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.

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.

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.

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.

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, 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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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%.

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.

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.

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.

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.

Through establishment of the numerical model and select of the appropriate parameters, this article obtained numerical results of the dynamic response for RC simply supported beam under blast loading. Comparing the  numerical results with the test results, good agreement was achieved. Further, an explosion problem of RC beam with 0.2kg TNT explosive on one end was investigated. The failure modes of the RC beam are analyzed. Extracting displacement-time curves of RC beam at different positions, we can obtain the detailed failure behavior of the RC beam and the process of the entire failure of the component caused by the partial failure. Determination of the blast pressure distribution is useful to simplify the load for the RC beam subjected to this kind of failure. By extracting the reaction forces at the beam ends, it shows that the shearing force at the end subjected to unilateral direct shear is much larger than the force at the other end. Through establishment of the models for three additional approximate conditions, we can know various conditions and risk factors by numerical calculation of the RC beam under unilateral direct shear failure. At the same time, the simplified form of unilateral direct shear failure load can be determined.

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.

Using the numerical simulations of 2-D equations of hydrodynamics，the growth of perturbation and the effects of Grashof number ( ) on convection in a cavity of heating locally from side wall with a Prandtl number   and in a rectangular cell with a high-aspect-ratio A=10 are studied. It is found that the growth rate of perturbation in linear stage of velocity field is a function of  number, and a formula for varition of the growth rate with  number is proposed. The convection pattern develops in the form of steady - periodic - quasi periodic with the increase of  number. Two new types of convection patterns are observed in periodic-stage, which are phase-dislocation and same phase. At last, the influence of the size of cell (d) on the convection amplitude and the heat transfer capability of hot wall is discussed.

A jointed rock slope stability analysis method was developed based on the independent cover meshless particle method (ICMP) and graph theory. In the ICMP method, the analysis model is described with the arbitrary discrete nodes, and a general polynomial is employed as the meshless interpolation function for each discrete node which results in a very simple formulation and numerical implementation. The complex rock joint, rock interface and supporting structure can be easily modeled and simulated in the ICMP. In this work, the ICMP is used to calculate the stress distributions of rock slope with joints, the slope stability analysis is converted to a graph problem. The Bellman-Ford algorithm is used to obtain the slip surface, and the safety factor is defined as the ratio of the resistant force over the slip force along the slip surface. The proposed method is easy to build complex 2D/3D geotechnical engineering numerical models, and removes the difficulties of the iterative calculations for the stability analysis of rock slope. Several typical numerical examples are presented to demonstrate the capability and robustness of the method in rock slope stability analysis.

The analytical solutions of the Yoffe-type moving crack along the interface between piezoelectric bi-materials with strip-like electrical saturation are obtained by using the Fourier transform and the method of Copson. The results show that the size of the electric saturation only depends on the electric load but has nothing to do with the velocity of crack. The stress intensity factor and potential jump at the tip of crack are related to the loads and the material parameters as well as the crack velocity, the stress intensity factor increases with the increase of velocity while the potential jump decreases with the change of velocity.

In order to investigate material’s local mechanical behavior, improved Smoothed Particle Hydrodynamics (SPH) method has been used to solve dynamic plane stress problems. Considering the correction of velocity, density and stress, SPH method has been used to simulate the movement and stress distributions of an elastic cantilever beam under simple harmonic excitation. FORTRAN programs have been developed to calculate the movement period and amplitude, and to compare with the FEM simulation results. Furthermore, the evolutions of normal stress and density at typical positions have been traced. Results showed that the improved SPH method can not only simulate the cantilever beam vibration problem accurately, but also trace the physical quantities of each material point in every single time step so that the structure strength can be detected, showing significant engineering application potential.