Doubly-curved shells are common thin-walled structural components in airplanes, automobiles and ships, in which their neutral plane can be regarded as a curved surface formed by sweeping one moving curve along another curve. The development of the nonlinear shell theory promotes the study of mechanical behavior of doubly-curved shells. With the continuous progress of practical engineering applications, such as the introduction of functionally-graded materials (FGM), stiffener shell, elastic foundation model, the research on strength, deformation and stability of doubly-curved shells is further promoted. This paper
reviews the development of nonlinear theories for doubly-curved shells. In particularly, theoretical background and basic formulations in the Donnell thin shell theory, the first order shear deformation shell theory, the higher order shear deformation theory, and 3D shell model are reviewed, and the relevance and differences among these theories are stated. Then, the latest research achievements on the nonlinear bending, the stability and the dynamics of doubly-curved shells are introduced. Finally, current limitations and needs in the area of mechanics of doubly-curved shells are discussed.

Compared to traditional alloys, high-entropy alloys exhibit significant atomic-scale lattice distortion, which endows them with excellent mechanical, chemical, and biological properties, granting them broad application prospects in engineering and biomedical fields. This article briefly reviews recent research progress in the experimental characterization, multi-scale simulations, and mechanical modeling of the lattice distortion effects in high-entropy alloys. Quantifying lattice distortion is a key challenge in the field, providing essential atomic-scale information for multi-scale simulations and mechanical modeling. Through hierarchical multi-scale simulation methods, which integrate small-scale simulations such as molecular dynamics and discrete dislocation dynamics, microstructural parameters can be extracted to inform macroscopic crystal plasticity models, thereby revealing the influence mechanisms of lattice distortion on mechanical behavior. Furthermore, by accounting for atomic size mismatch and shear modulus mismatch, corresponding mechanical models for lattice distortion strengthening have been developed.

All-solid-state lithium metal batteries (ASSLMBs) are promising substitutes for traditional lithium-ion batteries as the next generation of mobile storage thanks to their high energy density and low risk of fire hazard. However, the all-solid-state structure also brings new challenges to the wide application of ASSLMBs, which hinders their commercialization process. One of the most critical challenges is their mechanical instability. First, although solid electrolytes are expected to suppress lithium dendritic growth because of their high stiffness and strength, lithium dendrite can still be observed during charge and discharge, which is against the intuition that "strong" electrolyte can resist lithium dendrite. Secondly, compared with the liquid electrolytes, the solid electrolytes are much stiffer, making it much more difficult to maintain effective contact with active materials during charging and discharging cycles, which may lead to interface delamination between active particles and electrolyte. Hence, it is important to understand the mechanisms of these phenomena and provide solutions to promote the application of ASSLMBs. The purpose of this paper is to summarize the mechanically coupled models that account for interfacial failure of ASSLMBs in recent years, and it consists of two aspects: (1) the formation and growth of lithium dendrites at the lithium metal anode/solid electrolyte interface; (2) interfacial delamination and fragmentation caused by lithiation/delithiation of active particles. In this paper, the mechanical failure at different interfaces in ASSLMBs are summarized from the perspective of theoretical modeling, in order to provide reference ideas for the modeling and structural optimization of ASSLMBs.

In order to explore the applicability of self-piercing riveting (SPR) technology in aluminum alloy-copper foam "sandwich" structure, the connectivity of the joints was analyzed by the riveting tests using two kinds of copper foam with the thicknesses of 1.0mm and 1.5mm as interlayer sheet. The forming quality of the joints was observed by the visual inspection method. The static performance and failure mechanism of the joints were analyzed by static experiments. The results show that the SPR technology can realize the connection of aluminum alloy sandwich sheets embedded with copper foam effectively. The copper foam interlayer increases the residual thickness of the joint, which increases the static failure load of the joint. The copper foam of 1.5mm thick causes static failure load of SPR joint increase by 7.7%. The thicker the copper foam is, the more obvious its influence on the performance of the SPR joint is.

