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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.

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

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

In this paper, basis functions generated from B-spline or Non-Uniform Rational B-spline (NURBS), are used for approximating the boundary variables to solve the 3D linear elasticity Boundary Integral Equations (BIEs). The implementation is based on the BFM framework in which both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces to keep the exact geometric information in the BIEs. In order to reduce the influence of tensor product of B-spline and make the discretization of a body surface easier, the basis functions defined in global intervals are translated into local form. B-spline fitting function built with the local basis functions is converted into an interpolation type of function in which the nodal values of the boundary variables are used for control points. Numerical tests for 3D linear elasticity problems show that the BFM with B-spline basis functions outperforms that with the well-known Moving Least Square (MLS) approximation.

Both nanocrystalline and amorphous phases are observed from the near surface of nickel titanium shape memory alloy (NiTi SMA) with the B2 austenite phase after surface mechanical attrition treatment (SMAT). The microstructure and phase changes are systematically studied by cross-sectional and plane-view transmission electron microscopy. The strain induces grain refinement and it is accompanied by increased strain in the surface layer triggering the onset of highly dense dislocations and dislocation tangles (DTs), formation of the martensite plate via stress-induced martensite (SIM) transformation (B2 to B19′), and dislocation lines (DLs) as well as dense dislocation walls (DDWs) inside the martensite plate leading to the subdivision of the martensite plate. In addition, reverse martensite transformation (B19′ to B2) and amorphization take place concurrently in the surface region, and successive subdivision and amorphization finally result in the formation of well separated nanocrystalline and amorphous phases in the near surface. The average grain size of the nanocrystallites is about 20 nm. Owing to the almost complete reverse martensite transformation as well as thermal stability, the strain-induced nanocrystalline structure has the B2 austenite phase in the surface layer and no transformation occurs.

In this paper, bending and vibration analysis of laminated composite plates is carried out using a novel triangular composite plate element based on an edge-based smoothing technique. The present formulation is based on the first-order shear deformation theory, and the discrete shear gap (DSG) method is employed to mitigate the shear locking. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and edge-based smoothing domains are used for the numerical integration to improve the accuracy and the convergence rate of the method. The present formulation is coded and used to solve various example problems of bending and free vibration of laminated composite plates. It is found that the present method can provide excellent results with a wide range of thickness and is free of shear locking.

A general numerical method is proposed to compute nearly singular integrals arising in the boundary integral equations (BIEs). The method provides a new implementation of the conventional distance transformation technique to make the result stable and accurate no matter where the projection point is located. The distance functions are redefined in two local coordinate systems. A new system denoted as (α,β) is introduced here firstly. Its implementation is simpler than that of the polar system and it also performs efficiently. Then a new distance transformation is developed to remove or weaken the near singularities. To perform integration on irregular elements, an adaptive integration scheme is applied. Numerical examples are presented for both planar and curved surface elements. The results demonstrate that our method can provide accurate results even when the source point is very close to the integration element, and can keep reasonable accuracy on very irregular elements. Furthermore, the accuracy of our method is much less sensitive to the position of the projection point than the conventional method.

In this paper, a meshless natural neighbour Petrov–Galerkin method (NNPG) is presented for a plate described by the Mindlin theory. The discrete model of the domain Ω consists of a set of distinct nodes N, and a polygonal description of the boundary. In the NNPG, the trial functions on a local domain are constructed using natural neighbour interpolation and the three-node triangular FEM shape functions are taken as test functions. The natural neighbour interpolants are strictly linear between adjacent nodes on the boundary of the convex hull, which facilitate imposition of essential boundary conditions. The local weak forms of the equilibrium equations and the boundary conditions are satisfied in local polygonal sub-domains in the mean surface of the plate. These sub-domains are constructed with Delaunay tessellations and domain integrals are evaluated over included Delaunay triangles by using Gaussian quadrature scheme. Both elasto-static and dynamic problems are considered. The numerical results show the presented method is easy to implement and very accurate for these problems.

The isothermal oxidation behavior of Ti-45Al-8Nb and Ti-52Al-8Nb alloys at 900 °C in air was investigated. The early oxidation behaviors were studied by using XPS and AES. And the microstructure and the composition of the oxidation scale were studied by using XRD and SEM. The results show that the oxidation behavior of TiAl alloy is significantly improved by Nb addition. Nb substitutes for Ti in TiO 2 as a cation with valence 5, and thus to suppress TiO 2 growth. The (Ti,Nb)O 2 -rich layer is a dense and chemically uniform which is more protective than the TiO 2 layer. Nb addition also lowers the critical Al content to form an external alumina. Nb 2 Al phase is formed in the metallic matrix at the oxide–metal interface on the high Nb containing TiAl alloys.

