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A well-balanced and positivity-preserving meshless method based on smoothed particle hydrodynamics (SPH) is developed to simulate one-dimensional (1D) and two-dimensional (2D) shallow water (SW) fl...

In this study, a one- and two-dimensional (1D–2D) coupled model is developed to solve the shallow water equations (SWEs). The solutions are obtained using a Lagrangian meshless method called smoothed particle hydrodynamics (SPH) to simulate shallow water flows in converging, diverging and curved channels. A buffer zone is introduced to exchange information between the 1D and 2D SPH-SWE models. Interpolated water discharge values and water surface levels at the internal boundaries are prescribed as the inflow/outflow boundary conditions in the two SPH-SWE models. In addition, instead of using the SPH summation operator, we directly solve the continuity equation by introducing a diffusive term to suppress oscillations in the predicted water depth. The performance of the two approaches in calculating the water depth is comprehensively compared through a case study of a straight channel. Additionally, three benchmark cases involving converging, diverging and curved channels are adopted to demonstrate the ability of the proposed 1D and 2D coupled SPH-SWE model through comparisons with measured data and predicted mesh-based numerical results. The proposed model provides satisfactory accuracy and guaranteed convergence.

In this study, an upwinding SPH model with a non-symmetric kernel function is proposed to predict one-dimensional open channel flows. Due to the application of non-symmetric kernel function biased in favor of the upstream side, numerical diffusion is intrinsically added into the discretized momentum equation using SPH. The proposed model thus has shown to have good potential to resolve steep gradient or discontinuous solutions without the need of exactly adding artificial viscosity to the discretized equation. Furthermore, an upwinding coefficient for the determination of the degree of upwinding is derived to accommodate the dispersion-relation-preserving (DRP) property. In wave number space, the error between the discretized SPH equations and the original partial differential equations is minimized, thereby yielding the optimized upwinding coefficient. The proposed model has been validated by solving four benchmark problems involving non-rectangular cross section, varying channel width, non-uniform bed slope and hydraulic jump. Comparison of the numerical and exact solutions shows that the proposed model has the ability of accurately predicting various open channel flows involving complicated transcritical flows. The consistency condition of the proposed model is also analyzed theoretically for the sake of completeness.

The study aims to explore the reasons for why the fracture defects in the forging of a long circular pipe part occurred. Besides, the tool design has been proposed to eliminate the fracture defects. The flow direction, the velocity, the effective stress, the effective strain, the damage value, and so on, can be observed by using the point tracking function in the commercial simulation software. Moreover, the forging stream line occurring in the work-piece formation based on the simulation software is compared with that in the real product in order to understand the reasons for the fracture. The tool designs are modified accordingly, and the simulation software is used to confirm the acceptance of tool designs. Finally, appropriate forging has been performed to as per product requirements.

In this study, a novel treatment of adopting mass-varied particles in smoothed particle hydrodynamics (SPH) is proposed to solve the shallow water equations (SWEs) and model the rainfall-runoff process. Since SWEs have depth-averaged or cross-section-averaged features, there is no sufficient dimension to add rainfall particles. Thus, SPH-SWE methods have focused on modeling discharge flows in open channels or floodplains without rainfall. With the proposed treatment, the application of SPH-SWEs can be extended to rainfall-runoff processes in watersheds. First, the numerical procedures associated with using mass-varied particles in SPH-SWEs are introduced and derived. Then, numerical validations are conducted for three benchmark problems, including uniform rainfall over a 1D flat sloping channel, nonuniform rain falling over a 1D three-slope channel with different rainfall durations, and uniform rainfall over a 2D plot with complex topography. The simulated results indicate that the proposed treatment can avoid the necessity of a source term function of mass variation, and no additional particles are needed for the increase of mass. Rainfall-runoff processes can be well captured in the presence of hydraulic jumps, dry/wet bed flows, and supercritical/subcritical/transcritical flows. The proposed treatment using mass-varied particles was proven robust and reliable for modeling rainfall-runoff processes. It can provide a new alternative for investigating practical hydrological problems.