For an infinite thin plate with a circular hole and a nonhomogeneous ring, the analytical solution of stress concentration factor under biaxial tension and the series solution under pure shear are derived by assuming that the elastic modulus varies exponentially while Poisson’s ratio keeps constant. The influence of the variation of the elastic modulus on the stress concentration factor is analyzed in detail. The results of numerical examples show that the stress concentration can be relieved effectively by tuning the material parameters of the nonhomogeneous material. The solutions obtained in this paper can provide some reference for the design of the thin plate with a circular hole.

The principle of local action plays an important role in the development of constitutive relations of classical continuum mechanics, and the theory of simple materials that is derived from this principle has been widely applied. However, with the development of science and technology, various new materials which have microstructures are emerging. It has been theoretically and experimentally demonstrated that nonlocal theories may better depict the macroscopic behavior of these materials. In this article, we briefly review some traditional nonlocal elasticity theories, including the Eringen theory, the Kunin theory, the Mindlin theory, and the Willis theory that is developed for composite materials and is characterized by temporal and spatial nonlocality, the newly developed spatiotemporal nonlocal elastodynamic theory, and the peridynamic theory. The spatiotemporal nonlocal theory reflects the inherent nonlocal characteristics of the macroscopic properties of composite materials, and the spatially nonlocal peridynamic theory facilitates processing problems with discontinuities. Finally, we point out some issues that may deserve consideration in the development of nonlocal theories.

Crack propagation, aggregation, bifurcation plays the key role in the failure of brittle materials such as rock. In this paper, after verifying the effectiveness of the peridynamics in studying the crack dynamic growth of rock materials, the numerical simulations of rock with prefabricated double cracks under impacting loading, and rock with the pre-notch single crack under compression loading are carried out by using peridynamics method. The results show that for the pre-notch double vertical crack, the crack propagation path is approximately 70°from the pre-notch crack. For the pre-notch single crack, the crack propagation trajectory changes with the crack orientation angle, finally resulting in the overall failure of the component. The numerical simulation results show that the peridynamics can well simulate the propagation of cracks in brittle materials such as rocks, up to the failure status, and reflect the physical mechanism of crack propagation. As a new numerical method based on the nonlocal theory, peridynamics has very good application prospects in underground engineering and shale gas exploration.

In this paper, the boundary knot method is used to solve three-dimensional high frequency sound field. Because the solution of high frequency Helmholtz equation is oscillatory, which greatly affects the accuracy of numerical solution, it is necessary to add discrete points in the computational region, leading to the increase of calculation cost. At the same time, for large-scale acoustic problems, the interpolation matrix formed by the boundary knot method is full rank, resulting in excessive computation and excessive storage. The introduction of matrix compression technology can effectively reduce the memory requirement and time while at the same time effectively inherits the high accuracy of the boundary node method, leading to a significant improvement of the computational efficiency. Numerical experiments show that MC-BKM has high accuracy, fast convergence speed and less computation time, and has a wide application prospect in high frequency large scale acoustic wave problems.

In this paper, a cell model of porous concrete is established using Monte Carlo simulation and a bidirectional walk method. By using nanoindentation technique, the microscopic mechanical properties of each phase of concrete are obtained. The asymptotic homogenization theory is then used to predict the effective modulus of elasticity of concrete and evaluate the effect of pores with increasing freeze-thaw cycles, in comparison with numerical finite element analysis. The results show that as the volume fraction of pores increases due to increased freeze-thaw cycles, the indentation moduli of the interface and mortar decrease obviously and the one of aggregate seldom changes, resulting in the decrease of macroscopic modulus of elasticity of concrete. The theoretical analysis results are in good agreement with finite element simulation. The cell model of porous concrete is effective in predicting the modulus of elasticity of concrete, and it paves the foundation for evaluating aging mechanism of concrete under freeze-thaw actions.

We solve the elasto-static boundary-value problem of finite-size plates containing elliptical holes using the complex series expansion. Instead of using the usual conformal mapping which maps the elliptical hole into a circular hole, we calculate the coefficients of the series using the least square method that minimizes the difference between the calculated boundary traction and the given boundary condition. This method avoids the conformal mapping and thus greatly simplifies the procedure of solution. By comparison with the results of the finite element computation, we show that for a rectangular plate containing a central elliptical hole with a ratio of axes between 0.7 and 2.0, the stress concentration factors given by the complex series are quite accurate, and the method is much simpler than the conventional conformal mapping method and is easy to use. Moreover, we also give empirical formulas that calculate the stress concentration factors for a plate containing an elliptical hole (hole axes ratio 0.8, plate aspect ratio greater than 2) under uniaxial tension and a plate containing a circular hole (plate aspect ratio greater than 1) under shear. These formulas are simple and easy to use.

