension stages of the membrane are covered here in broad terms. An Euler–Lagrange equation of motion is implemented to deduce the governing dynamic model equation of the membrane system. The findings of the model solutions provide preliminary insights to characterize the dynamic response, instability analysis, periodic behavior, and resonance properties across varying parameters such as inertia, electric field, magnetic field, and prestress. Moreover, the study also evaluates the periodicity and stability of the nonlinear oscillations using Poincaré maps and phase portraits, facilitating an assessment of quasi-periodic to periodic transitions.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104906"},"PeriodicalIF":2.8,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319140","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":"Nonlinear analysis of spatial trusses with different strain measures and compressible solid","authors":"William T.M. Silva,&nbsp;Kamirã B. Ribeiro,&nbsp;A. Portela","doi":"10.1016/j.ijnonlinmec.2024.104907","DOIUrl":"10.1016/j.ijnonlinmec.2024.104907","url":null,"abstract":"<div><p>This paper investigates the nonlinear behavior of spatial truss elements under finite deformations, focusing on the impact of various strain measures in compressible materials. We examine both Total Lagrangian (using engineering and Green–Lagrange strains) and Eulerian formulations (using natural, Biot, and Almansi strains). The analysis assumes a linear spatial hyperelastic material where Cauchy stress is proportional to axial natural strain via Young’s modulus. For infinitesimal strains, Young’s modulus remains consistent across different stress/strain pairs. In the finite strain regime, we derive a nonlinear secant modulus based on Young’s modulus. Internal force vectors and tangent stiffness matrices are computed using the direction cosines of the truss element in its deformed state. The paper demonstrates that for infinitesimal deformations, adjusting the modulus of elasticity when using different stress/strain pairs is unnecessary. However, for finite deformations, it is essential to adjust the modulus of elasticity. Numerical simulations validate the performance of the proposed 3D truss element against established formulations. This research offers critical insights into the nonlinear response of spatial trusses, guiding the selection of appropriate strain measures for enhanced accuracy in engineering applications. These findings contribute to more reliable and efficient structural designs, especially in scenarios involving finite deformations and compressible materials.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104907"},"PeriodicalIF":2.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142272348","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":"Cascaded robust fixed-time terminal sliding mode control for uncertain cartpole systems with incremental nonlinear dynamic inversion","authors":"Changyi Lei ,&nbsp;Quanmin Zhu ,&nbsp;Ruobing Li","doi":"10.1016/j.ijnonlinmec.2024.104900","DOIUrl":"10.1016/j.ijnonlinmec.2024.104900","url":null,"abstract":"<div><p>This paper proposes a cascaded fixed-time terminal sliding mode controller (TSMC) for uncertain underactuated cartpole dynamics using incremental nonlinear dynamic inversion (INDI). Leveraging partial linearization and prioritizing pole dynamics for internal tracking, the proposed controller achieves efficient stabilization of the cart upon convergence of the pole. Stability analysis is carried out using Lyapunov stability theorem, proving that the proposed controller stabilizes the state variables to an arbitrarily small neighborhood of the equilibrium in fixed-time, along with the suboptimality (steady-state error), existence and uniqueness of the solutions. The INDI is also integrated into TSMC to further improve the robustness while suppressing the conservativeness of conventional TSMC. The stability of INDI is rigorously proved using sampling-based Lyapunov function under sampling-based control realm. The simulation results illustrate the superiority of the proposed method with comparison and ablation studies.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104900"},"PeriodicalIF":2.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020746224002658/pdfft?md5=88d11b37eb7f002ec2769b38725ef740&pid=1-s2.0-S0020746224002658-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230380","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":"Study on nonlinear relaxation properties of composite solid propellant","authors":"Xu Zhang ,&nbsp;Jiangtao Wang ,&nbsp;Xiangyang Liu ,&nbsp;Yanqing Wu ,&nbsp;Ningfei Wang ,&nbsp;Xiao Hou","doi":"10.1016/j.ijnonlinmec.2024.104908","DOIUrl":"10.1016/j.ijnonlinmec.2024.104908","url":null,"abstract":"<div><p>Under large deformations, the nonlinear relaxation properties of composite solid propellants result in significant prediction deviations. In this study, viscoelastic experiments of solid propellants at variable temperatures are conducted. A method for calculating the equal stress derivative in multi-step relaxation test results is proposed to calibrate the proportional relationship of nonlinear relaxation times. The relaxation times increase monotonically with deformation and exhibit a logarithmic evolution law. Under large deformations, the increase of relaxation times slows down. The nonlinear relaxation