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This study aimed to analyze element content, antioxidative response, and related gene expression in two new wheat (Tritium aestivum L.) cultivars Longchun 30 and Longchun 27 when exposed to different NaCl concentrations. Low NaCl concentration (25 mM) promoted root growth and decreased malondialdehyde (MDA) content and relative conductivity (REC) in Longchun 30. Differently, higher salinity stress (100 and 200 mM NaCl) inhibited root growth and increased MDA content and REC in both cultivars. Under salt stress, the increment of Na content in the roots and leaves and the reduction of Ca content in the roots were more remarkable in Longchun 27 than in Longchun 30. In contrast, the potassium content decreased in the roots but did not significantly change in the leaves in both cultivars under salinity. When the seedlings were exposed to salinity, the increases of superoxide dismutase (SOD) and catalase (CAT) activities in Longchun 27 roots were associated with high isoenzymes abundance and high TaCu/ZnSOD, TaMnSOD and TaCAT expression. Meanwhile, total peroxidase (POD) activity induced by NaCl treatment coincided with the changes of TaPOD expression and isoenzyme abundance in both cultivars. Besides, the inhibition of activities of apoplastic antioxidant enzymes, cell wall-bound POD, diamine oxidase, and polyamine oxidase was observed in salinity-stressed roots of both cultivars. Taken together, cv. Longchun 30 might be more suitable for growing in salinity environment in comparison with Longchun 27.

According to the complex flow dynamics of droplets impacting on the wall, an integrated smoothed particle hydrodynamics (SPH) method is developed by a series of improved techniques including artificial viscosity, kernel gradient correction (KGC) technique, boundary treatment and so on, combined with the surface tension based on the continuous surface force (CSF) model in this paper. This method is validated by simulations of the square cavity flow and natural variations of a square droplet, and effects of particle diameter, kernel function, and artificial viscosity coefficient are also analyzed. On this basis, dynamic behavior of the droplet impacting on the wall with heat transfer is studied, and the results agree well with the experimental results. It is observed that the wall characteristics have a significant influence on the droplet deformation, and the droplet tends to spread on the hydrophilic wall. In the investigated temperature difference, the influence of temperature difference could be ignored, but there is energy exchange between the droplet and the wall. In general, the spreading law of droplet is consistent with the physical phenomena, which shows that the integrated SPH method can effectively deal with engineering problems involving a droplet impacting on the wall with heat transfer.

Manipulating the twin morphology to achieve the reinforcement of strength is a great challenge in Al with high stacking fault energy. In this work, the influence of Zr addition on the twin morphology and strengthening response of nanostructured Al films was symmetrically studied. The results showed that, for low Zr addition (≤ 4.0 at.%), the Zr atoms were homogeneously distributed within the matrix, while Zr segregation at grain boundaries was evident at higher Zr addition (> 4.0 at.%). Twins were substantially observed in all the films, and the twin morphology was highly dependent on the Zr addition. In the pure Al film, only twins with a single coherent twin boundary were detected. In comparison, nanotwins with coplanar twin boundaries (C-nanotwins) and 9R phase were predominant in the Al-Zr films with Zr addition ≤ 4.0 at.%. Further raising the Zr content, multiple nanotwins (M-nanotwins) coexisted with the C-nanotwins and 9R phase. In particular, a zero-strain twinning mechanism was applied to account for the C-nanotwins and 9R phase formation, and a zig-zag grain boundary feature induced by Zr segregation was responsible for the M-nanotwin formation. The hardness also exhibited a strong Zr dependence that increased monotonically with the Zr addition. The Al-13.4 at.% Zr film displayed a hardness of ~4.3 GPa, about 11 times greater than the pure Al film. Strengthening mechanisms were quantitatively evaluated, and the highly-promoted hardness was mainly ascribed to the 9R phase and solid solution strengthening.

Clutch judder has serious impacts on the noise, vibration and harshness performance. In this article, a simplified dynamic model with nonlinear friction torque is developed to simulate clutch judde...

The driveline torsional vibration issue is one of the most significant Noise, Vibration and Harshness (NVH) problems, especially in rear-wheel drive vehicles with manual transmission. In this artic...

In the present study, high strength and high electrical conductivity Cu-0.65Cr-0.07Zr (wt.%) was prepared by aging and subsequent cryorolling. The influence of processing on microstructure and properties of alloy were investigated. After aging, the fine and uniformly dispersed nano-precipitates appeared in the matrix. The cryorolled sample was characterized by a finer microstructure than the sample rolled at room temperature. The desired balance between the tensile strength of 712 MPa and electrical conductivity of 70.2% was obtained in the sample aged and cryorolled for 90% reduction. The combination of aging and subsequent cryorolling is effective in optimizing mechanical strength and electrical conductivity of CuCrZr alloy due to grain refinement, precipitation and twinning.

