Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy projection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method (FEM) by recursive application of the one-dimensional (1D) element energy projection (EEP) technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element (FE) model is reached. This conceptual dimension-by-dimension (D-by-D) discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional (2D) and three-dimensional (3D) problems can be obtained over the domain. Numerical examples of 3D Poisson’s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.     

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.     

Nonlinear viscoelastic multi-scale repetitive unit cell model of 3D woven composites with damage evolution

Three-dimensional (3D) textile composites have great potential applications to aircrafts and high speed vehicles because of the high strength/weight ratios and the capabilities of manufacturing complex, net-shape preforms. This paper reports the nonlinear viscoelastic responses and damage mechanisms of one kind of 3D textile composites, named as 3D orthogonal woven composite (3DOWC) under quasi-static tensile loading based on a micro/meso-scale repetitive unit cells (RUCs) model. In the RUCs model, the resin is described with a nonlinear viscoelastic material and the fibers/tows with an elastic material. The damage initiation and propagation in resin are simulated by the post-damage constitutive models with maximum principal theory failure criteria. The fibers/tows impregnated with resin are defined by elastic transverse-isotropic material model with ultimate strengths failure of ‘expanded smeared crack’ both along and perpendicular to fibers/tows axis direction. The engineering parameters and ultimate strengths of homogenized fibers/tows filled with matrix in meso-RUCs model are transferred from the numerical analysis of the micro-RUCs. The results are compared with experimental and theoretical values of RUC deformation and damage initiation and propagation under monotonic axial loading. The methodology of establishing the nonlinear visco-elastic multi-scale model of 3D textile composites without introducing the real fabric architecture in finite element analyses is explained. With the multi-scale RUCs model, the mechanical behaviors of other kinds of 3D textile composites can also be predicted.     

Investigation of horizontal-axis wind turbine (HAWT) blade threedimensional rotational effect based on field experiments

Field experiments are performed on a two-bladed 33 kW horizontal-axis wind turbine (HAWT). The pressures are measured with 191 pressure sensors positioned around the surfaces of seven spanwise section airfoils on one of the two blades. Three-dimensional (3D) and two-dimensional (2D) numerical simulations are performed, respectively, on the rotor and the seven airfoils of the blade. The results are compared with the experimental results of the pressure distribution on the seven airfoils and the lift coefficients. The 3D rotational effect on the blade aerodynamic characteristics is then studied with a numerical approach. Finally, some conclusions are drawn as follows. From the tip to the root of the blade, the experimental differential pressure of the blade section airfoil increases at first and then decreases gradually. The calculated 3D result of the pressure distribution on the blade surface is closer to that of the experiment than the 2D result. The 3D rotational effect has a significant impact on the blade surface flow and the aerodynamic load, leading to an increase of the differential pressure on the airfoils and their lift coefficient than that with the 2D one because of the stall delay. The influence of the 3D rotational effect on the wind turbine blade especially takes place on the sections with flow separation.     

Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity

The main objective of this paper is to develop a generalized finite element formulation of stress integration method for non-quadratic yield functions and potentials with mixed nonlinear hardening under non-associated flow rule. Different approaches to analyze the anisotropic behavior of sheet materials were compared in this paper. The first model was based on a non-associated formulation with both quadratic yield and potential functions in the form of Hill’s (1948). The anisotropy coefficients in the yield and potential functions were determined from the yield stresses and r-values in different orientations, respectively. The second model was an associated non-quadratic model (Yld2000-2d) proposed by Barlat et al. (2003). The anisotropy in this model was introduced by using two linear transformations on the stress tensor. The third model was a non-quadratic non-associated model in which the yield function was defined based on Yld91 proposed by Barlat et al. (1991) and the potential function was defined based on Yld89 proposed by Barlat and Lian (1989). Anisotropy coefficients of Yld91 and Yld89 functions were determined by yield stresses and r-values, respectively. The formulations for the three models were derived for the mixed isotropic-nonlinear kinematic hardening framework that is more suitable for cyclic loadings (though it can easily be derived for pure isotropic hardening). After developing a general non-associated mixed hardening numerical stress integration algorithm based on backward-Euler method, all models were implemented in the commercial finite element code ABAQUS as user-defined material subroutines. Different sheet metal forming simulations were performed with these anisotropic models: cup drawing processes and springback of channel draw processes with different drawbead penetrations. The earing profiles and the springback results obtained from simulations with the three different models were compared with experimental results, while the computational costs were compared. Also, in-plane cyclic tension–compression tests for the extraction of the mixed hardening parameters used in the springback simulations were performed for two sheet materials.     

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

The natural dynamic characteristics of a circular cylindrical tube made of three-directional(3 D) functional graded material(FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse,and rotation deformations. By dint of the differential quadrature method(DQM), the governing equations are discretized to conduct the analysis of natural dynamic charact...     

