Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

Assessment of water depth change patterns in 120° sharp bend using numerical model

In this study,FLUENT software was employed to simulate the flow pattern and water depth changes in a 120° sharp bend at four discharge rates.To verify the numerical model,a 90° sharp bend was first modeled with a three-dimensional numerical model,and the results were compared with available experimental results.Based on the numerical model validation,a 120° bend was simulated.The results show that the rate of increase of the water depth at the cross-section located 40 cm before the bend,compared with the cross-sections located 40 cm and 80 cm after the bend,decreases with the increase of the normal water depth in the 120° curved channel.Moreover,with increasing normal water depth,the dimensionless water depth change decreases at all cross-sections.At the interior cross-sections of the bend,the transverse water depth slope of the inner half-width is always greater than that of the outer half-width of the channel.Hence,the water depth slope is nonlinear at each crosssection in sharp bends.Two equations reflecting the relationships between the maximum and minimum dimensionless water depths and the normal water depth throughout the channel were obtained.

FEM equivalent model for press bend forming of aircraft integral panel

An original plastic equivalent model was proposed to solve the problem of excessive FEM simulation time when designing the press bend forming path and optimizing the process parameters of press bend forming of the integrally stiffened aircraft panels. Based on the in-depth analysis of the mechanics of the bending and springback of the detailed model and the equivalent model of the integral panels,the plastic equivalent model of the virtual material with special initial yield stress and hardening coefficients was constructed. FEM results indicate that the objective of getting the similar contour with the same press bend forming path is achieved with the error less than 6%,and the efficiency of FEM simulation is improved by more than 80%. The plastic equivalent model is valuable and essential for the further research on the press bend forming process of large scale complicated integral panels.

Numerical modeling of flow in continuous bends from Daliushu to Shapotou in Yellow River

The upper reach of the Yellow River from Daliushu to Shapotou consists of five bends and has complex topography. A two-dimensional Re-Normalisation Group （RNG） k-ε model was developed to simulate the flow in the reach. In order to take the circulation currents in the bends into account, the momentum equations were improved by adding an additional source term. Comparison of the numerical simulation with field measurements indicates that the improved two-dimensional depth-averaged RNG k-e model can improve the accuracy of the numerical simulation. A rapid adaptive algorithm was constructed, which can automatically adjust Manning＇s roughness coefficient in different parts of the study river reach. As a result, not only can the trial computation time be significantly shortened, but the accuracy of the numerical simulation can also be greatly improved. Comparison of the simulated and measured water surface slopes for four typical cases shows that the longitudinal and transverse slopes of the water surface increase with the average velocity upstream. In addition, comparison was made between the positions of the talweg and the main streamline, which coincide for most of the study river reach. However, deviations between the positions of the talweg and the main streamline were found at the junction of two bends, at the position where the river width suddenly decreases or increases.

Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.

行为建模技术(Behavioral Modeling)在零件设计中的应用

为更好地把握设计意图,在Pro/ENGINEER软件中需要人工创建各种"关系",这种"关系"只能向前引用"尺寸参数",如果需要向后引用"尺寸参数"则要应用行为建模技术。行为建模技术通过建立"分析特征"实现优化目标的建立,以尺寸参数或用户自定义参数为变量对优化目标进行优化。本文通过一个轮胎模型,例证了上述方法的应用过程,得出了优化结果。

Three-point bending of honeycomb sandwich beams with facesheet perforations

A novel square honeycomb-cored sandwich beam with perforated bottom facesheet is investigated under threepoint bending,both analytically and numerically.Perforated square holes in the bottom facesheet are characterized by the area ratio of the hole to intact facesheet（perforation ratio）.While for large-scale engineering applications like the decks of cargo vehicles and transportation ships,the perforations are needed to facilitate the fabrication process（e.g.,laser welding）as well as service maintenance,it is demonstrated that these perforations,when properly designed,can also enhance the resistance of the sandwich to bending.For illustration,fair comparisons among competing sandwich designs having different perforation ratios but equal mass is achieved by systematically thickening the core webs.Further,the perforated sandwich beam is designed with a relatively thick facesheet to avoid local indention failure so that it mainly fails in two competing modes：（1）bending failure,i.e.,yielding of beam cross-section and buckling of top facesheet caused by bending moment;（2）shear failure,i.e.,yielding and buckling of core webs due to shear forcing.The sensitivity of the failure loads to the ratio of core height to beam span is also discussed for varying perforation ratios.As the perfo-ration ratio is increased,the load of shear failure increases due to thickening core webs,while that of bending failure decreases due to the weakening bottom facesheet.Design of a sandwich beam with optimal perforation ratio is realized when the two failure loads are equal,leading to significantly enhanced failure load（up to 60%increase）relative to that of a non-perforated sandwich beam with equal mass.