This experiment was conducted to investigate the effects of supplemental vitamin A (VitA) on the growth performance, nutrient digestibility, serum biochemical parameters, and liver histology of growing-furring mink kits (Neovison vison). Ninety healthy male mink were randomly assigned to 6 treatment groups, with 15 mink per group. Each mink was housed in an individual cage. Mink in the 6 groups were fed diets supplemented with vitamin A acetate at dosages of 0 kIU/kg (VitA 0), 5 kIU/kg (VitA5), 20 kIU/kg (VitA20), 80 kIU/kg (VitA80), 320 kIU/kg (VitA320) or 1280 kIU/kg (VitA1280) of the basal diet. A 7-day pretest period preceded a formal test period of 60 days. The results showed that the final body weight (BW), average daily gain (ADG), weight gain (WG), average daily feed intake (ADFI) and the digestibility of dry matter (DM), crude protein (CP), ether extract (EE), and carbohydrate (CHO) exhibited a quadratic relationship (P

We conducted an experiment to assess the predictive capability of a leaf optical meter for determining leaf pigment status of Acer mono Maxim., A. ginnala Maxim., Quercus mongolica Fisch., and Cornus alba displaying a range of visually different leaf colors during senescence. Concentrations of chlorophyll (Chl) a, Chl b, and total Chl [i.e., Chl (a+b)] decreased while the concentration of carotenoids (Car) remained relatively static for all species as leaf development continued from maturity to senescence. C. alba exhibited the lowest average concentration of Chl (a+b), Chl a, and Car, but the highest relative anthocyanin concentration, while Q. mongolica exhibited the highest Chl (a+b), Chl b, and the lowest relative anthocyanin concentration. A. mono exhibited the highest Chl a and Car concentrations. The relationships between leaf pigments and the values measured by the optical meter generally followed an exponential function. The strongest relationships between leaf pigments and optical measurements were for A. mono, A. ginnala, and Q. mongolica (R 2 ranged from 0.64 to 0.95), and the weakest relationships were for C. alba (R 2 ranged from 0.13 to 0.67). Moreover, optical measurements were more strongly related to Chl a than to Chl b or Chl (a+b). Optical measurements were not related to Car or relative anthocyanin concentrations. We predicted that weak relationships between leaf pigments and optical measurements would occur under very low Chl concentrations or under very high anthocyanin concentrations; however, these factors could not explain the weak relationship between Chl and optical measurements observed in C. alba. Overall, our results indicated that an optical meter can accurately estimate leaf pigment concentrations during leaf senescence — a time when pigment concentrations are dynamically changing — but that the accuracy of the estimate varies across species. Future research should investigate how species-specific leaf traits may influence the accuracy of pigment estimates derived from optical meters.

This paper proposes a stable nodal integration method for analyzing coupling problems of electromagnetic field and mechanical field using linear triangular mesh. For transient electromagnetic field analysis, the node-based smoothed solution is firstly formulated to compute system matrices, and then the equivalent smoothing domain and temporal integration points are constructed to achieve a stable nodal integration method (SNIM), whose coefficient matrix is finally computed using the smoothed shape function derivatives together with the variance terms over the equivalent smoothing domain associated with nodes of the mesh. For dynamic large-deformation analysis, the node-based smoothed finite element method (NS-FEM) is utilized after testifying its stability and effectiveness in thin-walled structures of electromagnetic forming (EMF) process. Furthermore, by treating the morphing region as a static mechanical problem, a weighted elastomer method is presented to accomplish the mesh updating in sequential coupling simulation. Finally, it turns out that the proposed methodologies can be applied successfully to simulate EMF process, and numerical examples for both tube bulging and tube compression are investigated to demonstrate the validity, accuracy and efficiency of the proposed methods.

This paper focuses on the accurate and efficient numerical implementation of acoustic-structure coupling formulations using the edge-based smoothed finite element method for the flexible shell and the gradient-weighted finite element method for the acoustic fluid field, namely, the ES/GW-FEM. The shell is discretized using the simplest linear triangular elements and the edge-based smoothing domain is then constructed. By introducing an edge local coordinate system, the edge-based smoothing operation is performed on the smoothing domain. As for the acoustic fluid domain, the tetrahedron elements are adopted. A compacted support domain is then constructed and the gradient weighted operation is performed on the support domain. To model the exterior acoustic domain, an artificial boundary is introduced and the Dirichlet-to-Neumann (DtN) boundary condition is imposed. Based on the appropriate compatibility and equilibrium conditions on the interface boundaries, the coupled ES/GW-FEM formulation is finally obtained. Both the interior acoustic-structure coupled problems and exterior acoustic-structure coupled problems are available as the DtN boundary is considered. Numerical examples demonstrate that the coupled ES/GW-FEM achieves much higher accuracy and works more reliably compared with the coupled FEM/FEM in solving practical engineering problems.