In the study, a Lagrangian particle method, smoothed particle hydrodynamics (SPH), is attempted to solve the one-dimensional shallow water equations (1D-SWEs) for modeling subcritical and supercritical flows at open channel junctions. SPH-SWEs is so far only limited in the applications of single channel flows. To extend SPH-SWEs to channel junction flows, a novel approach, which considers the internal boundary conditions at junctions in the numerical formulation, is proposed to investigate 1D hydrodynamic behavior of subcritical and supercritical flows at open channel junctions. The Shabayek and Rice junction models derived from the mass and momentum conservation at junctions are adopted to respectively specify the internal boundary conditions in subcritical and supercritical flows. The newly proposed approach is verified with five benchmark study cases, including steady and unsteady, subcritical and supercritical flows in channel junction systems. The numerical convergence and accuracy of the proposed approach are examined and discussed. It is concluded that the proposed SPH-SWEs approach can accurately handle various subcritical and supercritical flow conditions in channel junctions, and can provide an alternative to investigate practical junction flows in open channels.

In this paper, the response and failure of sharp-notched 6061-T6 aluminum alloy circular tubes with five different notch depths of 0.4, 0.8, 1.2, 1.6 and 2.0 mm subjected to cyclic bending were experimentally and theoretically investigated. The experimental moment-curvature relationship exhibits an almost steady loop from the beginning of the first cycle. And, the notch depth has almost no influence on its relationship. However, the ovalization-curvature relationship exhibits a symmetrical, increasing, and ratcheting behavior as the number of cycles increases. In addition, a higher notch depth of a tube leads to a more severe unsymmetrical trend of the ovalization-curvature relationship. Focusing on the aforementioned relationships, the finite element software ANSYS was used to continue the related theoretical simulation. Furthermore, the five groups of tubes tested have different notch depths, from which five unparallel straight lines can be observed from the relationship between the controlled curvature and the number of cycles required to produce failure in the log-log scale. Finally, a failure model was proposed to simulate the aforementioned relationship. Through comparison with the experimental data, the proposed model can properly simulate the experimental data.

This study aims at analyzing the influence of the maximum principal stress on Tungsten Carbide Steel die core in an extrusion die which caused the crack of die core, and then adjusts the dies assembly method in order to improve the service life of die. In this study, we combine FEM simulation software with the Taguchi Method L9(34) to choose the cobalt content for die core materials, and the quantity of shrink fit while assembling the die core and die case as the reference parameters. When carrying out the simulation process, we compared the changes of the maximum principal stress of the die core caused by the plastic deformation of die materials to achieve the minimum expected value as the goal for the most optimal die combination. Then, the results obtained are to make dies in trial and mass-production practically; as a result, the die life is improved from the original 1000 to 150,000 pcs, which is more than 150 times better than before.

This study intended to investigate the longitudinal crack on the tungsten carbide alloy die core that caused by the influence of receiving the hoop tensile stress in the process of inverse extrusion. Therefore, the shrink fit is adopted to design the die core and stress ring, and assemble the die case, in order to yield the hoop compressive stress in advance, which can be used to resist the tensile hoop stress yielded from the forging process. It also applied the FEM simulation software and Taguchi Method L9(34) in this study to simulate various combinations of different shrink fits, in order to obtain the best combination of die. Moreover, it focused on the compressive strength of material characteristics for the tungsten carbide alloy steel die core, and properly adjusted the shrink fit to prevent an early crack on the die core that caused by the hoop compressive stress in advance, in order to achieve the best result.

In this paper, an experimental investigation of the response and collapse of elliptical-notched tubes subjected to cyclic bending is discussed. It was found from moment-curvature curves that the loops show cyclic hardening and gradually steady after a few cycles. The ovalization-curvature curves show an unsymmetrical, ratcheting and increasing manner with the number of cycles. Based on the experimental relationship between the controlled curvature and the number of cycles necessary to produce buckling, the empirical formulation proposed by Kyriakides and Shaw in 1987 was modified for simulating the aforementioned relationship. In addition, it was found that the experimental curve of the ovalization and the number of cycles could be divided into three stages. The empirical relationship proposed by Chang and Pan in 2009 was modified for simulating the aforementioned curve of the initial and secondary stages. It has been shown that the simulations were in good agreement with the experimental data.