The multi-field coupling problems concerning chemical processes of solids involve complex kinetics of interactive material constituents driven by multiple thermodynamic forces in an open system. These processes may behave on different space-time scales and induce the evolution of material properties. The attempts to understand their thermodynamic mechanisms, to elucidate how chemical reactions and mechanical behaviors interact, and to develop theoretical models are vital important, not only for optimization design of material functionalities or prediction of structural performances, but also for development of modern solid mechanics. Within the context of these ubiquitous multi-field problems in diverse applications, this review summarizes the recent advance in theoretical modeling and applications of thermo-chemo-mechanically coupling problems of solids. Published works are reviewed regarding three categories including transport-deformation problems, chemical reaction-deformation problems and fully coupled thermo-chemo-mechanical problems. The critical issues in theoretical modeling are discussed, and some development trends in this area are briefly summarized to provide a theoretical guidance for the related research in the future.

Peridynamics are based on continuum theory considering the interaction of non-local forces, calculated by direct integration of the finite domain instead of the stress/strain relationship of classical elasticity. This method avoids the singularity of the traditional local equation in solving the discontinuous problem and the complexity of the existing multi-scale algorithm, and has the same advantages in dealing with multi-physics problems. In this paper, the problems of inclined crack propagation in functionally graded materials under dynamic tensile loading are studied based on peridynamics. The propagation path and failure mode of the oblique crack of the functionally graded material are given, and the influence of the gradient form of the material on the crack propagation behavior is discussed. It can be found from the results that the crack always propagates along the horizon direction and the graded form of the material has little influence on the propagation behavior.

Numerical dissipation for water-oil displacement problems not only cuts down accuracy of the numerical solutions, but also may introduce grid orientation effect. To reduce the influence of numerical dissipation, Finite Analytical Method and Range Discrete Grid method are introduced to solve the pressure equation and saturation equation, respectively. Numerical examples show that, sharpness of saturation discontinuities can be maintained by the proposed method, and numerical dissipations are sufficiently suppressed. Comparison with classical Finite Difference Method shows that the grid orientation effect is the mixed results of the physical instability and numerical dissipation of Finite Difference Method.

An analytical model is constructed for the homogeneous deformation of liquid crystal gel (LCG) membranes under coupled electro-mechanical action through inverse methods based on infinitesimal strain assumption. The results indicated that both electric field and tensile stress can rotate the LC director to their directions. There is a critical electric field intensity at which the initially perpendicularly oriented LC director will start to reorient. Tensile stress can enhance this threshold significantly. However, the director will start to rotate immediately under electric fields if it is not initially perpendicular to the applied electric field. The behavior of director rotation and the macroscopic deformations depend strongly on the initial alignment. Therefore the mechanical behaviors of LCG could be regulated and controlled through proper design of the initial alignment and right choice of the electro-mechanical loading.

A direct, explicit compressible multi-axial strain energy potential is proposed to simulate the deformation behavior of rubber-like materials up to softening and failure. First, a multi-axial strain energy function is given out. Second, the multi-axial strain energy can reduce to the one-dimensional shape function via specific invariables under the condition of uniaxial tension, equi-axial tension, and plane strain, respectively. Third, we explicitly give out the shape function up to failure. Finally, the model result can exactly match the test data, and further predict the behavior after the break point.

This paper studies the plane-stable walking control of quasi-passive biped robots. The biped robot system adopts the spring-mass model to obtain the dynamic equations of the single support phase and the double support phase within the system by using Lagrangian method, and obtain the periodic solution for the dynamic equation of the robot system. The controller design in this system is based on the nonlinear state feedback linearization theory, and achieves stable cycle walking by controlling the length of the telescopic leg of the biped robot. Based on the theoretical analysis, this paper simulates and studies the control algorithm. The simulation results show that the variable length control algorithm used in this paper can not only make the biped robot overcome the external interference during the period of walking, but also make it strong anti-interference.