The fiber-reinforced composites display the random fiber orientations and uncertain material parameters because of the manufacturing error and scattering feature. For this problem, the uncertain prediction and optimization based on the transformed perturbation stochastic method, the edged-based smoothing technique and the optimization theory is presented. In this method, the non-Gaussian probability density functions and the cumulative distribution functions of multi-variables for stochastic static responses of fiber-reinforced composite structure are explicitly exhibited as the prediction result compared with the Monte Carlo solution. Unlike the direct MCs, it only needs an iteration as the FEM and has the potential in the complex construction. In order to improve the efficiency and capability to resist the mesh distortion compared with the traditional stochastic FEM, the edged-based smoothing technique is introduced into the present framework. Furthermore, the stable performance feature of the fiber-reinforced composite in the uncertain working condition is presented. Consequently, objectives of the structural stability and insensitivity criteria based on the second-order perturbation expansion are proposed, and overall uncertain conditions coupled by uncertain fiber orientation, external load, material parameters and geometry sizes are analyzed and optimized within this framework, respectively. To verify the effectiveness and accuracy of the uncertain analysis and optimization in this study, three examples including the composite plates, the composite shell and the composite top cover of automobile are provided.

This paper presents a new approach for the topological design of materials with extreme properties. The method is based on hybrid cellular automaton (HCA), which is an implicit optimization technique that uses local rules to update design variables iteratively until meeting the described optimality conditions. By means of an energy-based homogenization approach, the effective properties of the considered material are calculated in terms of element mutual energies. By this method, no sensitivity information is required to find the optimal topology for the considered design objectives: bulk modulus, shear modulus, and negative Poisson’s ratio. The proposed method is validated by a series of numerical examples.

This paper presents a concurrent topology optimization approach for simultaneous design of composite structures and their periodic material microstructures with three or more phases. The effective properties of multi-phase materials are obtained via homogenization technique which serves as a bridge of the finite element models of the macrostructure and the material microstructure. The base materials of periodic microstructures used in each phase of the macrostructure are divided into several groups and sensitivity analysis are carried out on them one by one. Meanwhile, the sensitivity number at the macrostructure is derived which is coupled with the designed material properties. Then, the composite configurations of material microstructures and macrostructures are inversely optimized concurrently based on the bi-directional evolutionary structural optimization (BESO) algorithm. Several 2D and 3D numerical examples are presented to demonstrate the effectiveness of proposed design approach.

Summary It is well-known that the traditional finite element method (FEM) fails to provide accurate results to the Helmholtz equation with the increase of wave number due to the “pollution error” caused by numerical dispersion. In order to overcome this deficiency, a gradient-weighted finite element method (GW-FEM) that combines Shepard interpolation and linear shape functions is proposed in this work. Three-node triangular and four-node tetrahedral elements that can be generated automatically are first used to discretize the problem domain in 2D and 3D spaces, respectively. For each independent element, a compacted support domain is then formed based on the element itself and its adjacent elements sharing common edges (or faces). With the aid of Shepard interpolation, a weighted acoustic gradient field is then formulated, which will be further used to construct the discretized system equations through the generalized Galerkin weakform. Numerical examples demonstrate that the present algorithm can significantly reduces the dispersion error in computational acoustics.

The accuracy of numerical results using standard finite element method (FEM) in acoustic problems will deteriorate with increasing frequency due to the "dispersion error". Such dispersion error depends on the balance between the "stiffness" and "mass" of discretization equation systems. This paper reports an improved finite element method (FEM) for solving acoustic problems by re-distributing the mass in the mass matrix to "tune" the balance, aiming to minimize the dispersion errors. This is done by shifting the integration point locations when computing the entries of the mass matrix, while ensuring the mass conservation. The new method is verified through the detailed numerical error analysis, and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error. The relative dispersion error of present mass-redistributed finite element method (MR-FEM) is found to be much smaller than the FEM solution, in both theoretical prediction and numerical examination. The present MR-FEM works well by using the linear triangular elements that can be generated automatically, which enables automation in computation and saving computational cost in mesh generation. Numerical examples demonstrate the advantages of MR-FEM, in comparison with the standard FEM using the same triangular meshes and quadrilateral meshes.

The widely-used numerical modeling approaches such as the finite element method (FEM) and statistical energy analysis (SEA) often have limited applicability to the transmission loss prediction in mid-frequency range. In this paper, a novel hybrid edge-based smoothed FEM coupled with statistical energy analysis (ES-FE-SEA) method is proposed to further improve the accuracy of “mid-frequency” transmission loss predictions. The application of ES-FEM will “soften” the well-known ‘‘overly-stiff’’ behavior in the standard FEM solution and reduce the inherent numerical dispersion error. While the SEA approach deals with the physical uncertainty in the relatively higher frequency range. The plate of interest is appropriately described by an ES-FEM model, due to its relative robustness to perturbations. Its adjacent reverberation cavities are modeled by employing the SEA approach, because of their high model density. The coupling and interaction between SEA subsystems and the FE subsystem is governed by the “reciprocity relationship” theorem. A standard numerical example for benchmarking is examined and excellent agreement was achieved between the prediction and reference results. The proposed ES-FE-SEA is also verified by various numerical examples. The method is finally applied to the modeling a complicated engineering problem–acoustic fields on both sides of the front windshield in a passenger car.