This study aims at analyzing the influence of the maximum principal stress on Tungsten Carbide Steel die core in an extrusion die which caused the crack of die core, and then adjusts the dies assembly method in order to improve the service life of die. In this study, combining FEM simulation software with Taguchi Method L9(34) is to choose the cobalt content for die core materials, and the quantity of shrink fit while assembling the die core and die case as the reference parameters. When carrying out the simulation process, compared the changes of the maximum principal stress of the die core caused by the plastic deformation of die materials to achieve the minimum expected value as the goal be chosen the most optimal die combination. Then, the results obtained are to make dies in trial and mass-production practically; as a result, it can be achieved that the die life is improved from the original 1000pcs to 150000pcs, which is more 150 times better than before.

Summary A new approach to model weakly nonhydrostatic shallow water flows in open channels is proposed by using a Lagrangian meshless method, smoothed particle hydrodynamics (SPH). The Lagrangian form of the Boussinesq equations is solved through SPH to merge the local and convective derivatives as the material derivative. In the numerical SPH procedure, the present study uses a predictor–corrector method, in which the pure space derivative terms (the hydrostatic and source terms) are explicitly solved and the mixed space and time derivatives term (the material term of B1 and B2) is computed with an implicit scheme. It is thus a convenient tool in the processes of the space discretization compared to other Eulerian approaches. Four typical benchmark problems in weakly nonhydrostatic shallow water flows, including solitary wave propagation, nonlinear interaction of two solitary waves, dambreak flow propagation, and undular bore development, are selected to employ model validation under the closed and open boundary conditions. Numerical results are compared with the analytical solutions or published laboratory and numerical results. It is found that the proposed approach is capable of resolving weakly nonhydrostatic shallow water flows. Thus, the proposed SPH approach can supplement the lack of the SPH–Boussinesq researches in the literatures, and provide an alternative to model weakly nonhydrostatic shallow water flows in open channels.

In this study, the authors solve the shallow water equations (SWE) with smoothed particle hydrodynamics (SPH) for one-dimensional (1D) nonrectangular and nonprismatic channel flows with open boundaries. To date, 1D SPH-SWE has been only developed to simulate rectangular prismatic channel flows with closed and open boundaries. However, for practical hydraulic problems, channel cross sections are not always rectangular and prismatic. A general approach is proposed in this study to extend the engineering application range of 1D SPH-SWE to nonrectangular and nonprismatic channels with open boundaries by introducing the wetted cross-sectional area and the water discharge in SWE and combining the method of specified time interval with the inflow/outflow algorithm. Three benchmark study cases, aiming at testing various steady flow regimes in nonrectangular and nonprismatic channels, are adopted to validate the newly proposed approach. Through the investigation of the convergence analysis and numerical ac...

This study discusses an experimental investigation of the effect of the mean moment on the response and collapse of sharp-notched circular tubes subjected to cyclic bending. To highlight the influence of the mean moment effect, five different moment ratios r (minimum moment / maximum moment) were experimentally investigated. We found that the moment-curvature loop gradually shrinks, and stabilizes after a few cycles for r = −1. However, the moment-curvature loop exhibits ratcheting and increases with the number of cycles for r ≠ −1. In addition, the ovalization-curvature curve shows unsymmetrical, ratcheting and increasing manner with the number of cycles for any r. Finally, the empirical formulation proposed by Chang et al. [1] was modified to simulate the relationship between the controlled moment range and the number of cycles necessary to produce buckling. The results of the experimental investigation and the simulation were in good agreement with each other.

The purpose of this paper is mainly to develop a method to simulate the bump height variation and probe mark profile for Eutectic (Sn63/ Pb37) bump wafer probing with continuing-touchdown probing. Certainly, the bump height variation and probe mark area on the solder bump influence the quality of the wafer probing and further impacts reliability of the packaging process after wafer probing to cause issues of cold-joint and needle damage. A three-dimensional computational model of was developed to analyze the contact phenomena between the vertical needle and the solder bump. Finite element simulation software, ANSYS, is used to analyze the loading force distributed on the vertical needle with various overdrives. In addition, the results of the bump height variation and probe mark area, which predicted by the finite element method (FEM), were verified against the on-line experimental results. Finally, the results predicted by the finite element model is consistent with experimental results and the numerical method presented in the paper can be used as a useful evaluating method to support the choice of suitable probe geometry and wafer probe testing parameters.