The effects of shear on delamination in layered materials

The effect of transverse shear on delamination in layered, isotropic, linear-elastic materials has been determined. In contrast to the effects of an axial load or a bending moment on the energy-release rate for delamination, the effects of shear depend on the details of the deformation in the crack-tip region. It therefore does not appear to be possible to deduce rigorous expressions for the shear component of the energy-release rate based on steady-state energy arguments or on any type of modified beam theory. The expressions for the shear component of the energy-release rate presented in this work have been obtained using finite-element approaches. By combining these results with earlier expressions for the bending-moment and axial-force components of the energy-release rates, the framework for analyzing delamination in this type of geometry has been extended to the completely general case of any arbitrary loading. The relationship between the effects of shear and other fracture phenomena such as crack-tip rotations, elastic foundations and cohesive zones are discussed in the final sections of this paper.     

Green’s functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper, we obtain Green’s functions of two-dimensional (2D) piezoelectric quasicrystal (PQC) in half-space and bimaterials. Based on the elastic theory of QCs, the Stroh formalism is used to derive the general solutions of displacements and stresses. Then, we obtain the analytical solutions of half-space and bimaterial Green’s functions. Besides, the interfacial Green’s function for bimaterials is also obtained in the analytical form. Before numerical studies, a comparative study is carried out to validate the present solutions. Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force, the line dislocation, the line charge, and the phason line force. As a result, the coupling effect among the phonon field, the phason field, and the electric field is prominent, and the butterfly-shaped contours are characteristic in 2D PQCs. In addition, the changes of material parameters cause variations in physical quantities to a certain degree.     

Parabolic metamaterials and Dirac bridges

A new class of multi-scale structures, referred to as ‘parabolic metamaterials’, is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which correspond to so-called ‘Dirac bridges’ on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the ‘parabolic metamaterial’ regimes.     

Finite element modeling of elasto-plastic contact between rough surfaces

This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an elasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elasto-plastic response of the material is described by a J₂ isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. In all cases, the contact area A rises linearly with the applied load. The rate of increase grows as the yield stress σ_y decreases, scaling as a power of σ_y over the range typical of real materials. Results for A from different plasticity laws and surface morphologies can all be described by a simple scaling formula. Plasticity produces qualitative changes in the distributions of local pressures in the contact and of the size of connected contact regions. The probability of large local pressures is decreased, while large clusters become more likely. Loading-unloading cycles are considered and the total plastic work is found to be nearly constant over a wide range of yield stresses.     

3D Numerical heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with electrohydrodynamic enhancement

Three-dimensional laminar fluid flow and heat transfer over a four-row plate-fin and tube heat exchanger with electrohydrodynamic (EHD) wire electrodes are studied numerically. The effects of different electrode arrangements (square and diagonal), tube pitch arrangements (in-line and staggered) and applied voltage (V_E=0–16 kV) are investigated in detail for the Reynolds number range (based on the fin spacing and frontal velocity) ranging from 100 to 1,000. It is found that the EHD enhancement is more effective for lower Re and higher applied voltage. The case of staggered tube pitch with square wire electrode arrangement gives the best heat transfer augmentation. For V_E=16 kV and Re = 100, this study identifies a maximum improvement of 218% in the average Nusselt number and a reduction in fin area of 56% as compared that without EHD enhancement.     

Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires

Previous atomistic simulations and experiments have shown an increased Young's modulus and yield strength of fivefold twinned (FT) face-centered cubic metal nanowires (NWs) when compared to single crystalline (SC) NWs of the same orientation. Here we report the results of atomistic simulations of SC and FT Ag, Al, Au, Cu and Ni NWs with diameters between 2 and 50 nm under tension and compression. The simulations show that the differences in Young's modulus between SC and FT NWs are correlated with the elastic anisotropy of the metal, with Al showing a decreased Young's modulus. We develop a simple analytical model based on disclination theory and constraint anisotropic elasticity to explain the trend in the difference of Young's modulus between SC and FT NWs. Taking into account the role of surface stresses and the elastic properties of twin boundaries allows to account for the observed size effect in Young's modulus. The model furthermore explains the different relative yield strengths in tension and compression as well as the material and loading dependent failure mechanisms in FTNWs.     

An experimental study of the combustion characteristics in SCCI and CAI based on direct-injection gasoline engine

Emissions remain a critical issue affecting engine design and operation, while energy conservation is becoming increasingly important. One approach to favorably address these issues is to achieve homogeneous charge combustion and stratified charge combustion at lower peak temperatures with a variable compression ratio, a variable intake temperature and a trapped rate of the EGR using NVO (negative valve overlap). This experiment was attempted to investigate the origins of these lower temperature auto-ignition phenomena with SCCI and CAI using gasoline fuel. In case of SCCI, the combustion and emission characteristics of gasoline-fueled stratified-charge compression ignition (SCCI) engine according to intake temperature and compression ratio was examined. We investigated the effects of air–fuel ratio, residual EGR rate and injection timing on the CAI combustion area. In addition, the effect of injection timing on combustion factors such as the start of combustion, its duration and its heat release rate was also investigated.     