times are introduced into the thermo-hyper-viscoelastic constitutive model constructed by the generalized Maxwell model and the eight-chain tube model. After calibrating the constitutive model parameters based on experimental results, the accuracy of the constitutive model is verified through double-step relaxation tests on center-holed samples. The incorporation of the nonlinear relaxation times reduces the prediction deviations of composite solid propellants from 11% to 5%. The nonlinear relaxation properties of solid propellants originate from the nonlinearity of moduli and viscosities. The moduli and viscosities exhibit a pattern of initially increasing and then dropping with deformation. The microscopic mechanism involves the time consumption of rearrangement due to heightened friction following deformation, as well as the fracture of the molecular chain under large deformation. The temperatures reduce relaxation times and viscosities by increasing the extensibility of molecular chains.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104908"},"PeriodicalIF":2.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142233715","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":"Neural networks based surrogate modeling for efficient uncertainty quantification and calibration of MEMS accelerometers","authors":"Filippo Zacchei ,&nbsp;Francesco Rizzini ,&nbsp;Gabriele Gattere ,&nbsp;Attilio Frangi ,&nbsp;Andrea Manzoni","doi":"10.1016/j.ijnonlinmec.2024.104902","DOIUrl":"10.1016/j.ijnonlinmec.2024.104902","url":null,"abstract":"<div><p>This paper addresses the computational challenges inherent in the stochastic characterization and uncertainty quantification of Micro-Electro-Mechanical Systems (MEMS) capacitive accelerometers. Traditional methods, such as Markov Chain Monte Carlo (MCMC) algorithms, are often constrained by the computational intensity required for high-fidelity (e.g., finite element) simulations. To overcome these limitations, we propose to use supervised learning-based surrogate models, specifically artificial neural networks, to effectively approximate the response of MEMS capacitive accelerometers. Our approach involves training the surrogate models with data derived from initial high-fidelity finite element analyses (FEA), providing rich datasets to be generated in an offline phase. The surrogate models replicate the FEA accuracy in predicting the behavior of the accelerometer under a wide range of fabrication parameters, thereby reducing the online computational cost without compromising accuracy. This enables extensive and efficient stochastic analyses of complex MEMS devices, offering a flexible framework for their characterization. A key application of our framework is demonstrated in estimating the sensitivity of an accelerometer, accounting for unknown mechanical offsets, over-etching, and thickness variations. We employ an MCMC approach to estimate the posterior distribution of the device’s unknown fabrication parameters, informed by its response to transient voltage signals. The integration of surrogate models for mapping fabrication parameters to device responses, and subsequently to sensitivity measures, greatly enhances both backward and forward uncertainty quantification, yielding accurate results while significantly improving the efficiency and effectiveness of the characterization process. This process allows for the reconstruction of device sensitivity using only voltage signals, without the need for direct mechanical acceleration stimuli.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104902"},"PeriodicalIF":2.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020746224002671/pdfft?md5=d3c229018b2515fd00c03dfc0eaf811b&pid=1-s2.0-S0020746224002671-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142233718","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":"Static analysis using flexibility disassembly perturbation for material nonlinear problem with uncertainty","authors":"X. Peng ,&nbsp;Q.W. Yang ,&nbsp;H.F. Cao","doi":"10.1016/j.ijnonlinmec.2024.104901","DOIUrl":"10.1016/j.ijnonlinmec.2024.104901","url":null,"abstract":"<div><p>Nonlinear finite element analysis of large-scale structures usually requires a lot of calculation cost, because it is necessary to repeatedly inverse the modified stiffness matrix caused by nonlinearity in the calculation process. When considering the uncertainty in materials, the calculation of the nonlinear analysis will be more unbearable. To improve the computational efficiency, this work develops a new method for nonlinear analysis with material uncertainty based on flexibility disassembly perturbation (FDP) approach. The FDP is an algorithm that can quickly calculate the inverse of a stiffness matrix. The basic idea of the proposed method is to introduce the FDP formula into Newton-Raphson iteration method to accelerate the nonlinear iterative calculation. Three numerical examples, one statically determinate structure and two statically indeterminate structures, are used to verify the accuracy and efficiency of the proposed method. The results show that the calculation time of the proposed method is far less than that of the existing complete analysis and combined approximation algorithms. In terms of computational accuracy, for statically determinate structures, the proposed algorithm can obtain exact solutions that are identical to the complete analysis results, while for statically indeterminate structures, the proposed algorithm can obtain approximate solutions that are very close to the complete analysis results.