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A physics-informed neural network for simulation of finite deformation in hyperelastic-magnetic coupling problems

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Applied Mathematics and mechanics(English Edition) 2024年第10期45卷 1717-1732页

作者： WANG Lei LUO Zikun LU Mengkai TANG Minghai department of engineering mechanics College of Mechanics and Engineering SciencesHohai UniversityNanjing 211100China School of mechanical engineering and mechanics Ningbo UniversityNingbo 315211Zhejiang ProvinceChina

Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation *** this paper,a PINN framework for tackling hyperelastic-magnetic coupling problems is *** the solution space consists of two-phase domains,two separate networks are constructed to independently predict the solution for each phase *** addition,a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp *** the developed framework,the magnetic fields and deformation fields of magnetorheological elastomers(MREs)are solved under the control of hyperelastic-magnetic coupling *** examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed ***,the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated,particularly in handling small data sets,as well as its ability in swiftly and precisely forecasting magnetostrictive motion.

关键词： physics-informed neural network(PINN) deep learning hyperelastic-magnetic coupling finite deformation small data set

Control and vibration analyses of a sandwich doubly curved micro-composite shell with honeycomb,truss,and corrugated cores based on the fourth-order shear deformation theory

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Applied Mathematics and mechanics(English Edition) 2024年第10期45卷 1773-1790页

作者： F.SHIRDELAN M.MOHAMMADIMEHR F.BARGOZINI department of Solid mechanics Faculty of Mechanical EngineeringUniversity of KashanKashan 87317-53153Iran

Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures,flexibility,and attractive ***,the inability of controlling and regulating vibrations and destroying them afterward is a challenge to *** this paper,the curve shell equations and a linear quadratic regulator are adopted for the state feedback design to manage the structure vibrations in state space forms.A five-layer sandwich doubly curved micro-composite shell,comprising two piezoelectric layers for the sensor and actuator,is modeled by the fourth-order shear deformation *** core(honeycomb,truss,and corrugated)is analyzed for the bearing of transverse shear *** results show that the honeycomb core has a greater effect on the *** the parameters related to the core and the weight percentage of graphene increase,the frequency *** uniform distribution of graphene platelets results in the lowest natural frequency while the natural frequency ***,without taking into account the piezoelectric layers,the third-order shear deformation theory(TSDT)and fourth-order shear deformation theory(FOSDT)align ***,when the piezoelectric layers are incorporated,these two theories diverge significantly,with the frequencies in the FOSDT being lower than those in the TSDT.

关键词： vibration and control doubly curved shell micro-composite honeycomb truss corrugate core

Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core

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Applied Mathematics and mechanics(English Edition) 2024年第6期45卷 963-982页

作者： S.JAHANGIRI A.GHORBANPOUR ARANI Z.KHODDAMI MARAGHI department of Solid mechanics Faculty of Mechanical EngineeringUniversity of KashanKashan ***Iran Faculty of engineering Mahallat Institute of Higher EducationMahallat ***Iran

The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is *** shell is modeled utilizing the first-order shear deformation theory(FSDT)incorporating the relative,centripetal,and Coriolis accelerations alongside the initial hoop tension created by the *** governing equations,compatibility conditions,and boundary conditions are attained using Hamilton’s *** trigonometric functions,an analytical solution is derived in the circumferential direction,and a numerical one is presented in the meridional direction via the differential quadrature method(DQM).The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are *** present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.

关键词： free vibration conical shell rotating shell ring support auxetic honeycomb

Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

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Applied Mathematics and mechanics(English Edition) 2024年第3期45卷 461-478页

作者： Haitao LI Tianyu ZHENG Weiyang QIN Ruilan TIAN Hu DING J.C.JI Liqun CHEN department of engineering mechanics North University of ChinaTaiyuan 030051China department of engineering mechanics Northwestern Polytechnical UniversityXi'an 710072China department of engineering mechanics Shijiazhuang Tiedao UniversityShijiazhuang 050043China Shanghai Key Laboratory of mechanics in Energy engineering Shanghai Frontier Science Center of MechnoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China School of mechanical and Mechatronic engineering University of Technology SydneyNew South Wales 2007Australia

In the practical environment,it is very common for the simultaneous occurrence of base excitation and *** the combined energy of vibration and wind with a single energy harvesting structure is *** this purpose,the effects of the wind speed and random excitation level are investigated with the stochastic averaging method(SAM)based on the energy *** results of the analytical prediction are verified with the Monte-Carlo method(MCM).The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester(BEH)realize the performance enhancement for a weak base ***,as the strength of the wind increases to a particular level,the influence of the random base excitation on the dynamic responses is weakened,and the system exhibits a periodic galloping response.A comparison between a BEH and a linear energy harvester(LEH)indicates that the BEH demonstrates inferior performance for high-speed *** experiments are conducted to investigate the validity of the theoretical prediction and numerical *** experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind ***,as the speed of the incoming wind is up to a particular level,the disadvantage of the BEH becomes clear and evident.

关键词： bi-stability inter-well response galloping band-limited random

Isogeometric Analysis for the Arbitrary AFG Microbeam with Two-Phase Nonlocal Stress-Driven Model

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Acta Mechanica Solida Sinica 2024年第2期37卷 341-360页

作者： Pei-Liang Bian Zhaowei Liu Hai Qing Tiantang Yu department of engineering mechanics Hohai UniversityNanjing211100China State Key Laboratory of mechanics and Control of mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing210016China

Scale effects play critical roles in the mechanical responses of *** isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded *** Euler–Bernoulli beam model was utilized,and size effects in the structure were modeled with a stress-driven two-phase local/nonlocal integral *** governing equation of microstructures was given in an equivalent differential form with two additional constitutive boundary *** framework was verified and utilized to analyze the microbeam’s static and dynamic mechanical *** present work showed great potential for modeling various types of functionally graded microstructures.

