Table of Content

01 January 2026, Volume 47 Issue 1

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A novel scaling method for the elastic ring supporting structure of an aero-engine rotor system: analytical and experimental investigations

Lei LI, Tianyue MA, Zhong LUO, Dongwu GAO, Xiangdong GE, Hui MA, Shibin WANG

2026, 47(1):  1-18.  doi:10.1007/s10483-026-3331-6

Abstract ( 35 )   PDF (9417KB) ( 74 )  

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The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.

Deformation and stability of a circular-arc arch compressed by a rigid plate: incorporating tension, shear, and bending

Yunkai TANG, Shengyi TANG, Kai LING, Donghui LIU, Huadong YONG, Youhe ZHOU

2026, 47(1):  19-38.  doi:10.1007/s10483-026-3330-9

Abstract ( 40 )   PDF (1786KB) ( 24 )  

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The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling, arterial stents, and energy harvesting. This has attracted widespread attention from researchers. In this paper, the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension, shearing, and bending. In comparison with the existing models that solely consider the bending energy, the deflection curve, the internal force distribution, and the critical load of the present model show good agreement with the finite element results. Through the dimensional analysis and order-of-magnitude estimation, we examine the factors influencing the critical load. The study reveals that the semi-central angle of the arch has the most significant effect. The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30{}^{\circ }, while Poisson’s ratio and the cross-sectional shear correction factor exhibit negligible influence. Furthermore, the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter, thereby delineating the applicable ranges of both the original model (OM) and the modified model (MM).

Micropolar homogenization constitutive modeling and size effect analysis of lattice materials

Tingrui CHEN, Fan YANG, Jingchun ZHANG, Dong HAN, Qingcheng YANG

2026, 47(1):  39-60.  doi:10.1007/s10483-026-3338-9

Abstract ( 33 )   PDF (2273KB) ( 28 )  

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Lattice materials have demonstrated promising potential in engineering applications owing to their exceptional lightweight, high specific strength, and tunable mechanical properties. However, the traditional homogenization methods based on the classical elasticity theory struggle to accurately describe the non-classical mechanical behaviors of lattice materials, especially when dealing with complex unit-cell geometries featured by non-symmetric configurations or non-single central node connections. In response to this limitation, this study establishes a generalized homogenization model based on the micropolar theory framework, employing Hill’s boundary conditions to precisely predict the equivalent moduli of complex lattice materials. By introducing the independent rotational degree of freedom (DOF) characteristic of the micropolar theory, the proposed model successfully overcomes the limitation of conventional methods in accurately describing the asymmetric deformation and scale effects. We initially calculate the constitutive relations of two-dimensional (2D) cross-shaped multi-node chiral lattices and subsequently extend the method to three-dimensional (3D) lattices, successfully predicting the mechanical properties of both traditional and eccentric body-centered cubic (BCC) lattices. The theoretical model is validated through the finite element numerical verification which shows excellent consistency with the theoretical predictions. A further parametric study investigates the influence of geometric parameters, revealing the underlying size-effect mechanism. This paper provides a reliable theoretical tool for the design and property optimization of complex lattice materials.

The steady-state dynamic contact of a viscoelastic FGM-coated half-plane under a rigid flat punch

Xiaomin WANG, Liaoliang KE, Jie SU, Junhong GUO

2026, 47(1):  61-76.  doi:10.1007/s10483-026-3332-7

Abstract ( 27 )   PDF (389KB) ( 22 )  

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This study explores the dynamic contact response of a viscoelastic functionally graded material (FGM)-coated half-plane under a rigid flat punch subjected to a time-harmonic vertical force. The elastic modulus and mass density of the FGM coating vary exponentially along the thickness direction. The FGM coating and the homogeneous half-plane possess viscoelastic properties, which are described by a linearly hysteretic damping model. By applying the asymptotic method and the Fourier integral transform technique, the contact problem is converted into a Cauchy singular integral equation. The effects of excitation frequency, gradient index, damping factor ratio, and punch width on the vertical impedance and dynamic contact stress are analyzed. The results indicate that adjusting the gradient index of the FGM coating can significantly affect the contact stress and vertical impedance.

Nonlinear characteristics of a magnetorheological bearing-rotor system

Liang MA, Lang MU, Wangchi LAN, Peian LI, Jun WANG, Zhaoye QIN, Fulei CHU

2026, 47(1):  77-98.  doi:10.1007/s10483-026-3333-8

Abstract ( 34 )   PDF (5772KB) ( 30 )  

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Magnetorheological (MR) bearings, with their field-controllable rheological properties, offer new possibilities for control of rotor instabilities. However, their nonlinear dynamic behaviors and the underlying physical mechanisms governing these instabilities remain insufficiently understood. This work develops a coupled MR bearing-rotor system model, where the oil film force is derived from a novel bilinear constitutive equation to capture the field-sensitive shear behaviors of MR fluids. Complex nonlinear dynamic behaviors including period doubling, quasi-period, and chaos are revealed, which emerge from the interaction between oil film vortex dynamics and magnetic excitation. The critical instability mechanism is identified from the evolution of intrinsic dynamic characteristics of MR bearings. When the whirl speed within the oil film reaches approximately half of the rotor speed, the damping force balances the destabilizing force, thereby defining a critical threshold beyond which the system transitions to instability. This threshold can be effectively tuned by adjusting the excitation current, which modifies the yield stress of MR fluids and consequently regulates the damping force. As a result, the nonlinear vibrations of oil whirl and whip can be suppressed, and the system stability can be significantly enhanced. These findings provide both theoretical insight and practical guidance for the design and control of MR bearing supported rotor systems.