ABA is important for plant growth and development; however, it also inhibits photosynthesis by regulating the stomatal aperture and ribulose-1,5-bisphosphate carboxylase/oxygenase activity. Noteworthy, this negative effect can be alleviated by antioxidants including ascorbic acid (AsA) and catalase (CAT), but the underlying mechanism remains unclear. Two rice cultivars, Zhefu802 (recurrent parent) and its near-isogenic line, fgl were selected and planted in a greenhouse with 30/24 °C (day/night) under natural sunlight conditions. Compared to fgl, Zhefu802 had significantly lower net photosynthetic rate (PN) and stomatal conductance (Cond) as well as significantly higher ABA and H2O2 contents. However, AsA and CAT increased PN, Cond, and stomatal aperture, which decreased H2O2 and malondialdehyde (MDA) levels. In this process, AsA and CAT significantly increased the ribulose-1,5-bisphosphate carboxylase activity, while they strongly decreased the ribulose-1,5-bisphosphate oxygenase activity, and finally caused an obvious decrease in the ratio of photorespiration (Pr) to PN. Additionally, AsA and CAT significantly increased the expression levels of RbcS and RbcL genes of leaves, while H2O2 significantly decreased them, especially the RbcS gene. In summary, the removal of H2O2 by AsA and CAT can improve the leaf photosynthesis by alleviating the inhibition on the stomatal conductance and ribulose-1,5-bisphosphate carboxylase capacity caused by ABA.

The traditional stochastic finite element method based on the finite element method fails to give the fine solution in precise determination of reliable problems when the computer power consumption is limited. To cure this fatal defect, the generalized n th order stochastic perturbation technique based on a stable node-based smoothed finite element method (GS_SNS-FEM) is presented. The framework intends to essentially improve the accuracy, lower the mesh limitation and occupy much less computational consumption for stochastic problems, especially when its second order realization is ineffective for large variations of input random fields. Besides, the n th orders expansion makes it possible to get the prefect accuracy for expected values and variances. Numerical examples including the static and dynamic problems are completed and compared with the solution of Monte Carlo simulation. It is found that the SNS-FEM applied in the stochastic problem can improve the accuracy of static and dynamic results, largely decrease the time cost, and lower the requirement of mesh.

Plukenetia volubilis Linneo, a tropical recurrent woody oilseed plant native to South America, was successfully introduced in China. A field experiment was conducted to determine the effect of the dry-season foliar sprays once every 2 weeks with 50 μm water or five different plant growth regulators (PGRs) viz., gibberellic acid (GA3), kinetin (KIN), indole-3-acetic acid (IAA), abscisic acid (ABA), and salicylic acid (SA) on the growth and yield of P. volubilis plants in Xishuangbanna, southwest China. Results showed that PGRs affected the leaf stomatal conductance (gS) and water-use efficiency (WUEi), rather than the net photosynthetic rate (PN). The phenological development of P. volubilis plants, including the time of flowering and maturity, and the dynamic pattern of fruit ripening, was not altered by PGR treatments. ABA and SA resulted in highest fruit set, seed oil content, and total fruit or seed oil yield, whereas GA3, IAA, and KIN were effective in increasing seed size. The nonstructural carbohydrates (NSC) are related to subsequent abscission or retention of the developing fruit, which was indicated by the positive relationship between carbohydrate concentration and fruit set across PGR treatments. The positive influences of PGRs on the total fruit yield (increased 4.3% to 15.2%) and total seed oil yield (increased 4.9% to 24.9%) per unit area throughout a growing season were found when compared with the control, depending to a great extent on the balance between vegetative and reproductive growth during the reproductive stage. This study suggests that PGRs, especially for ABA and SA, can become a valuable tool for promoting the seed oil yield of P. volubilis plants while maintaining high seed quality in the field.

Combined isogeometric analysis (IGA) and shape optimization, this paper provides a method that can accurately analyze Tailor Rolled Blanks (TRB) and optimize its thickness profile continuously. While existed traditional methods can hardly solve these problems. TRB has a continuous transition between the thick and thin and a better surface quality. We found in IGA, two-dimension NURBS could present TRB geometry model exactly, but Kirchhoff shell element whose control points are allocated different thicknesses could not simulate TRB effectively. So, this paper uses three-dimension NURBS element to exactly present and accurately analyze TRB. It could avoid error caused by inaccurate presentation of geometry model and decrease error caused by solution field (displacement) approximation in numerical computation. Meanwhile, the positions of control points are taken as design variables in process of optimizing thickness profile. It can avoid the appearance of "unrealistic" shape and save lots of time spent in traditional tediously mesh updating as well as having better accuracy. This method makes accurate analysis and continuous thickness optimization of TRB become possible. It pushes the development of TRB engineering and extends the applications of IGA optimization. Several examples including benchmarks and application used the proposed method verified its effectivity, reliability and efficiency.

This paper proposed a nodal integration model for elasto-static, free vibration, forced vibration and geometric nonlinear analyses of axisymmetric thin shells using two-node truncated conical elements. The formulation is based on the Kirchhoff–Love theory, in which only the two translational displacements are treated as the independent field variables. A gradient smoothing technique (GST) is employed to relax the continuity requirement for trial function, so that linear shape functions can be used to interpolate both the tangent and normal displacement fields to the meridian. Based on each node, the integration domains are further formed, where the membrane strains and curvature changes are computed using a strain smoothing operation incorporated with a tensor transformation manipulation. The smoothed Galerkin weakform is then used to establish the discretized system equations. In order to accurately track the deformation path in geometric nonlinear analysis, the Newton–Raphson iteration in conjunction with the arc-length technique are employed here to solve the equilibrium equation. Numerical examples demonstrate that the present method can achieves higher accuracy and lower computing cost compared with the conventional finite element model.