Continuous Tow Shearing (CTS) technology is a new manufacturing technology of Variable Angle Tow (VAT) composite laminates. This new technology can significantly reduce the defects of composite such as tow overlap and tow gap, and so on. However, the thickness of laminates will change with the variation of fiber angle when laying with CTS technology. Based on the first-order shear deformation theory and the Chebyshev-Ritz method, the thermal buckling of VAT composite laminates with variable thickness is studied in this paper. Assumed that the fibre angle of each ply varies linearly along the length of composite
laminate, the critical thermal buckling load of VAT composite plate under uniform temperature rise is obtained. The correctness of this method is verified by comparing with the existing literature. The effects of fibre laying technology, fibre orientation angle and boundary conditions on the critical buckling temperature of VAT composite laminates are further discussed in numerical examples. The results show that the critical buckling temperature of VAT laminates fabricated by CTS can be further increased than those by AFP under the same volume. The results obtained here can provide a reference for the design of VAT composite laminates.

In this study, bio-inspired tadpole swimming is investigated numerically by solving the three-dimensional Navier-Stokes equations for the unsteady incompressible viscous flow. The hydrodynamics and vortex structures in the flow field are analyzed. The influence of various controllable parameters is studied. Also, the effect of tadpole’s blunt snout and its specific kinematics is discussed in detail. The results show that the wake vortex structures vary with the fluid force on the tadpole. In addition, the kinematics of tadpoles is closely matched to their special shape.

Cable-buoy systems serve as critical components in ocean engineering, where their dynamic response under complex flow conditions is directly linked to structural safety and functionality. The fluid drag force is a key factor influencing their dynamic behavior and is commonly modeled using the Morison equation, which can be formulated in either an absolute or a relative velocity framework. The absolute velocity model captures fluid-structure interaction more comprehensively but introduces mathematical complexity that challenges nonlinear vibration analysis. In contrast, the relative velocity model is widely adopted due to its simplicity and computational efficiency, though its approximation errors warrant further investigation. This study aims to systematically compare these two drag force models in the context of nonlinear dynamic response analysis of cable-buoy systems. Based on elastic cable theory, nonlinear governing equations are derived for both models, and the intrinsic modal characteristics of the system are examined through linear vibration analysis, with particular attention to the Veering phenomenon and the associated strong modal coupling. Direct numerical integration is then performed to compare system responses under different reference frames. The results indicate that the coupling term between current velocity and structural velocity in the absolute velocity model enhances system damping, leading to smaller predicted response amplitudes compared with the relative velocity model. In the strong coupling regions where modal Veering occurs, discrepancies between the two models are significantly amplified, but the overall impact on global dynamic behavior remains limited. Therefore, the study reveals that under conditions of low current velocity, dominant structural damping, or engineering applications with moderate accuracy requirements, the relative velocity model, despite its approximation errors, serves as an efficient and practically valuable simplification. This conclusion provides theoretical guidance for the rational selection of drag force models in the engineering design of cable-buoy systems.

Stiffness is a quantitive characterization of the elastic deformation of the material, which is closely related to the static and dynamic characteristics of a DNA nanotube and its structural bio-functions. This paper focuses on the torsional rigidity of a DNA nanotube. First, under the condition of the hexagonal homogenous packing, considering the statically indeterminate characteristic for bending-torsional coupling problem of a single DNA bar, the bending-torsional coupling deformation of a single DNA bar in the torsional experiment of DNA nanotubes was accurately predicted by using the equilibrium equations, the deformation compatibility equations and the elastic constitutive equations. An analytical model for predicting the torsional rigidity of a DNA nanotube was thereafter presented. The results show that the bending rigidity is greatly increased whereas the torsional rigidity is almost not changed with increase of the number of DNA bars, which well explains the phenomenon found in the torsional experiment. The related conclusion can provide useful information for design and application of DNA folding structures.