Moderately large amplitude forced vibration of sandwich functionally graded auxetic beams: an analytical approach

F. M. NASREKANI, H. EIPAKCHI

2026, 47(1):  99-114.  doi:10.1007/s10483-026-3340-7

Abstract ( 35 )   PDF (807KB) ( 49 )  

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Sandwich functionally graded (FG) auxetic beams are extensively utilized in aerospace, automotive, and biomedical industries due to their excellent strength-to-weight ratio, impact resistance, and tunable mechanical properties. The integration of FG materials with auxetic structures enhances their adaptability in advanced engineering applications. However, understanding their dynamic behavior under external excitations is essential for optimal design and structural reliability. Nonlinear interactions in such structures pose significant challenges in vibration analysis, necessitating robust analytical methods. This study presents a closed-form solution for the nonlinear forced vibration analysis of sandwich FG auxetic beams, offering an accurate and efficient method for predicting their dynamic response. The beam consists of two FG face sheets with material properties varying through the thickness and a re-entrant honeycomb auxetic core with an adjustable Poisson’s ratio. The governing nonlinear equations of motion are derived using the first-order shear deformation theory (FSDT), the modified Gibson model, and the von Kármán relations, formulated through Hamilton’s principle. A closed-form solution is obtained via the Galerkin method and multiple-scale technique. The results demonstrate that FG layers enable control of the overweight and dynamic response amplitude, with positive power law indexes reducing weight. Comparisons with finite element results confirm the accuracy of the proposed formulation.

Multi-material topology optimization under stress constraints of respective materials in multi-physics structures

M. N. NGUYEN, S. JUNG, D. LEE

2026, 47(1):  115-134.  doi:10.1007/s10483-026-3339-6

Abstract ( 43 )   PDF (9706KB) ( 30 )  

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The stress minimization multi-material topology optimization (MMTO) approach has recently attracted significant attention because of its applications in aerospace and mechanical engineering. Nonetheless, the stress minimization MMTO approach may result in stress surpassing the material’s tolerance limit, potentially culminating in failure. This research proposes a novel way for imposing stress constraints on each material to regulate their respective stress levels. The fundamental concept is that each material possesses its own interpolation function for the stress model. The maximum von Mises stress for each material can be established with the definition of an upper limit, ensuring that the materials will perform safely and effectively. This aids topological structures in resisting failure and augmenting strength. A multi-physics system including thermoelastic and self-weight loads is concurrently examined alongside stress limitations. The global stress constraint utilizes the p-norm function, and the adjoint method is used to derive sensitivity. This work employs a three-field strategy utilizing density filtering and Heaviside projection functions to mitigate the artificial stress in low density. The technique is assessed through two-dimensional (2D) and three-dimensional (3D) examples, illustrating the influence of stress limits on the compliance minimization under heat and self-weight loads. The optimized results indicate a substantial decrease in the stress levels accompanied by a minor gain in compliance, while maintaining the stress within the specified range for all materials.

Stiffness and natural vibration of a rotating sandwich metal porous cantilever pre-twisted plate reinforced by graphene

Chengmin NIE, Fu GUO, Yuxin HAO, Xiaojun GU

2026, 47(1):  135-152.  doi:10.1007/s10483-026-3341-8

Abstract ( 31 )   PDF (5233KB) ( 20 )  

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With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors, designing lightweight and high-strength blade structures with excellent dynamic characteristics has become critical. This paper puts forward a dynamic model for a rotating functionally graded graphene-reinforced (FG-GPR) sandwich metal porous cantilever pre-twisted plate (PTP), aiming to analyze its natural vibration characteristics. To this end, the mixture principle and the revised Halpin-Tsai model are used to determine the parameters of graphene and porosity distributions in the core layer. With the classical plate theory, the Rayleigh-Ritz method, and the polynomials, the dynamic equations are derived to solve for the free vibration mode shapes and frequencies of the rotating FG-GPR sandwich metal porous cantilever PTP. The comparison of natural frequencies and mode shapes with available literature results confirms the precision of the theoretical formulation and numerical computations. The bending stiffnesses are analyzed. Finally, the effects of different graphene/pore distributions, length-to-thickness/width ratios, layer thickness ratios, twist angles, and rotational speeds on the natural frequencies of the system are systematically investigated.