A stable nodal integration method with strain gradient (SNIM-SG) for curing the temporal instability of node-based smoothed finite element method (NS-FEM) is proposed for dynamic problems using linear triangular and tetrahedron element. In each smoothing domain, except for considering the smoothed strain into the calculation of potential energy functional as NS-FEM, a term related to strain gradient is taken into account as a stabilization term. The proposed SNIM-SG can achieve appropriate system stiffness in strain energy between FEM and NS-FEM solutions and obtains quite favorable results in elastic and dynamic analysis. The accuracy and stability of SNIM-SG solution are studied through detailed analyzes of benchmark cases and practical engineering problems. In elastic-static analysis, it is found that SNIM-SG can provide higher accuracy in displacement field than the reference approaches do. In free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that SNIM-SG solution strengths the original relatively soft NS-FEM, and SNIM-SG is confirmed to obtain fairly accurate natural frequency values in various examples. All in all, SNIM-SG cures the flaws of NS-FEM and enhances the dominant of nodal integration. Thus, the efficacy of the presented formulation in solving solid mechanics problems is well represented and clarified.

In this paper, a coupled smoothed finite element method (S-FEM) is developed to deal with the structural-acoustic problems consisting of a shell configuration interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements that can be generated automatically for any complicated geometries are adopted to discretize the problem domain. A gradient smoothing technique (GST) is introduced to perform the strain smoothing operation. The discretized system equations are obtained using the smoothed Galerkin weakform, and the numerical integration is applied over the further formed edge-based and face-based smoothing domains, respectively. To extend the edge-based smoothing operation from plate structure to shell structure, an edge coordinate system is defined local on the edges of the triangular element. Numerical examples of a cylinder cavity attached to a flexible shell and an automobile passenger compartment have been conducted to illustrate the effectiveness and accuracy of the coupled S-FEM for structural-acoustic problems.

It is well-known that the classical “overly-soft” node-based smoothed finite element method (NS-FEM) fails to provide reliable results to the Helmholtz equation due to the “temporal instability”. To cure the fatal drawback of NS-FEM and reduce the dispersion error in computational acoustics, this paper proposed a stable node-based smoothed finite element method (SNS-FEM) for analyzing acoustic problems using linear triangular (for 2D space) and tetrahedral (for 3D space) elements that can be generated automatically for any complicated configurations. In the present formulation, the system stiffness matrix is computed using the smoothed acoustic pressure gradients together with the gradient variance items over the smoothing domains associated with nodes of element mesh. It turns out the addition of stabilization term makes the SNS-FEM possess an ideal stiffness, thus successfully cures the temporal instability and significantly reduces the dispersion error in acoustic problems. Numerical examples, including both benchmark cases and practical engineering problems, demonstrate that the SNS-FEM possesses the following important properties: (1) temporal stability; (2) super accuracy and super convergence; (3) higher computational efficiency; (4) insensitive to mesh distortion.

The alpha finite element method (α-FEM) developed recently has showed outstanding features in solving solid mechanics and acoustic problems. In the α-FEM, a parameter alpha has been introduced to make the best use of “over-stiffness” of the FEM model and “over-softness” of the NS-FEM model to achieve the ultimate performance. Because the parameter alpha varies with the problems and the mesh size, it is difficult to find a general approach to determine, which holds back the application of the α-FEM method. In this paper, acoustic simulation using α-FEM with a general approach for reducing dispersion error is proposed. We first carry out a theoretical analysis of dispersion error, leading to a very important relation between the dispersion error and the parameter alpha. Next, the parameter of alpha is then determined by minimizing the dispersion error. The determined parameter alpha enables a proper gradient smoothing operation in the α-FEM, and provides a perfect balance between the stiffness and mass in the discrete system matrix, which dramatically reduces the dispersion error. The properties of the present α-FEM have been confirmed numerically via examples of 1D, 2D and 3D acoustic problems with various boundary conditions.

A destructive earthquake occurred in Northeast Xi'an, Shaanxi province, on May 25th, 1568 AD, causing many casualties, severe damage to property, and significant disruption to livelihoods. This earthquake has been chosen as a plausible basis for calculating a seismic scenario for the modern city of Weinan, and its surrounding urban areas. Previous studies agreed in assigning a magnitude 6 ¾ to the earthquake but yielded differing epicentral locations and isoseismal intensity maps. We combine textual research on historical earthquake reports with field investigations to reduce the uncertainties, and to place constraints on the ground shaking that would be experienced if such an earthquake were to recur. We show that the counties of Jingyang, Gaoling, and Xianning were the worst hit by the earthquake, with the townships of Yongle, Huijun, Pisha, and Fengzheng (present-day Gaozhuang and Zhangbu township), likely being in the mesoseismal area of this earthquake. Reinterpretation of the historical texts, combined with field observations, indicates that the epicenter of the earthquake was at about 34°28′N and 108°59′E, with an epicentral intensity of Ⅸ+ and an estimated magnitude of 7. The isoseismal contours have major axes-oriented WNW-ESE, in contrast to the more NS alignment inferred from the earlier study of the historical documents. The isoseismal of intensity VIII+encloses, and has its major axis parallel to, the active Weinan-Jingyang fault, which we infer to be the fault that slipped in the May 25th, 1568 earthquake.