This study aims at investigating the simulation error and computational efficiency of indoor particulate matter (PM) concentration estimation for various kernel functions and particle search algorithms of the kernel method. Firstly, five kernel functions (the Gaussian, quadratic, cubic, quartic and quintic kernels) together with five released particle number are applied to establish twenty-five scenarios of indoor concentration estimation. Measured PM concentration profiles in indoor chambers are used to identify the most appropriate kernel function among the above scenarios. The simulated results show that the cubic and quartic kernel functions both give the minimum simulation error and they only need about 40% CPU time of the Gaussian kernel function. Next, two particle search algorithms (the all-pair and linked-list algorithms) with the cubic kernel function are tested for various numbers of the released particles and concentration observation points. The present study demonstrates that the linked-list algorithm provides the same accuracy as the all-pair algorithm for indoor PM concentration estimation. However, for the computational efficiency, the linked-list algorithm is proved to be much better than the widely used all-pair algorithm. The required CPU time of the all-pair algorithm can be 28 times as large as the linked-list algorithm when the number of the concentration observation points is more than O (10 4 ).

This study develops a new concentration estimation method for Lagrangian modeling of airborne particulate matter (PM) in indoor environment. This new method, based on the cubic spline kernel function with the smoothing length and solid building boundary treatment, is considered herein to study the accuracy and efficiency of indoor airborne PM concentration calculation. The commonly used sampling volume method is also adopted for numerical performance test. Reliable measured PM concentration profiles in indoor chambers are used to verify the accuracy and efficiency of the above methods. A comparison of the relative merits and shortcomings of these two methods is emphasized. The results show that the sampling volume method is simple and easy to formulate in indoor environment. However, it produces sensitive and scattered concentration profiles, especially in recirculation zones, if the released particle number is not large enough. This problem can only be solved by using a sufficient number of particles, which should be determined by the sensitivity analysis. The kernel method can provide accurate and smooth profiles even though the released particle number is one order less than the sampling volume method. Under the same PM concentration estimation accuracy, the kernel method is much more efficient compared to the sampling volume method.

Cyclic bending of tubes leads to progressive ovalization of the tube cross-section, and persistent cycling causes catastrophic buckling of the tube. This paper presents the response and stability of SUS304 stainless steel tubes with local sharp-notched depths of 0.2, 0.4, 0.6, 0.8, and 1.0[Formula: see text]mm and notch directions of 0[Formula: see text], 30[Formula: see text], 60[Formula: see text], and 90[Formula: see text] under cyclic bending. The experimental results reveal that the moment–curvature relationship first exhibits cyclic hardening and then a steady loop after a few cycles. Because the notches are small and localized, notch depth and direction show minimal influence on the moment–curvature relationship. In contrast, the ovalization–curvature relationship demonstrates an increasing and ratcheting pattern along with the bending cycle, whereas notch depth and direction show a strong influence on this relationship. Finite-element analysis via ANSYS is used to simulate the moment–curvature and ovalization–curvature relationships, and an empirical model is proposed to simulate the relationship between the controlled curvature and number of cycles required to ignite buckling. The experimental and analytical data agree well with each other.

In this paper, experimental and theoretical investigations on the response and collapse of 310 stainless steel tubes with different diameter-to-thickness ratios subjected to cyclic bending are discussed. The tube-bending device and curvature-ovalization measurement apparatus were used to conduct the experiment. The endochronic theory combined with the principle of virtual work and finite element software, ANSYS, were used to simulate the moment-curvature and ovalization-curvature relationships. It is shown that although the two methods lead to good simulation of the moment-curvature relationship, the endochronic theory combined with the principle of virtual work has the better simulation of the ovalization-curvature response when compared with experimental data and the simulation by ANSYS. In addition, the theoretical formulations proposed by Kyriakides and Shaw (1987) and Lee et al. (2001) were used to simulate the controlled curvature– number of cycles to produce buckling relationship. It is shown that the theoretical formulations effectively simulate the experimental data

In this paper, experimental and theoretical investigations of the effect of the mean moment on the response and collapse of circular thin-walled tubes subjected to cyclic bending are discussed. To highlight the influence of the mean moment effect, three different moment ratios r (minimum moment/ maximum moment) of -1, -0.5 and 0, respectively, were experimentally investigated. It has been found that the moment-curvature loop gradually shrinks with the number of cycles, and becomes stable after a few cycles for symmetric cyclic bending (r