Non-Newtonian rivulet flows on an inclined planar surface applying the 2nd Stokes problem

S. V. ERSHKOV, E. S. BARANOVSKII, A. V. YUDIN

2026, 47(1):  153-164.  doi:10.1007/s10483-026-3336-7

Abstract ( 25 )   PDF (190KB) ( 28 )  

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The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface, with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics, are demonstrated in the current research. Hereby, the 2nd Stokes problem assumes that the surface, with a thin shared layer of the fluid on it, oscillates in a harmonic manner along the x-axis of the rivulet flow, which coincides with the main flow direction streaming down the underlying surface. We obtain the exact extension of the rivulet flow family, clarifying the structure of the pressure field, which fully absorbs the arising perturbation. The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity. Hence, the absolutely non-Newtonian case of the viscoplastic flow solution, which satisfies the motion and continuity equations, is considered (with particular cases of exact solutions for pressure). The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation (ODE), describing the dynamics of the coordinate x(t). The approximated schematic dynamics are presented in graphical plots.

Stability of k-\epsilon model in Kolmogorov flow

Jiashuo GUO, Le FANG

2026, 47(1):  165-184.  doi:10.1007/s10483-026-3337-8

Abstract ( 56 )   PDF (7955KB) ( 19 )  

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The Reynolds-averaged Navier-Stokes (RANS) technique enables critical engineering predictions and is widely adopted. However, since this iterative computation relies on the fixed-point iteration, it may converge to unexpected non-physical phase points in practice. We conduct an analysis on the phase-space characteristics and the fixed-point theory underlying the k-\epsilon turbulence model, and employ the classical Kolmogorov flow as a framework, leveraging its direct numerical simulation (DNS) data to construct a one-dimensional (1D) system under periodic/fixed boundary conditions. The RANS results demonstrate that under periodic boundary conditions, the k-\epsilon model exhibits only a unique trivial fixed point, with asymptotes capturing the phase portraits. The stability of this trivial fixed point is determined by a mathematically derived stability phase diagram, indicating the fact that the k-\epsilon model will never converge to correct values under periodic conditions. In contrast, under fixed boundary conditions, the model can yield a stable non-trivial fixed point. The evolutionary mechanisms and their relationship with boundary condition settings systematically explain the inherent limitations of the k-\epsilon model, i.e., its deficiency in computing the flow field under periodic boundary conditions and sensitivity to boundary-value specifications under fixed boundary conditions. These conclusions are finally validated with the open-source code OpenFOAM.

Similarity transformation-based modeling of the thermally-radiative tetra-hybrid Casson nanofluid flow over a nonlinear stretching sheet using the Clique polynomial collocation method

U. L. MANIKANTA, K. J. GOWTHAM, B. J. GIREESHA, P. VENKATESH

2026, 47(1):  185-202.  doi:10.1007/s10483-026-3335-6

Abstract ( 37 )   PDF (562KB) ( 97 )  

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The flow of a tetra-hybrid Casson nanofluid (Al₂O₃-CuO-TiO₂-Ag/H₂O) over a nonlinear stretching sheet is investigated. The Buongiorno model is used to account for thermophoresis and Brownian motion, while thermal radiation is incorporated to examine its influence on the thermal boundary layer. The governing partial differential equations (PDEs) are reduced to a system of nonlinear ordinary differential equations (ODEs) with fully non-dimensional similarity transformations involving all independent variables. To solve the obtained highly nonlinear system of differential equations, a novel Clique polynomial collocation method is applied. The analysis focuses on the effects of the Casson parameter, power index, radiation parameter, thermophoresis parameter, Brownian motion parameter, and Lewis number. The key findings show that thermal radiation intensifies the thermal boundary layer, the Casson parameter reduces the velocity, and the Lewis number suppresses the concentration with direct relevance to polymer processing, coating flows, electronic cooling, and biomedical applications.

A hybrid method based on particle swarm optimization and machine learning algorithm for predicting droplet diameter in a microfluidic T-junction

F. ESLAMI, R. KAMALI

2026, 47(1):  203-214.  doi:10.1007/s10483-026-3334-9

Abstract ( 28 )   PDF (352KB) ( 33 )  

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Droplet-based microfluidics is a transformative technology with applications across diverse scientific and industrial domains. However, predicting the droplet size generated by individual microchannels before experiments or simulations remains a significant challenge. In this study, we focus on a double T-junction microfluidic geometry and employ a hybrid modeling approach that combines machine learning with metaheuristic optimization to address this issue. Specifically, particle swarm optimization (PSO) is used to optimize the hyperparameters of a decision tree (DT) model, and its performance is compared with that of a DT optimized through grid search (GS). The hybrid models are developed to estimate the droplet diameter based on four parameters: the main width, side width, thickness, and flow rate ratio. The dataset of more than 300 cases, generated by a three-dimensional numerical model of the double T-junction, is used for training and testing. Multiple evaluation metrics confirm the predictive accuracy of the models. The results demonstrate that the proposed DT-PSO model achieves higher accuracy, with a coefficient of determination of 0.902 on the test data, while simultaneously reducing prediction time. This methodology holds the potential to minimize design iterations and accelerate the integration of microfluidic technology into the biological sciences.