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104901"},"PeriodicalIF":2.8,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142233716","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":"Nonparametric identification of multi-degree-of-freedom nonlinear systems from partially measured responses under uncertain dynamic excitations","authors":"Ye Zhao ,&nbsp;Bin Xu ,&nbsp;Genda Chen","doi":"10.1016/j.ijnonlinmec.2024.104903","DOIUrl":"10.1016/j.ijnonlinmec.2024.104903","url":null,"abstract":"<div><p>With the rapid advent of new materials and novel structures, it becomes difficult, if not impossible, to accurately model and simulate the nonlinear response of complex systems under uncertain dynamic excitations based on close-formed nonlinear functions and parametric identification. In this study, a two-step structural nonlinearity localization and identification approach for multi-degree-of-freedom (MDOF) nonlinear systems under uncertain dynamic excitations is developed by integrating an extended Kalman filter with unknown inputs into the equivalent linearized systems. In the first step, unmeasured responses and excitations are estimated as well as unknown structural parameters and nonlinearity locations are identified by fusing acceleration with displacement time histories at the observed degrees of freedom (DOFs). In the second step, the nonlinear restoring force of the detected nonlinear structural members is identified nonparametrically using three polynomial models, including a power series polynomial model (PSPM), a double Chebyshev polynomial model (DCPM), and a Legendre polynomial model (LPM). Linear multi-story shear frames controlled by nonlinear magnetorheological (MR) dampers are modelled computationally to demonstrate the generality of the proposed methodology. The multi-source uncertainties considered in these representative examples include the location and the type of nonlinearities represented by a Bingham model and a modified Dahl model of the dampers, the location of response measurements, the location and intensity of dynamic excitations, the level of measurement noise, and the initial assignment of structural parameters. The acceleration, velocity, and displacement time histories of structures can be evaluated accurately with a maximum error of 2.62% even with the presence of 8% measurement noise, while the external excitations can be estimated within an error of 1.77%. The location of nonlinear elements can be detected correctly. The structural parameters, the NRFs provided by MR dampers and the corresponding energy dissipation can be identified with a maximum error of 2.08%, 1.19% and 0.39%, respectively, even 8% measurement noise and very rough initial assignment of structure parameters (−70%) are considered. Moreover, the numerical results change little (&lt;0.20%) even the initial assignment of structural parameters varies from 50% to 30% of their original values, no matter which nonparametric model is employed. Results indicate that the presented algorithm can effectively identify unmeasured dynamic responses, structural parameters, unknown excitations, nonlinear locations, and NRF of nonlinear elements in a nonparametric way.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104903"},"PeriodicalIF":2.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171854","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":"Non-linear filtration model with splitting front","authors":"Liudmila I. Kuzmina ,&nbsp;Yuri V. Osipov ,&nbsp;Artem R. Pesterev","doi":"10.1016/j.ijnonlinmec.2024.104905","DOIUrl":"10.1016/j.ijnonlinmec.2024.104905","url":null,"abstract":"<div><p>We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the front boundary of suspended particles and the front of the carrier fluid was observed. This article proposes a modification of the standard model that provides a description of the separation between the fluid front and the particle front. For this purpose, a non-smooth non-linear function depending on the concentration of the suspension is introduced into the deposit growth equation. In case of a non-smooth suspension function, the concentration of suspended particles at the front decreases to zero in a finite time. At this moment the united front splits into the front of pure injected water and the front of suspended and retained particles. The particle front moves slower than the pure water front. In case of a linear filtration function (Langmuir coefficient), an exact solution is constructed in a closed form. For the filtration problem with a suspension function in the form of a square root, explicit analytical formulae are obtained. In case of a non-smooth filtration function, the filtration time is finite. The curvilinear boundary separates the filtration domain, where concentrations increase with time, from the stabilization domain, where the concentrations of suspended and retained particles have reached their limits. The limit speeds of the stabilization border and of the particle front coincide.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104905"},"PeriodicalIF":2.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239735","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}