关键词： Isogeometric analysis Size effect Functionally graded material Nonlocal theory Euler-Bernoulli beam

Effects of surface energy and substrate on modulus determination of biological films by conical indentation

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Science China(Technological Sciences) 2024年第6期67卷 1757-1764页

作者： DING Yue LI Cheng-Ya NIU XinRui WANG Gang-Feng department of engineering mechanics SVLXi’an Jiaotong UniversityXi’an710049China department of mechanical engineering City University of Hong KongHong Kong SAR999077China

Micro-/nano-indentation has become prevalent in evaluating the mechanical characteristics of biological samples,such as cells and ***,the existing contact models describing conical indentation ignore the joint effects of surface energy and substrate,and consequently cannot accurately extract the Young's modulus of biological samples deposited on *** finite element methods,we examine the conical indentation of biological films on substrates while taking surface energy into *** on the dimensional analysis,the explicit relationship between load and indentation depth is achieved for films with their moduli varying from 0.001 to 100 times that of the *** the classical Sneddon's model was employed to analyze the load-depth data,the measured modulus could reach 18 times the real modulus for films on harder substrates,but only 4%of the real modulus for films on softer ***,in micro-/nano-indentations,neglecting the contribution of surface energy would result in an overestimation of the Young's modulus of films depending on the contact *** analytical expression provided here can be utilized to precisely deduce the mechanical characteristics of biological films deposited on substrate from the load and indentation depth data of a conical indentation.

关键词： biological film surface effect substrate effect indentation

Semi-analytical Solutions for Wellbores with Graded Skin Zones in Poroelastic Media

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Acta Mechanica Solida Sinica 2024年第3期37卷 385-395页

作者： Zhiqiang Fan Zhihe Jin School of mechanics Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’an710072China department of mechanical engineering University of MaineOronoME04469USA

In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role in determining flow dynamics and the resulting formation *** models of the wellbore skin zone generally assume a constant permeability throughout,resulting in a sharp permeability discontinuity at the skin-reservoir *** paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic *** solutions are derived using the Laplace transform method,addressing both positive and negative skin *** results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a *** results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.

关键词： Poroelastic Graded permeability Analytical solution Wellbore Skin zone

Analytical Expression for the Atomic Friction of a Single Asperity Based on the Prandtl-Tomlinson Model

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Acta Mechanica Solida Sinica 2024年第3期37卷 416-422页

作者： Weike Yuan Yue Ding Gangfeng Wang Xinrui Niu department of engineering mechanics SVLMMLXi’an Jiaotong UniversityXi’an710049China department of mechanical engineering City University of Hong KongHong Kong SAR999077China

The Prandtl-Tomlinson(PT)model has been widely applied to interpret the atomic friction mechanism of a single *** this study,we present an approximate explicit expression for the friction force in the one-dimensional PT model under quasi-static ***‘stick-slip’friction curves are first approximated properly by sawtooth-like lines,where the critical points before and after the‘slip’motion are described analytically in terms of a dimensionless parameterη.Following this,the average friction force is expressed in a closed form that remains continuous and valid forη>***,an analytical expression for the load dependence of atomic friction of a single asperity is derived by connecting the parameterηwith the normal *** the parameters reported in experiments,our prediction shows good agreement with relevant experimental results.

关键词： Atomic friction Stick-slip friction Prandtl-Tomlinson model Friction force microscope

A robust implicit high-order discontinuous Galerkin method for solving compressible Navier-Stokes equations on arbitrary grids

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Acta Mechanica Sinica 2024年第8期40卷 96-119页

作者： Jia Yan Xiaoquan Yang Peifen Weng Shanghai Institute of Applied Mathematics and mechanics Shanghai Key Laboratory of Mechanics in Energy EngineeringSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai200072China College of Energy and mechanical engineering Shanghai University of Electric PowerShanghai200090China

The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and *** challenges impose significant constraints on computational efficiency,particularly in the domain of engineering *** address these concerns,this paper proposes a robust implicit high-order discontinuous Galerkin(DG)method for solving compressible Navier-Stokes(NS)equations on arbitrary *** method achieves a favorable equilibrium between computational stability and *** solve the linear system,an exact Jacobian matrix solving strategy is employed for preconditioning and matrix-vector generation in the generalized minimal residual(GMRES)*** approach mitigates numerical errors in Jacobian solution during implicit calculations and facilitates the implementation of an adaptive Courant-Friedrichs-Lewy(CFL)number increasing strategy,with the aim of improving convergence and *** further enhance the applicability of the proposed method for intricate grid distortions,all simulations are performed in the reference *** practice significantly improves the reversibility of the mass matrix in implicit calculations.A comprehensive analysis of various parameters influencing computational stability and efficiency is conducted,including CFL number,Krylov subspace size,and GMRES convergence *** computed results from a series of numerical test cases demonstrate the promising results achieved by combining the DG method,GMRES solver,exact Jacobian matrix,adaptive CFL number,and reference domain calculations in terms of robustness,convergence,and *** analysis results can serve as a reference for implicit computation in high-order calculations.

关键词： Discontinuous Galerkin method Exact Jacobian matrix GMRES solver Adaptive CFL number Reference domain High-order