An ultrafine grain layer consisting of nanocrystallites as well as submicrometer grains is produced on NiTi shape memory alloy by surface mechanical attrition treatment (SMAT) and the effects of the ultrafine grain layer on the tribological properties are investigated under dry sliding conditions. Compared to the coarse grain (CG) NiTi, the SMAT NiTi has smaller friction coefficients and improved wear resistance at applied loads from 5 to 15 N due to the grain refinement effect. Examination of the worn surfaces indicates that materials delamination and particles co-exist on both the CG and SMAT NiTi samples. Our results indicate that delamination is the main wear mechanism on CG NiTi whereas abrasive particles dominate the wear process on SMAT NiTi.

Influence of Y addition on the long time isothermal and cyclic oxidation behaviors of Ti45Al8Nb alloys containing 0.1–1.0 at.% Y with full lamellar microstructure was investigated in air at 900 °C. Only a proper amount of Y addition (0.3 at.%) can improve the long time oxidation resistance under both isothermal and cyclic oxidation. Either excessive or deficient addition of Y was detrimental to the oxidation resistance. Under isothermal oxidation, much thinner oxide scale was formed on 0.3 at.% Y-added alloy than it on Y-free alloy. Meanwhile, Y addition can effectively suppress the outmost TiO 2 layer and enhance the protective Al 2 O 3 layer on the sample surface. Under cyclic oxidation, different from the oxide scale formed on Y-free and Y-lean (0.1 at.%) alloys, the oxide scales on higher Y-added alloys were not typical layered structure and oxide pegs protruding into the substrate were formed at the oxide scale/substrate interface. As a result, no spallation was observed in the higher Y-added alloys even after 1000 cycles while spallation occurred on Y-free alloy after 280 cycles and 0.1 at.% Y added alloy after 460 cycles. However, high Y added alloys (>0.3 at.%) suffered severe internal oxidation. Therefore, the oxidation rate on high Y added alloys was significantly high.

In automotive industry, structural optimization for crashworthiness criteria is of special importance in the early design stage. To reduce the vehicle design cycle, metamodeling techniques have become so widespread... In this study, a time-based metamodeling technique is proposed for the vehicle design. The characteristics of the proposed method are the construction of a time-based objective function and establishment of a metamodel by support vector regression (SVR). Compared with other popular metamodel-based optimization methods, the design space of the proposed method is expanded to time domain. Thus, more information and features can be extracted in the expanded time domain. To validate the performance of the time-based metamodeling technique, cylinder impacting and full vehicle frontal collision are optimized by the proposed method. The results demonstrate that the proposed method has potential capability to solve the crashworthiness vehicle design.

A cell-based smoothed radial point interpolation method (CS-RPIM) based on the generalized gradient smoothing operation is proposed for static and free vibration analysis of solids. In present method, the problem domain is first discretized using triangular background cells, and each cell is 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 edges of the background cells. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM). The effects of the number of divisions smoothing cells on the solution properties of the CS-RPIM are investigated in detail, and preferable numbers of smoothing cells is recommended. To verify the accuracy and stability of the present formulation, a number of numerical examples are studied to demonstrate numerically the efficiency of the present CS-RPIM.

In this paper, an edge-based smoothed finite element method (ES-FEM) is formulated for stress field determination of elastic–plastic problems using triangular meshes, in which smoothing domains associated with the edges of the triangles are used for smoothing operations to improve the accuracy and the convergence rate of the method. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and the numerical integration becomes a simple summation over the edge-based smoothing domains. The pseudo-elastic method is employed for the determination of stress field and Hencky's total deformation theory is used to define effective elastic material parameters, which are treated as field variables and considered as functions of the final state of stress fields. The effective elastic material parameters are then obtained in an iterative manner based on the strain controlled projection method from the uniaxial material curve. Some numerical examples are investigated and excellent results have been obtained demonstrating the effectivity of the present method.

In this work, a hybrid fuzzy regression-based metamodeling technique is proposed to optimize the sheet metal forming design. Compared with other metamodeling techniques, the distinctive character of the proposed approach is to consider uncertainties and certainties in one metamodel. In order to further improve the efficiency of optimization, an intelligent scheme is incorporated to generate samples at the stage of design of experiment. Additionally, one step and incremental FE forming methods are implemented to calculate values of response functions. Finally, the proposed metamodeling technique and sampling schemes are integrated and applied to optimize sheet forming design; the corresponding optimized results demonstrate that the proposed hybrid metamodeling technique is able to produce good approximation model of sheet metal forming system.