The Weinan-Jingyang fault is one of the southern boundary faults of the Gushi secondary depression of the Weihe Basin, China. Geophysical exploration work and field geological surveys have demonstrated that this fault system has a length of approximately 105 km, and extends at least 5 km into the subsurface, with a northerly dip that shallows with depth. Under the influence of long-term displacement on the fault zone, the strata on the north side of the fault within the fault zone dip to the south, and the subsidence centre of the Gushi depression has migrated continuously southward. The Cenozoic activity of the Weinan-Jingyang fault has resulted in a significant dislocation between Paleozoic and Cenozoic strata on either side of the fault. This fault has been active during the Quaternary, especially the late Quaternary, in some places offsetting strata formed during the Ming Dynasty(1368–1644 CE), suggesting that this fault can reliably be regarded being active during Holocene time. Comprehensive re-examination of historical earthquake records, combined with field studies, confirm that the Weinan-Jingyang fault is likely the fault that slipped during a magnitude ~7 earthquake in northeast Xi'an, China in 1568 CE. That earthquake is here re-named the Shaanxi Gaoling Earthquake.

The early-stage diagnosis and treatment for the recurrence of larynx carcinoma needs further investigation. Mesenchyme homeobox 2 (MEOX2) was speculated as a novel suppressor gene in larynx carcinoma in our study, the molecular mechanism was studied. Real-time quantitative PCR (RT-qPCR) and Western blot were used to detect mRNA and protein levels of MEOX2 in laryngeal cancer tissues and cells (Hep-2, TU212, AMC-NH-8 and TU686 cells), and also apoptosis and phosphoinositide 3-kinase (PI3K)/protein kinase (Akt) related factors in TU212 cells transfected with MEOX2. Cell counting kit-8 (CCK8) assay and Annexin-Ⅴ/PI staining assay were conducted to determine cell viability and apoptosis rates respectively.46 patients with larynx carcinoma were involved in this study. The expression of MEOX2 was lower in larynx carcinoma tissues than normal tissues, correlated with clinical stages, differentiated degrees, and survival times. The expression of MEOX2 was the lowest among those laryngeal cancer cells, and was chosen to be transfected with MEOX2 in the following study. Over-expression of MEOX2 inhibited cell viability and promoted apoptosis of TU212 cells, via increasing the expression levels of Caspase-3, and decreasing levels of C-Myc, XIAP, PI3K p110α, PI3K p110β, PI3K class III and p-Akt. In summary, the expression levels of MEOX2 were inhibited in larynx carcinoma than normal tissues, correlated with the progression of the cancer. Over-expression of MEOX2 in laryngeal cancer cells inhibited cell viability and promoted apoptosis, via regulating apoptosis and PI3K/Akt pathway related factors. It would provide evidence for MEOX2 to be used as a therapeutical gene in larynx carcinoma.

Summary This paper proposed a rotation-free thin shell formulation with nodal integration for elastic–static, free vibration, and explicit dynamic analyses of structures using three-node triangular cells and linear interpolation functions. The formulation is based on the classic Kirchhoff plate theory, in which only three translational displacements are treated as the filed variables. Based on each node, the integration domains are further formed, where the generalized gradient smoothing technique and Green divergence theorem that can relax the continuity requirement for trial function are used to construct the curvature filed. With the aid of strain smoothing operation and tensor transformation rule, the smoothed strains in the integration domain can be finally expressed by constants. The principle of virtual work is then used to establish the discretized system equations. The translational boundary conditions are imposed same as the practice of standard finite element method, while the rotational boundary conditions are constrained in the process of constructing the smoothed curvature filed. To test the performance of the present formulation, several numerical examples, including both benchmark problems and practical engineering cases, are studied. The results demonstrate that the present method possesses better accuracy and higher efficiency for both static and dynamic problems. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a curvature-constructed triangular element for static, free vibration and explicit dynamic analyses of shell structures by using a continuity re-relaxed technique. In the present method, the formulation is based on the classical thin shell theory, and only the translational displacements are treated as the filed variables that are assumed piecewisely linear. A set of three-node triangular background cells is adopted to discretize the problem domain. The curvature field in an element is constructed using the continuity re-relaxed technique, which can relax the continuity requirement of the trial function. The membrane strain filed is formulated same as the practice of standard FEM. Based on the principle of virtual work, the discertized system equations are finally formed. As the rotational displacements are not considered as the basic degrees of freedom, the essential boundary conditions of this part are imposed in the process of forming the curvature field. In order to validate the efficiency and accuracy of the present method, several numerical examples are studied. The results demonstrate that the present formulation can achieve very stable and accurate solutions with the less consuming of CPU time.