An elastomer, long polymers cross-linked by chemical bonds, may imbibe solvents, aggregating into a polymeric gel. Many scholars have studied polymeric gels based on Flory-Rehner free energy function without giving any consideration to the influence of chain entanglements on the mechanical behavior of gels. In this paper, a new hybrid free energy function was constructed by combining the Edwards-Vilgis slip-link model and the Flory-Huggins solution theory, in which the influence of entanglements has been taken into consideration. In the light of the reformed free energy function, a theory of coupled large deformation and diffusion in polymeric gels is constructed by combining the kinematics of large deformation and migration of solvent molecules. In the end, the influence of entanglements upon the deformation gradient and the nominal concentration of solvent in the gel is demonstrated.

Underfill is widely used in electronics industry to enhance the stability and reliability of electronic products working in harsh environments. In this paper, thermostresses are calculated for the interconnection of IC package with underfill based on the meso-mechancis models. Utilizing the periodic characteristics in the structure of the solder-underfill interconnection, a homogenization model is established. The equivalent modulus, coefficient of thermal expansion (CTE), and the thermal conductivity are deduced theoretically. The homogenization model is then used to calculate the temperature and the thermo-stresses for the problem of heat generation by the working chip using finite element (FE) simulations. The proposed method generates results that agree well with the conventional FE simulations without interconnection homogenization, and at the same time possesses much higher computational efficiency. The results demonstrate the feasibility of the proposed method in the thermostress calculation of electronics.

Dragonfly wings possess unique morphologies with corrugations. Utilizing the bionic principle, researchers were working on creating corrugated airfoils with better aerodynamic performance in low Reynolds numbers. In this paper, aerodynamic performances of four airfoils (flat airfoil, streamline airfoil, corrugated airfoils with lower amplitudes and corrugated airfoils with higher amplitudes) were calculated by solving the 2-D incompressible Navier-Stokes equations with the CFD method. Then we got results in conditions of low Reynolds numbers as follows: (1) the corrugations with lower amplitudes could increase the lift and decrease the drag. (2) The lift of corrugated airfoil changed nonlinearly when the Reynolds number varied. (3) The drag reduction was due to recirculation zones within corrugations as they decreased the viscous drags. (4) The lift was under a significant influence of pulsing high-lift generated at the leading edge of the airfoils. These results demonstrated that the adjustment of corrugation amplitude would be an effective method to achieve the aerodynamic optimization of corrugated airfoils.

In order to realize the sustainable development of nuclear energy, research and development for the Generation-IV advanced nuclear systems need to be performed. They should have the characteristics being of high safety and economic benefits together with minimal wastes and proliferation resistance. Accelerator-driven Subcritical System is such a kind of advanced system. The performances of nuclear fuels directly relate to the safety, the economic benefits and the reliability of nuclear reactors, and dispersion nuclear fuels have a promising application prospect in advanced nuclear systems. Dispersion nuclear fuels are a kind of heterogeneous fuel, similar to particle composites in the structure, and are also called inert-matrix fuels (IMF). Mainly for the dispersion nuclear fuels used in ADS, the key mechanical problems under the high-temperature, high-pressure and irradiation environment are given in this review and the characteristics of multi-scale and multi-field coupling are elaborated. Besides, the relevant research status and progress in theoretical modeling and numerical solution are given and some research trends are pointed out.

In this paper, LES research is carried out on pre-mixing combustion of methane and air in a sudden expansion combustion chamber. The influence of the equivalence ratio of premixed fuel on power supplied for the combustion chamber and the generated pollutants is mainly studied. By means of LES approach, distributions of temperature, concentration, vorticity and pressure of the reaction flow field of turbulent premixed combustion in the combustion chamber under different equivalence ratios are obtained. Finally, the EMD decomposition of the temperature field and velocity field at Point B and C of 0.5 equivalence ratio is carried out, and the average period of each mode of temperature and velocity field is obtained. Analysis results show that as the equivalence ratio increases from 0.5 to 0.7, the combustion reaction becomes more intense. The maximum temperature of the combustion chamber is increased by 350K, the average pressure increases from 32.876pa to 34.833 Pa, and the maximum transient radial concentration from combustion increases from 0.5% to 0.95%.