A meshless local radial point interpolation method (LRPIM) for the bending and free vibration analysis of a nonhomogeneous moderately thick plate is presented in this paper. It uses a radial basis function coupled with a quadratic polynomial basis function as a trail function and a quartic spline function as a test function of the weighted residual method. The shape functions obtained in the trail function have the Kronecker delta function property, and the essential boundary conditions can be easily imposed. The present method is a true meshless method as it does not need any grids and all integrals can be easily evaluated over regularly shaped domains and their boundaries. In computational procedures, variations of material properties in the considered domain are modelled by adopting proper material parameters at Gauss points in integrations. Examples show that results obtained by the presented method are found to agree well with the existing solutions in the literature and with the results obtained by the finite element method, and the presented method has a number of advantages, such as high efficiency, quite good accuracy and easy implementation.

The least square support vector regression (LS-SVR) metamodel technique is proposed for sheet metal forming optimization. The major advantage of proposed approach is to build metamodel by consideration of empirical risk minimization (ERM) and structure risk minimization (SRM). In order to construct robust and accurate metamodel based LS-SVR, suitable quantity and intervals of samples are recommended. Thus, a parallel intelligent sampling scheme based on a boundary and best neighbor searching method (BBNS) is proposed to improve the efficiency and accuracy of metamodel. The BBNS was suggested and corresponding practical engineer problems were successfully solved by Hu and Li [Hu W, Li GY, Zhong ZH. Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J Mater Process Technol 2008;197(1–3):77–88; Hu Wang, Li GY, Li Enying, Zhong ZH. Development of metamodeling based optimization system for high nonlinear engineering problems. Adv Eng Software 2008;39(8)629–45]. To increase the efficiency of metamodel based optimization method, the parallel architecture is implemented for BBNS due to its drawbacks. For validation of developed method, both of serial and parallel BBNS scheme are applied for the nonlinear function. The parallel BBNS is also verified to be an accuracy and efficiency scheme. Finally, the practical nonlinear engineering problems are optimized by suggested methodology and satisfied results are also obtained.

A metamodeling optimization system for nonlinear problems was developed in this study. Boundaries and best neighbors searching (BBNS) intelligent sampling method and fuzzy based progressive metamodeling for space reduction were integrated and applied for this system. The BBNS scheme generates new samples derived from information of boundaries and the best samples of initial sparse distributed samples. It is easy to obtain better samples and avoid local convergence due to boundary information. In order to construct accuracy metamodel, the fuzzy based progressive metamodeling method was implemented to cluster samples generated by BBNS several patches in optimization domain. Only better sets of them are involved in construction of metamodels in each patch by response surface and kriging method. The nonlinear problems with multi-humps as test functions were used for proving accuracy and efficiency of developed system. The practical nonlinear engineering problems were also successfully optimized by this system.

A series of cyclic deformation and subsequent aging treatments at room temperature were performed on ultrafine-grained Cu processed by equal-channel angular pressing in order to investigate their influences on tensile properties. It was found that a combination of both high strength and good ductility can be achieved by means of cyclic deformation together with aging treatments. The microstructure analysis gave the explanations for these phenomena.

Laser diodes (LD) are usually bonded onto heat sinks for the purposes of heat dissipation, mechanical support and electrical interconnect. In this study, energy dispersive X-ray analysis (EDX) and electron backscatter diffraction (EBSD) are employed to investigate the microstructure evolution of 80Au/20Sn solder joint in LD package. During reflow, Pt-Sn and (Au, Ni)Sn IMCs were formed at the respective LD/solder and solder/heatsink interfaces, while ?, ? and ?' phases of Au/Sn intermetallics were found in the solder joint. The Au-rich ? and ?' phases in the solder joint limit the growth of interfacial IMCs. Chip shear testing showed that the failure occurred within the LD, with partial brittle fracture at the GaAs substrate and partial interfacial delamination at the GaAs/SiN interface. The strong solder bond can be attributed to the high mechanical strength of 80Au/20Sn solder, which provides improved stability for high temperature applications.

In this study, the thermomechanical behaviour of a magnesium alloy AZ31B during extrusion through a porthole die to form a square tube was revealed. Three-dimensional numerical simulation demonstrated that metal flow into the portholes, welding chamber and die bearing of the porthole die corresponded to the stepped increases of extrusion pressure at the initial stages of an extrusion cycle. Experimental measurements of extrusion pressure and extrudate temperature were found to be in agreement with the predicted values. Extrusion pressure decreased continuously after the pressure peak while the workpiece temperature increased steadily, leading to gradual increases of the recrystallised grain sizes of the extrudate along its length. Expansion tests showed consistent quality of the longitudinal weld seams along the extrudate length, although the temperature on the welding plane increased and the maximum normal pressure in the welding chamber decreased during extrusion. It is thus the ratio of the maximum normal pressure in the welding chamber to the flow stress of the workpiece material on the welding plane that determines the weld seam quality.