Presenting a stabilized nodal integration method for analysis of Reissner-Mindlin plate.Squared-residual of equilibrium equations are considered in the potential energy functional.Giving an empirical value range of stabilization parameter through numerical tests.Numerical examples shown efficiency of the new method to improve calculation accuracy.The proposed scheme can eliminates the temporal instability successfully. In this paper, a temporal stabilized nodal integration method (sNIM) using 3-node triangular elements is formulated for elastic-static, free vibration and buckling analyses of Reissner-Mindlin plates. Two stabilization terms are added into the smoothed potential energy functional of the original nodal integration, consisting of squared-residual of equilibrium equations. A gradient smoothing technique (GST) is used to relax the continuity requirement of shape function. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are formed to perform the smoothing operation and the numerical integration. A stabilization parameter is finally introduced to the modified system for the sake of curing temporal instability. Numerical tests provide an empirical value range of stabilization parameter, within which very accurate and stable results can be obtained for both static and eigenvalue problems.

Summary Predicting the frequency response of a complex vibro-acoustic system becomes extremely difficult in the mid-frequency regime. In this work, a novel hybrid face-based smoothed finite element method/statistical energy analysis (FS-FEM/SEA) method is proposed, aiming to further improve the accuracy of ‘mid-frequency’ predictions. According to this approach, the whole vibro-acoustic system is divided into a combination of a plate subsystem with statistical behaviour and an acoustic cavity subsystem with deterministic behaviour. The plate subsystem is treated using the recently developed FS-FEM, and the cavity subsystem is dealt with using the SEA. These two different types of subsystems can be coupled and interacted through the so-called diffuse field reciprocity relation. The ensemble average response of the system is calculated, and the uncertainty is confined and treated in the SEA subsystems. The use of FS-FEM ‘softens’ the well-known ‘overly stiff’ behaviour in the standard FEM and reduces the inherent numerical dispersion error. The proposed FS-FEM/SEA approach is verified and its features are examined by various numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

A cell-based smoothed radial point interpolation method (CS-RPIM) is formulated for three-dimensional elasticity problems. In present method, the problem domain is firstly discretized by tetrahedron background cells, and each tetrahedron cell is then further divided into several smoothing cells. The displacement field function is approximated using RPIM shape functions which have Kronecker delta function property. Supporting node selection for shape function construction uses the efficient T2L-scheme associated with the background cells. The smoothed Galerkin weak form is employed to create discretized system equations, and then the gradient smoothing operation is adopted to construct smoothed strain fields in every smoothing cell. Numerical examples are used to examine the present method in terms of accuracy, convergence, and efficiency. Compared with the finite element method using linear interpolation and node-based smoothed finite element method, the CS-RPIM solutions can achieve better efficiency, higher accuracy, and greater stability in static and free vibration analysis in presented examples.

In this paper, a coupled numerical method of the edge-based smoothed finite element (ES-FEM) with the fast multipole BEM (FM-BEM) is proposed to analyze structural acoustic problems. The vibrating structure is modeled using the so-called ES-FEM-DSG3 method, where the 3-node linear triangle plate elements based on the Reissner-Mindlin plate theory with the discrete shear gap (DSG) technique for overcoming the shear locking are applied. The edge-based gradient smoothing operations are applied to “soften” the “overly-stiff” behavior in the standard FEM, which significantly reduces the inherent numerical dispersion error. The normal velocities on the surface of the structure are imposed as boundary conditions for the acoustic domain which is modeled using the FM-BEM for both the interior and exterior acoustic domains. Comparing with the conventional BEM, the matrix vector multiplication and the memory requirement in the FM-BEM are reduced dramatically. The coupled ES-FEM/ FM-BEM method takes the advantages of both ES-FEM and FM-BEM, which can avoid drawbacks of the “overly-stiff” behavior in FEM and computational inefficiency in the conventional BEM. Two numerical examples are presented to verify and demonstrate the effectiveness of the combined method: one academic problem for studying in detail the accuracy and efficiency of the present method, and one application to a practical vehicle noise simulation.

A new smoothed finite element method (S-FEM) is proposed using hybrid smoothing operations based on nodes and edges of the mesh for static and free vibration analyses of plates governed by the Reissner---Mindlin plate theory. In the present approach, both the node-based smoothed finite element method (NS-FEM) and edge-based smoothed finite element method (ES-FEM) are utilized in a careful designed manner to overcome the shear locking. The formulations use 3-node triangular elements for easy automatic mesh creation, and linear interpolation functions are used for simplicity and robustness. The bending strains field are smoothed by the means of gradient smoothing technique over smoothing domains constructed by element edges, while the shear strains filed is smoothed based on the combination of NS-FEM and ES-FEM with a proper weightage controlled by a coefficient. A simple formula is developed for automatic selection of the coefficient by considering mesh size and thickness of the plate. For easy reference, the present technique is termed as NS+ES-FEM. The numerical examples demonstrate that the proposed method passes the shear-locking test and improves accuracy of the solution.