Comparative efficiency analysis of different nonlinear modelling strategies to simulate the biaxial response of RC columns

The performance of different nonlinear modelling strategies to simulate the response of RC columns subjected to axial load combined with cyclic biaxial horizontal loading is compared. The models studied are classified into two categories according to the nonlinearity distribution assumed in the elements： lumped-plasticity and distributed inelasticity. For this study, results of tests on 24 columns subjected to cyclic uniaxial and biaxial lateral displacements were numerically reproduced. The analyses show that the global envelope response is satisfactorily represented with the three modelling strategies, but significant differences were found in the strength degradation for higher drift demands and energy dissipation.

Analysis of bending on the front end of sheet during hot rolling

The analysis of bending in finishing rolling was performed. An asymmetrical rolling force model was established, and the upper and lower neutral points were determined. Thc bending which resulted from the asymmetrical rolling force at the roll gap was studied and related flexibility equations were proposed according to elastic mechanics. Moreover, material mechanics was used to analyze the effects of temperature difference and self-weight on the bending out of the roll gap, and the flexibility equations were constructed. The main factors on bending were summed up, and the bending rule in the rolling could be obtained. In addition practical calculation was made with the production data of ribbon steel from Laiwu Iron ＆ Steel Group Co. Ltd.

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.

Bending of orthotropic plates resting on Pasternak's foundations using mixed shear deformation theory

The mixed first-order shear deformation plate theory（MFPT） is employed to study the bending response of simply-supported orthotropic plates.The present plate is subjected to a mechanical load and resting on Pasternak＇s model or Winkler＇s model of elastic foundation or without any elastic foundation.Several examples are presented to verify the accuracy of the present theory.Numerical results for deflection and stresses are presented.The proposed MFPT is shown simplely to implement and capable of giving satisfactory results for shear deformable plates under static loads and resting on two-parameter elastic foundation.The results presented here show that the characteristics of deflection and stresses are significantly influenced by the elastic foundation stiffness,plate aspect ratio and side-to-thickness ratio.

Basic Characteristics of a New Flexible Pneumatic Bending Joint

Several typical flexible pneumatic actuators （FPA） and different mechanical models describing their behaviors have been proposed, however, it is difficult to balance compliance and load capacity in conventional designs, and these models still have limitations in predicting behavior of FPAs. A new flexible pneumatic bending joint （FPBJ） with special anisotropic rigidity structure is proposed. The FPBJ is developed as an improvement with regard to existing types of FPA, and its principal characteristic is derived from the special anisotropic rigidity structure. With this structure, the load capacity in the direction perpendicular to bending plane is strengthened. The structure of the new FPBJ is explained and a mathematical model is derived based on Euler-Bernoulli beam model and Hook’s law. To obtain optimum design and usage, some key structure parameters and input-output characteristics are simulated. The simulation results reveal that the relationship between the structure parameters and FPBJ’s bending angle is nonlinear. At last, according to the simulation results, the FPBJ is manufactured with optional parameters and tested. The experimental results show that the joint’s statics characteristics are reflected by the mathematical model accurately when the FPBJ is deflated. The maximum relative error between simulation and experimental results is less than 6%. However, the model still has limitations. When the joint is inflated, the maximum relative error reaches 20%. This paper proposes a new flexible pneumatic bending joint which has sufficient load capacity and compliance, and the mathematical model provides theoretical guidance for the FPBJ’s structure design.

Modeling of normal faulting in the subducting plates of the Tonga,Japan,Izu-Bonin and Mariana Trenches:implications for near-trench plate weakening

The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate. The observed average trench relief is found to be the smallest at the Japan Trench(3 km) and the largest at the Mariana Trench(4.9 km), and the average fault throw is the smallest at the Japan Trench(113 m) and the largest at the Tonga Trench(284 m). A subducting plate is modeled to bend and generate normal faults subjected to three types of tectonic loading at the trench axis: vertical loading, bending moment, and horizontal tensional force. It is inverted for the solutions of tectonic loading that best fit the observed plate flexure and normal faulting characteristics of the four trenches. The results reveal that a horizontal tensional force(HTF) for the Japan Trench is 33%, 50% and 60% smaller than those of the Mariana, Tonga and Izu-Bonin Trenches, respectively. The normal faults are modeled to penetrate to a maximum depth of 29, 23, 32 and 32 km below the sea floor for the Tonga,Japan, Izu-Bonin and Mariana Trenches, respectively, which is consistent with the depths of relocated normal faulting earthquakes in the Japan and Izu-Bonin Trenches. Moreover, it is argued that the calculated horizontal tensional force is generally positively correlated with the observed mean fault throw, while the integrated area of the reduction in the effective elastic thickness is correlated with the trench relief. These results imply that the HTF plays a key role in controlling the normal faulting pattern and that plate weakening can lead to significant increase in the trench relief.