Particle accumulation is a common phenomenon in geological engineering, and its stable repose angle can reflect the basic feature of particle accumulation to a certain extent. The DEM method is used to study the accumulation process of particles with different density distributions, which can help us to study the effect of particle density on the particle accumulation results and verify the rationality of particle accumulation simulations by DEM method. This study uses circular particles to simplify the simulation of granular particles. The first step is to establish the relevant model with EDEM software and to generate simplified particles in the model. It simulates the process of free falling and accumulation stability of particles under gravity. In the second step, after the particle falling and accumulation are stabilized, the bottom boundary of the model is retained, and the upper boundary of the model is removed. The repose angle of the accumulation body is then measured. The third step is to conduct relevant experimental tests to compare with the numerical model for verification purpose. The results show that the smaller the density of the deposited granular material is, the larger the resting angle is after the accumulation is stable, when considering the effect of the density of particles and neglecting the influence of other parameters.

This paper focused on experimental research of the effect of steady torsion on mode I fatigue crack growth in two kinds of automobile steel sheet, SAPH440 and DP780. The effects of different steady torsion values combined-with same cyclic tension loading were discussed. The experimental results showed that steady torsion significantly retarded mode I fatigue crack growth rate in both types of steel sheet. It decreased with increased constant torque when the torque was smaller than the critical value at which crack growth rate was slowest; otherwise, the retarding influence started to weaken. Procedure of crack propagation in automobile steel sheet under mode I fatigue loading with a steady torsion was divided into the initial low-rate section and the subsequent accelerating section since crack growth rate was very low initially but increased rapidly subsequently with increase of crack length. To describe the crack growth rate data of the subsequent accelerating section, an effective stress intensity factor range and the modified Paris law were proposed based on linear elastic fracture mechanics.

The controller order for active flutter suppression of a flexible wing is usually very high and aerodynamic states of the wing is unobservable. In this paper, sub-optimal control based on partial-state feedback for flutter suppression of a flexible wing is investigated, and the control effectiveness by the sub-optimal controller is compared with that by the full-state optimal controller. Firstly, the state-space aeroservoelastic model of the flexible wing with control surface is given, and optimal controller with full-state feedback is designed. Then, the importance of each state variable on the performance of control is studied using the second-order sensitivity of the performance index with respect to the control gain to determine the important state variables of the wing that are used for control feedback. Finally, the effectiveness of sub-optimal controller is compared with optimal controller through numerical simulations. Simulation results show that the importance of state variables can be effectively determined by the second-order sensitivity, and the sub-optimal controller can achieve nearly the same control effect as the optimal controller with full-state feedback. The suboptimal controller designed in this paper does not use the aerodynamic states and the controller order is lower, so it shows more engineering significance.

Curved beam are a common thin-walled structure in bridge, building, ship, airplane and aerospace. It is referred to as the arch or the planar curved beam according to the relationship between the external load and the principal curvature plane. The application of the curved beams is expanded by the development of engineering materials, such as the composite material and the functionally-graded material (FGM), which further promotes the research on the stability of curved beams. The buckling mode of thin-walled beam is discussed firstly, with the basic assumptions of thin-walled structures elaborated. The linear and nonlinear theories of isotropic thin-walled curved beams are reviewed, where the relevance and difference among those theories are discussed, and the constitutive behavior is summarized for the composite laminated curved beam. The differential governing equation is derived based on the equilibrium principle, the energy principle and the virtual principle of displacement. Three methods, i.e., the closed-form analytical method, the semi-analytical method and the numerical method, are used to solve the stability behavior of thin-walled curved beams. The importance of the bearing capacity tests on the curved beams for verifying the accuracy of the thin-walled curved beam theory is emphasized. Finally, the current limitations and the future perspectives in the research area of thin-walled curved beams are discussed.

Fractional derivative calculation method based on fractional gene is adopted in this paper, and the canonical equations of conservative fractional singular systems are derived from the Hamilton variational principle. The invariance of system differential and algebraic equations under infinitesimal transformations is further discussed, and the criterion equation of Lie symmetry is given. Through the structural equation of Lie symmetry, the conserved quantities in phase space are obtained. Finally, an example is given to illustrate the application of the proposed approach.