A cell-based smoothed radial point interpolation method (CS-RPIM) is further extended to solve 2D and 3D heat transfer problems. For this method, the problem domain is first discretized using triangular elements or tetrahedral elements, and each element is further divided into several smoothing cells. Then, the field functions are approximated using RPIM shape functions. Finally, the CS-RPIM utilizes the smoothed Galerkin weak form to obtain the discretized system equations in these smoothing cells. Several numerical examples with different kinds of boundary conditions are investigated to verify the validity of the present method. It has been found that the CS-RPIM can achieve better accuracy and higher convergence rate, when dealing with the 2D and 3D heat transfer analysis.

The standard finite element method (FEM) is known for its “over-stiff” behavior, which leads to the pollution error in acoustic and acoustic-structural problems. In this paper, a generalized mass-redistributed smoothed FEM (MR-SFEM) is proposed to analyze the acoustic and acoustic-structure interaction problems. In the new MR-SFEM, the generalized mass matrix reconstitution technology is used for both the structural and acoustic discretized system based on the SFEM, which can provide a perfect balance of the discretized system matrix both in the structure and acoustic domain. The global equations of acoustic-structural interaction problems are established by coupling the MR-SFEM for the structure and for the acoustic domain. Some numerical examples of acoustic and acoustic-structure interaction problems have been used to assess the present formulation, and the results show that the present method has much better performance in terms of accuracy, convergence, and efficiency than those obtained using the standard FEM, edge-based FEM (ES-FEM), and face-based FEM (FS-FEM).

A face-based smoothed finite element method (FS-FEM) is formulated for transient thermal mechanical analyses of 3-D solids with nonlinearity. For this face-based smoothed finite element method, the problem domain is first discretized into a set of tetrahedral elements, and the face-based smoothing domains are further formed along the faces of the tetrahedral meshes. The smoothing operations are performed in these smoothing domains. Several numerical examples with different kinds of boundary conditions are investigated in this paper. Compared with the 4-node tetrahedral FEM, the FS-FEM can achieve much better accuracy and higher convergence when dealing with the thermal mechanical analyses of 3-D solids.

In this paper, an edge-based smoothed finite element method (ES-FEM) is further formulated to deal with the thermo-mechanical analyses of functionally graded cylindrical vessels. In the ES-FEM, the problem domain is first discretized into triangular elements, and the edge-based smoothing domains are further formed along the edges of the triangular meshes. In order to improve the accuracy, the stiffness matrices are calculated using the strain smoothing technique in these smoothing domains. The FGM cylindrical vessels are assumed to be made of ceramics and metals whose volume fractions vary continuously in the radius direction according to a power law. Different material model and thermal boundary conditions are studied. The present formulation is straight-forward and no penalty parameters or additional degrees of freedom are utilized. Numerical examples are given to demonstrate the effectivity of ES-FEM for thermo-mechanical analysis of functionally graded cylindrical vessels.

A stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis. In this method, shape functions are generated using finite element method by adopting four-node tetrahedron element. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stabilization term for 3-D problems is worked out, and then propose a strain energy based empirical rule to confirm the stabilization parameter in the formula. The accuracy and stability of the sNS-FEM solution are studied through detailed analyses of benchmark cases and actual elastic problems. In elastic-static analysis, it is found that sNS-FEM can provide higher accuracy in displacement and reach smoother stress results than the reference approaches do. And in free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that sNS-FEM solution strengths the original relatively soft node-based smoothed finite element method (NS-FEM), and the natural frequency values provided by sNS-FEM are confirmed to be far more accurate than results given by traditional methods. Thus, the feasibility, accuracy and stability of sNS-FEM applied on 3-D solid are well represented and clarified.

An edge-based smoothed finite element method (ES-FEM) is extended to deal with the transient thermo-elastic problems. For this edge-based smoothed finite element method, the problem domain is first discretized into a set of triangular elements, and the edge-based smoothing domains are further formed along the edges of the triangular meshes. In order to improve the accuracy, the ES-FEM utilizes the smoothed Galerkin weak form to obtain the discretized system equations in smoothing domains, in which the gradient field is obtained using a gradient smoothing operation. After applying these approaches, the numerical integration becomes a simple summation over each edge-based smoothing domain. The transient thermo-elastic problem is decoupled into two separate parts. At first, the temperature field is acquired by solving the transient heat transfer problem and it is then employed as an input for the mechanical problem to calculate the displacement and stress fields. Several numerical examples with different kinds of boundary conditions are investigated. It has been found that ES-FEM can achieve better accuracy and higher convergence in energy norm than the finite element method (FEM) when using the same triangular mesh.

This paper applies the boundary face method (BFM) to solve both steady-state and unsteady-state heat conduction problems in the dam construction. Instead of employing the isoparametric elements as in the boundary and finite element methods, the BFM uses directly geometric models from CAD packages to avoid geometric errors for any complex structures. Moreover, the variable approximations and the boundary integration are all performed in the parametric space of the boundary surfaces, which means that the elements and integral patches are defined in the parametric space. A numerical example of steady-state analysis presented in this paper is a concrete dam structure which consists of several blocks. The example of unsteady-state analysis, which concerns a single block with several holes in it, has also been presented to illustrate the validity and the efficiency of the proposed method.