Articulated Lifting System Modeling Based on Dynamics of Flexible Multi-Body Systems

In lifting sub-system of deep-sea mining system, spherical joint is used to connect lifting pipes to replace fixed joint. Based on Dynamics of Flexible Multi-body systems, the mechanics model of articulated lifting system is established. Under the four-grade and six-grade oceanic condition, dynamic responses of lifting system are simulated and experiment verified. The simulation results are consistent with experimental ones. The maximum moment of flexion is 322 kN-m on the first pipe under six-grade sea condition. It is seen that the articulated connection can reduce the moment of flexion. The bending deformation of pipe center is researched, and the maximum is 0. 000479 m on the first pipe. Deformation has a little effect on the motion of system. It is feasible to analyze articulated lifting system by applying the theory of flexible multi-body dynamics. The articulated lifting system is obviously better than the fixed one.

Experimental and Numerical Study of Dilute Gas-Solid Flow inside a 90°Horizontal Square Pipe Bend

A pneumatic test rig is built to test a curved 90° square bend in an open-circuit horizontal-to-horizontal suction wind tunnel system. Sand particles are used to represent the solid phase with a wide range of particle diameters. Velocity profiles are constructed by measuring the gas velocity using a 3-hole probe. Flow patterns inside the bend duct are introduced using sparks caused by burning sticks of incense with the air flow inside the piping system for flow visualization purpose. Numerical calculations are performed by Lagrangian-particle tracking model for predicting particle trajectories of dispersed phase, and standard k-ε model for predicting the turbulent gas-solid flows in bends. Comparisons made between the theoretical results and experimental data for the velocity vectors and particle trajectories show good agreement.

STRAIN-GRADIENT STRESS ANALYSIS IN SAINT-VENANT BENDING

Light beam deflections caused by stress or strain gradients are inves- tigated analytically and experimentally in homogeneous beam specimens which are subjected to a particular case of flexure with shear. This study is a generalization of the prior an alytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where in- formation of interest is collected along a line of symmetry of the stress field. Main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state. The most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and the longitudinal axes of the beam are in pure shear. The obtained results are compared with the predictions of the developed analytical models and with the pre- dictions of Filon's stress function. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively.

Micro Mechanical Model of 3D Woven Composites

A combined beam model representing the periodicity of the microstructure and micro deformation of 3D woven composites is developed for predicting mechanical properties. The model considers the effects of off axial tension/compression and bending/shearing couplings as well as the mutual reactions of fiber yarns. The method determining microstructure by using woven parameters is described for a typical 3D woven composite material. An analytical cell, constructed by a minimum periodic section of yarn and interlayer matrix, is adopted. Micro stresses in the cell under in-plane tensile loading are obtained by using the proposed beam model and macro modulus is then obtained by the averaging method. Material tests and a 2D micro FEM analysis are made to evaluate this model. Analyses reveal that micro stress caused by tensile/bending coupling effect is not negligible in the stress analysis.

碳纤维含量对碳纤维增强聚醚醚酮复合材料弯曲性能和失效行为的影响

基于渐进损伤的VUMAT子程序,并引入了Johnson-Cook模型,通过Matlab生成了不同碳纤维占比的碳纤维增强聚醚醚酮(CFRP)复合材料,建立了三点弯曲有限元模型。通过分析应力—应变分布、载荷—位移曲线和吸收能—位移曲线得出以下结论:添加碳纤维有效改善了基体聚醚醚酮(PEEK)内部的应力—应变分布,显著提升了材料的力学性能、刚度和抗断裂性能。CFRP复合材料在三点弯曲过程中表现出更好的性能,能够承受明显的塑性变形,且有效避免裂纹扩展。此外,在相同位移载荷条件下,随着碳纤维含量增加,CFRP复合材料的位移逐渐减小。特别是在碳纤维质量分数为10%和20%的复合材料中,上表面和下表面的最大位移呈现出曲折的特点。结合应力—应变场的分布情况,这表明碳纤维的添加能有效提高材料的刚度和抗弯性能。

盾构机始发井深基坑力学和变形特性离心模型试验研究

为探究盾构机始发井深基坑开挖过程中周边土体的应力、变形和土压力分布规律,通过对工程原型进行概化,在典型土层条件下,采用停机-开挖-支护的模拟方式开展了方形基坑和圆形基坑两种方案共2组离心模型试验,从地连墙的弯矩和其后土体的水平位移、基坑外侧土压力分布以及地表沉降等角度,对比分析了两种盾构机始发井深基坑开挖过程的工程特性。结果表明:地面沉降随基坑开挖深度增大逐渐增加,形成沉降槽状;地连墙土压力变化呈非线性,随着基坑开挖不断深入的,离地表较近处的土压力逐渐变大,而深处的土压力则逐渐减小;在第5步开挖时2组模型地下连续墙水平位移均达到最大值,圆形基坑是方形基坑的1.4倍,同时地连墙的弯矩也达到最大值,圆形基坑比方形基坑小320 kN·m。研究成果可为深埋隧道深基坑的优化设计和开挖提供指导。