Micromechanical analysis of kinematic hardening in natural clay

This paper presents a micromechanical analysis of the macroscopic behaviour of natural clay. A microstructural stress–strain model for clayey material has been developed which considers clay as a collection of clusters. The deformation of a representative volume of the material is generated by mobilizing and compressing all the clusters along their contact planes. Numerical simulations of multistage drained triaxial stress paths on Otaniemi clay have been performed and compared the numerical results to the experimental ones in order to validate the modelling approach. Then, the numerical results obtained at the microscopic level were analysed in order to explain the induced anisotropy observed in the clay behaviour at the macroscopic level. The evolution of the state variables at each contact plane during loading can explain the changes in shape and position in the stress space of the yield surface at the macroscopic level, as well as the rotation of the axes of anisotropy of the material.     

A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming

In this paper an anisotropic material model based on non-associated flow rule and mixed isotropic–kinematic hardening was developed and implemented into a user-defined material (UMAT) subroutine for the commercial finite element code ABAQUS. Both yield function and plastic potential were defined in the form of Hill’s [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. Lond. A 193, 281–297] quadratic anisotropic function, where the coefficients for the yield function were determined from the yield stresses in different material orientations, and those of the plastic potential were determined from the r-values in different directions. Isotropic hardening follows a nonlinear behavior, generally in the power law form for most grades of steel and the exponential law form for aluminum alloys. Also, a kinematic hardening law was implemented to account for cyclic loading effects. The evolution of the backstress tensor was modeled based on the nonlinear kinematic hardening theory (Armstrong–Frederick formulation). Computational plasticity equations were then formulated by using a return-mapping algorithm to integrate the stress over each time increment. Either explicit or implicit time integration schemes can be used for this model. Finally, the implemented material model was utilized to simulate two sheet metal forming processes: the cup drawing of AA2090-T3, and the springback of the channel drawing of two sheet materials (DP600 and AA6022-T43). Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior and the Bauschinger ratio. The in-plane anisotropy (r-value and yield stress directionalities) of these sheet materials was also compared with the results of numerical simulations using the non-associated model. These results showed that this non-associated, mixed hardening model significantly improves the prediction of earing in the cup drawing process and the prediction of springback in the sidewall of drawn channel sections, even when a simple quadratic constitutive model is used.     

FLUIDIZATION OF CARBON NANOTUBES

Carbon nanotubes (CNTs) can be fluidized in the form of fluidlike agglomerates made of many three-dimensional sub-agglomerates, having a multi-stage agglomerate (MSA) structure and containing large amounts of twisting CNTs of micrometer magnitude.     

Mass and isotopic concentrations of water-insoluble refractory carbon in total suspended particulates at Mt. Waliguan Observatory (China)

Mass concentration and isotopic values δ¹³C and ¹⁴C are presented for the water-insoluble refractory carbon (WIRC) component of total suspended particulates (TSP), collected weekly during 2003, as well as from October 2005 to May 2006 at the WMO-GAW Mt. Waliguan (WLG) site. The overall average WIRC mass concentration was (1183 ± 120) ng/m³ (n = 79), while seasonal averages were 2081 ± 1707 (spring), 454 ± 205 (summer), 650 ± 411 (autumn), and 1019 ± 703 (winter) ng/m³. Seasonal variations in WIRC mass concentrations were consistent with black carbon measurements from an aethalometer, although WIRC concentrations were typically higher, especially in winter and spring. The δ¹³C PDB value (−25.3 ± 0.8)‰ determined for WIRC suggests that its sources are C₃ biomass or fossil fuel combustion. No seasonal change in δ¹³C PDB was evident. The average percent Modern Carbon (pMC) for ¹⁴C in WIRC for winter and spring was (67.2 ± 7.7)% (n = 29). Lower pMC values were associated with air masses transported from the area east of WLG, while higher pMC values were associated with air masses from the Tibetan Plateau, southwest of WLG. Elevated pMC values with abnormally high mass concentrations of TSP and WIRC were measured during a dust storm event.     

柔性机构动态可靠性分析的新方法

为了改善柔性机构动态可靠性分析的效率和精度,基于支持向量机SVM(Support Vector Machine)回归理论,提出了一种柔性机构动态可靠性分析高效率高精度的SVM回归极值法SREM(SVM Regression Extremum Method)。首先,介绍了柔性机构可靠性分析的基本理论;其次,融合蒙特卡洛法MC(Monte Carlo)和SVM回归理论,建立了柔性机构动态响应极值的代理模型,并利用代理模型进行柔性机构可靠性分析。最后,利用SREM法对柔性机构实例进行了可靠性分析,并与MC和人工神经网络ANN(Artificial Neural Networks)的分析结果进行比较。结果显示,在小样本情况下,进行柔性机构动态可靠性分析时,SREM的计算效率和计算精度都比ANN高;SREM的计算效率比MC大大提高,计算精度与MC相当。验证了在柔性机构可靠性分析中SREM的高效率和高精度,并证明了SREM在柔性机构可靠性分析中的可行性和有效行性。