Table of Content

01 May 2024, Volume 45 Issue 5

Previous Issue    Next Issue

Articles

Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

Hanxiao GUO, Peifeng GAO, Xingzhe WANG

2024, 45(5):  747-762.  doi:10.1007/s10483-024-3112-8

Abstract ( 169 )   HTML ( 14)   PDF (5789KB) ( 221 )  

Figures and Tables | References | Related Articles | Metrics

Second-generation high-temperature superconducting (HTS) conductors, specifically rare earth-barium-copper-oxide (REBCO) coated conductor (CC) tapes, are promising candidates for high-energy and high-field superconducting applications. With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components, the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields. Traditional numerical models include homogenized orthotropic models, which simplify overall field calculation but miss detailed multi-physics aspects, and full refinement (FR) ones that are thorough but computationally demanding. Herein, we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils. This approach combines a global homogenization (GH) scheme based on the homogenized electromagnetic T-A model, a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A, and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale. We then identify "dangerous regions" at the macroscopic scale and obtain finer details using a local refinement (LR) scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale. The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature, indicating that the present approach is accurate and efficient. The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

Comparison of nonlinear modeling methods for the composite rubber clamp

Yiming CAO, Hui MA, Xumin GUO, Bingfeng ZHAO, Hui LI, Xin WANG, Bing WANG

2024, 45(5):  763-778.  doi:10.1007/s10483-024-3114-6

Abstract ( 160 )   HTML ( 9)   PDF (6478KB) ( 94 )  

Figures and Tables | References | Related Articles | Metrics

The cubic stiffness force model (CSFM) and Bouc-Wen model (BWM) are introduced and compared innovatively. The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments. By fitting the identified nonlinear coefficients under different excitation amplitudes, the nonlinear vibration responses of the system are predicted. The results show that the accuracy of the BWM is higher than that of the CSFM, especially in the non-resonant region. However, the optimization time of the BWM is longer than that of the CSFM.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell: an experimental and numerical study

Lele REN, Wei ZHANG, Ting DONG, Yufei ZHANG

2024, 45(5):  779-794.  doi:10.1007/s10483-024-3111-7

Abstract ( 141 )   HTML ( 1)   PDF (7241KB) ( 136 )  

Figures and Tables | References | Related Articles | Metrics

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches. An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition, which is composed of an asymmetric region and a symmetric region. The symmetric region of the experimental specimen is entirely clamped, which is rigidly connected to an electromagnetic shaker, while the asymmetric region remains free of constraint. Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker, and the displacement responses of the shell are collected by the laser displacement sensors. The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell, and an off-axis three-dimensional dynamic snap-through domain is obtained. The numerical solutions are in good agreement with the experimental results. The nonlinear stiffness characteristics, dynamic snap-through domain, and chaos and bifurcation behaviors of the shell are quantitatively analyzed. Due to the asymmetry of the boundary condition and the shell, the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic, and the lower stable-state shows a linear stiffness characteristic of the shell.

Kinematic analysis of flexible bipedal robotic systems

R. FAZEL, A. M. SHAFEI, S. R. NEKOO

2024, 45(5):  795-818.  doi:10.1007/s10483-024-3081-8

Abstract ( 151 )   HTML ( 1)   PDF (5564KB) ( 338 )  

Figures and Tables | References | Related Articles | Metrics

In spite of its intrinsic complexities, the passive gait of bipedal robots on a sloping ramp is a subject of interest for numerous researchers. What distinguishes the present research from similar works is the consideration of flexibility in the constituent links of this type of robotic systems. This is not a far-fetched assumption because in the transient (impact) phase, due to the impulsive forces which are applied to the system, the likelihood of exciting the vibration modes increases considerably. Moreover, the human leg bones that are involved in walking are supported by viscoelastic muscles and ligaments. Therefore, for achieving more exact results, it is essential to model the robot links with viscoelastic properties. To this end, the Gibbs-Appell formulation and Newton's kinematic impact law are used to derive the most general form of the system's dynamic equations in the swing and transient phases of motion. The most important issue in the passive walking motion of bipedal robots is the determination of the initial robot configuration with which the system could accomplish a periodic and stable gait solely under the effect of gravitational force. The extremely unstable nature of the system studied in this paper and the vibrations caused by the impulsive forces induced by the impact of robot feet with the inclined surface are some of the very serious challenges encountered for achieving the above-mentioned goal. To overcome such challenges, an innovative method that uses a combination of the linearized equations of motion in the swing phase and the algebraic motion equations in the transition phase is presented in this paper to obtain an eigenvalue problem. By solving this problem, the suitable initial conditions that are necessary for the passive gait of this bipedal robot on a sloping surface are determined. The effects of the characteristic parameters of elastic links including the modulus of elasticity and the Kelvin-Voigt coefficient on the walking stability of this type of robotic systems are also studied. The findings of this parametric study reveal that the increase in the Kelvin-Voigt coefficient enhances the stability of the robotic system, while the increase in the modulus of elasticity has an opposite effect.

Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

D. LEE, S. CHANG, J. LEE

2024, 45(5):  819-836.  doi:10.1007/s10483-024-3108-8

Abstract ( 144 )   HTML ( 5)   PDF (2283KB) ( 103 )  

Figures and Tables | References | Supplementary Material | Related Articles | Metrics

This paper presents a new computational method for forward uncertainty quantification (UQ) analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs. The method consists of a generalized polynomial chaos expansion (GPCE) for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set. In the reanalysis, we employ substructuring for a structure to isolate its local regions that vary due to random inputs. This allows for avoiding repeated computations of invariant substructures while generating the input-output data set. Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy. Consequently, the GPCE with the static reanalysis method can achieve significant computational saving, thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs. The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses (FEAs). We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional (all-dependent) random inputs.

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Yu TAN, Fan PENG, Chang LIU, Daiming PENG, Xiangyu LI

2024, 45(5):  837-856.  doi:10.1007/s10483-024-3118-9

Abstract ( 118 )   HTML ( 0)   PDF (1929KB) ( 105 )  

Figures and Tables | References | Related Articles | Metrics

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance. In this paper, a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle. Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations. A staggered algorithm is used to simulate the crack propagation. The polynomial splines over hierarchical T-meshes (PHT-splines) are adopted as the basis function, which owns the C¹ continuity. Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials. The electric boundary conditions may influence crack paths and fracture loads significantly. The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

Parallelization strategies for resolved simulations of fluid-structure-particle interactions

Jianhua QIN, Fei LIAO, Guodan DONG, Xiaolei YANG

2024, 45(5):  857-872.  doi:10.1007/s10483-024-3115-7

Abstract ( 107 )   HTML ( 2)   PDF (14036KB) ( 80 )  

Figures and Tables | References | Related Articles | Metrics

Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows. This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary (IB) method developed in our previous work. For the moving structure modeled using the sharp interface IB method, a recursive box method is developed for efficiently classifying the background grid nodes. For the particles modeled using the diffuse interface IB method, a 'master-slave' approach is adopted. For the particle-particle interaction (PPI) and particle-structure interaction (PSI), a fast algorithm for classifying the active and inactive Lagrangian points, which discretize the particle surface, is developed for the 'dry' contact approach. The results show that the proposed recursive box method can reduce the classifying time from 52 seconds to 0.3 seconds. Acceptable parallel efficiency is obtained for cases with different particle concentrations. Furthermore, the lubrication model is utilized when a particle approaches a wall, enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem. At last, the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.

Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system

Jinghu TANG, Chaofeng LI, Jin ZHOU, Zhiwei WU

2024, 45(5):  873-890.  doi:10.1007/s10483-024-3110-6

Abstract ( 103 )   HTML ( 2)   PDF (2469KB) ( 70 )  

Figures and Tables | References | Related Articles | Metrics

The modeling and self-excited vibration mechanism in the magnetic levitation-collision interface coupling system are investigated. The effects of the control and interface parameters on the system's stability are analyzed. The frequency range of self-excited vibrations is investigated from the energy point of view. The phenomenon of self-excited vibrations is elaborated with the phase trajectory. The corresponding control strategies are briefly analyzed with respect to the vibration mechanism. The results show that when the levitation objects collide with the mechanical interface, the system's vibration frequency becomes larger with the decrease in the collision gap; when the vibration frequency exceeds the critical frequency, the electromagnetic system continues to provide energy to the system, and the collision interface continuously dissipates energy so that the system enters the self-excited vibration state.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

N. D. NGUYEN, T. N. NGUYEN

2024, 45(5):  891-910.  doi:10.1007/s10483-024-3116-5

Abstract ( 151 )   HTML ( 6)   PDF (932KB) ( 182 )  

Figures and Tables | References | Related Articles | Metrics

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams. The analyses include three models for porosity distribution and two scenarios for thermal distribution. The material properties are assessed under two conditions, i.e., temperature dependence and temperature independence. The theoretical framework for the beams is based on the higher-order shear deformation theory, which incorporates shear deformations with higher-order polynomials. The governing equations are established from the Lagrange equations, and the beam displacement fields are approximated by the Chebyshev polynomials. Numerical simulations are performed to evaluate the effects of thermal load, slenderness, boundary condition (BC), and porosity distribution on the buckling and vibration behaviors of metal foam beams. The findings highlight the significant influence of temperature-dependent (TD) material properties on metal foam beams' buckling and vibration responses.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

Dan ZHANG, Liangping YI, Zhaozhong YANG, Jingqiang ZHANG, Gang CHEN, Ruoyu YANG, Xiaogang LI

2024, 45(5):  911-930.  doi:10.1007/s10483-024-3113-9

Abstract ( 140 )   HTML ( 6)   PDF (9641KB) ( 115 )  

Figures and Tables | References | Related Articles | Metrics

A novel phase-field model for the propagation of mixed-mode hydraulic fractures, characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids, is proposed. In this model, the driving force for the phase field consists of both tensile and shear components, with the fluid contribution primarily manifesting in the tension driving force. The displacement and pressure are solved simultaneously by an implicit method. The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson (NR) iterative methods. The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks, and the limitations of the hydraulic fracture expansion phase-field model, which only considers mode Ⅰ fractures, are revealed. In addition, the influence of matrix mode Ⅱ fracture toughness value, natural fracture mode Ⅱ toughness value, and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.