This paper presents the experimental and theoretical results of the viscoplastic response and collapse of 316L stainless steel tubes subjected to cyclic bending. The tube bending machine and curvature-ovalization measurement apparatus, which was designed by Pan et al. (1998), were used for conducting the cyclic curvature-controlled experiment. Three different curvature-rates were controlled to highlight the characteristic of viscoplastic response and collapse. Next, the endochronic theory and the principle of virtual work were used to simulate the viscoplastic response of 316L stainless steel tubes under cyclic bending. In addition, a proposed theoretical formulation (Lee and Pan 2001) was used to simulate the relationship between the controlled cyclic curvature and the number of cycles to produce buckling under cyclic bending at different curvature-rates (viscoplastic collapse). It has been shown that the theoretical simulations of the response and collapse correlate well with the experimental data.

This paper presents the experimental and theoretical results of the response and collapse of 316L stainless steel tubes subjected to cyclic bending. The tube bending machine and curvature-ovalization measurement apparatus were used for conducting the curvature-controlled experiment. It was found that the response and collapse are similar to that of metal tubes found in literatures. Next, the endochronic theory and the principle of virtual work were used to simulate the response of 316L stainless steel tubes under cyclic bending. In addition, a proposed theoretical formulationwas used to simulate the relationship between the controlled curvature and the number of cycles to produce buckling. It has been shown that the theoretical simulations of the response and collapse correlate well with the experimental data.

In this study, the endochronic theory was used to investigate the collapse of thick-walled tubes subjected to external pressure and axial tension. The experimental and theoretical findings of Madhavan et al. (1993) for thick-walled tubes of 304 stainless steel subjected to external pressure and axial tension were compared with the endochronic simulation. Collapse envelopes for various diameter-to-thickness tubes under two different pressure-tension loadings were involved. It has been shown that the experimental results were aptly described by the endochronic approach demonstrated from comparison with the theoretical prediction employed by Madhavan et al. (1993). Furthermore, by using the rate-sensitivity function of the intrinsic time measure proposed by Pan and Chern (1997) in the endochronic theory, our theoretical analysis was extended to investigate the viscoplastic collapse of thick-walled tubes subjected to external pressure and axial tension. It was found that the pressure-tension collapse envelopes are strongly influenced by the strain-rate during axial tension. Due to the hardening of the metal tube of 304 stainless steel under a faster strain-rate during uniaxial tension, the size of the tension-collapse envelope increases.

Because bolt usages always have the requirement of tensile strength, with a view to reach the requirement of tensile strength, the material property or forming method and dies design can be used to obtain it. The study aims at the forming method and dies design to perform the multistage analysis of bolt to realize the effect of forging stream line continuity on tensile strength. The study uses Simufact-FEM software to do the multistage forming simulation to modify the dies design and forming method. The amount of broken forging stream line can be used to identify whether the bolt is good or not. From the comparison of realistic forging product, the results can verify the acceptance of FEM simulation.

In this paper, an experimental investigation of the degradation and buckling of circular tubes subjected to cyclic bending is discussed. The machinery specimens (with different diameter-to-thickness ratios but the same inside diameter) and method of testing (cyclic bending) in this study were the same as the ones used by Lee et al. (Lee, K.L., Pan, W.F., Kuo, J.N., 2001. The influence of the diameter-to-thickness ratio on the stability of circular tubes under cyclic bending. International Journal of Solids and Structures 38, 2401–2413.) for 316L stainless steel circular tubes. The experimental investigation was extended to different outside and inside diameters of the same circular tubes subjected to cyclic bending. Based on the experimental findings, the empirical formulation proposed by Lee et al. (2001) was modified so that it can now be used to simulate the relationship between the prescribed curvature and the number of cycles necessary to produce buckling. In addition, it was found that the experimental curve of the ovalization and the number of cycles necessary to produce buckling could be divided into three stages – an initial, secondary and tertiary stage. An empirical relationship, similar to the Bailey–Norton creep formulation, was proposed for simulating the aforementioned curve for the initial and secondary stages in this study. The derived empirical relationship was in good agreement with the experimental data.