A meshless method based on the local Petrov–Galerkin formulation is applied to the large deformation contact analysis of elastomeric components. Trial functions are constructed using the radial-basis function (RBF) coupled with a polynomial-basis function. The plane stress hypothesis and a pressure projection method are employed to overcome the incompressibility or nearly incompressibility in the plane stress and plane strain problems, respectively. Two different sets of equations are used for the nodes on the contact surface and nodes not on the contact surface, respectively, which is based on the meshless local Petrov–Galerkin method (MLPG) establishing equations node by node. Numerical results for several examples show that the present method is effective in dealing with large deformation contact problems.

Based on an optimized bonding technique for semiconductor lasers, parametric investigations of different bonding configurations were performed using AuSn solder. No abrupt electrical degradation was observed for both face-up and face-down bonding configurations. The typical optical output achieved for face-up and face-down bonding approach was about 100 mW/facet and 150 mW/facet, respectively. Face-up bonded LDs exhibited a steady differential quantum efficiency ηD of ∼ 0.425 mW/mA before gradual degradation at 200 mA, while face-down bonded LDs improved its performance beyond 350 mA. The characteristic temperature T0 also improved to as much as 643 K for face-down bonded LDs. Spectrally-resolved emission measurement showed that the temperature rise in unbonded, face-up bonded and face-down bonded LDs were approximately 11, 7–8 and 2–3 °C, respectively. These investigations showed that the improved performances for face-down bonding approach compared to face-up approach were due to better thermal management.

SiO2@Gd2MoO6:EU3+ core-shell phosphors were prepared by the sol-gel process. X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FESEM), energy-dispersive X-ray spectra (EDS), transmission electron microscopy ITEM), photoluminescence (PL) spectra as well as kinetic decays were used to characterize the resulting SiO2@Gd2MoO6:Eu3+ core-shell phosphors. The XRD results demonstrate that the Gd2MoO6:Eu3+ layers on the SiO2 spheres begin to crystallize after annealing at 600 degrees C and the crystallinity increases with raising the annealing temperature. The obtained core-shell phosphors have a near perfect spherical shape with narrow size distribution (average size ca. 600 nm), are not agglomerated, and have a smooth surface. The thickness of the Gd2MoO6:Eu3+ shells on the SiO2 cores could be easily tailored by varying the number of deposition cycles (50 nm for four deposition cycles). The Eu3+ shows a strong PL luminescence (dominated by D-5(0)-F-7(2) red emission at 613 nm) under the excitation of 307 nm UV light.

Europium-doped nanocrystalline GdVO4 phosphor layers were coated on the surface of preformed submicron silica spheres by sol-gel method. The resulted SiO2@Gd0.95Eu0.05VO4 core-shell particles were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (FESEM), energy-dispersive X-ray spectra (EDS), transmission electron microscopy (TEM), photoluminescence (PL) spectra, low voltage cathodoluminescence (CL), time resolved PL spectra and kinetic decays. The XRD results demonstrate that the Gd0.95Eu0.05VO4 layers begin to crystallize on the SiO2 spheres after annealing at 600 C and the crystallinity increases with raising the annealing temperature. The obtained core-shell phosphors have spherical shape, narrow size distribution (average size ca. 600 nm), non-agglomeration. The thickness of the Gd0.95Eu0.05VO4 shells on the SiO2 cores could be easily tailored by varying the number of deposition cycles (50 nm for four deposition cycles). PL and CL show that the emissions are dominated by D-5(0)-F-7(2) transition of Eu3+ (618 nm, red).

A modified meshless local Petrov–Galerkin (MLPG) method is presented for elasticity problems using the moving least squares (MLS) approximation. It is a truly meshless method because it does not need a mesh for the interpolation of the solution variables or for the integration of the energy. In this paper, a simple Heaviside test function is chosen to overcome the computationally expensive problems in the MLPG method. Essential boundary conditions are imposed by using a direct interpolation method based on the MLPG method establishes equations node by node. Numerical results in several examples show that the present method yielded very accurate solutions. And the sensitivity of the method to several parameters is also studied in this paper.

This work investigates the effects of Sb on the tensile property of the Sn–3.5Ag–0.7Cu lead-free solder alloy and joints. Results show that the Sb-containing solder alloys and joints have higher ultimate tensile strength (UTS) than Sb-free solder alloy and solder joints due to solid solution hardening and particle hardening. UTS of solder alloys have a logarithmic increase relation with strain rate and decreases with the increase of testing temperature. The tensile strength of Sn–3.5Ag–0.7Cu solder joint reaches the highest value when 1.0 wt.% Sb is added and drops with the ageing time due to intermetallic compounds (IMC) growth at solder/IMC interface.

By means of Gleeble-1500 testing machine, the simulation of continuous casting process for AH32 steel was carried out and hot ductility and strength were determined. The cracking sensitivity was studied under the different temperatures and strain rates. The Precipitations of AIN at different temperatures and the fractures of high-temperature tensile samples were observed by using TEM (transmission electron microscope) and SEM (scanning electron microscope). The factors affecting the brittle temperature zone were discussed.