含椭圆孔有限大薄板弯曲应力分析

利用各向异性体弹性平面理论中的复势方法,以Faber级数为工具,对含椭圆孔有限大各向异性板弯曲问题进行应力分析,得出有限大含椭圆孔各向异性板弯曲的级数解形式,分析了有限大含椭圆孔板在受到弯曲载荷时孔边的应力分布,并讨论了各种参数对应力分布的影响,给出了有益的结论.

反应诱导聚合物双层结构弯曲行为的建模与分析

聚合物软材料兼具柔软性和大变形能力,作为一种智能材料在软体机器人等领域应用广泛.化学活性聚合物分子内包含具有较高反应活性的官能团,如环氧、酯键、羟基、羧基等,可以在一定条件下发生化学反应引起材料体积和性质变化.因此研究化学反应如何调控聚合物变形对开发新的功能型聚合物材料有重要指导意义.本文建立化学活性聚合物-弹性基底双层结构的理论模型并分析其在化学反应诱导下的有限弯曲行为.引入化学反应进度作为Helmholtz自由能独立的状态变量,考虑化学反应对聚合物体积变化和模量的影响,以及反应过程独立的能量耗散机制,并基于Neo-Hookean模型建立起各层内的超弹性本构关系.最后利用Newton-Raphson方法对反应完全时的平面应变稳态问题进行数值求解,得到不同几何和反应影响参数下各层内的弯曲变形和应力分布.

Effect of geometrical parameters on forming quality of high-strength TA18 titanium alloy tube in numerical control bending

The forming quality of high-strength TA18 titanium alloy tube during numerical control bending in changing bending angle β, relative bending radius R/D and tube sizes such as diameter D and wall thickness t was clarified by finite element simulation. The results show that the distribution of wall thickness change ratio Δt and cross section deformation ratio ΔD are very similar under different β; the Δt and ΔD decrease with the increase of R/D, and to obtain the qualified bent tube, the R/D must be greater than 2.0; the wall thinning ratio Δto slightly increases with larger D and t, while the wall thickening ratio Δti and ΔD increase with the larger D and smaller t; the Δto and ΔD firstly decrease and then increase, while the Δti increases, for the same D/t with the increase of D and t.

L~∞-Error Estimate of a Nonconfoming Rectangular Plate Element

In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.

An analytical model for predicting sheet springback after V-bending

Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simu-lating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.

Semi analytical modeling of springback in arc bending and effect of forming load

The analytical model for springback in arc bending of sheet metal can serve as an excellent design support.The amount of springback is considerably influenced by the geometrical and the material parameters associated with the sheet metal.In addition,the applied load during the bending also has a significant influence.Although a number of numerical techniques have been used for this purpose,only few analytical models that can provide insight into the phenomenon are available.A phenomenological model for predicting the springback in arc bending was proposed based on strain as well as deformation energy based approaches.The results of the analytical model were compared with the published experimental as well as FE results of the authors,and the agreement was found to be satisfactory.

Significance-based optimization of processing parameters for thin-walled aluminum alloy tube NC bending with small bending radius

Thin-walled aluminum alloy tube numerical control （NC） bending with small bending radius is a complex process with multi-factor coupling effects and multi-die constraints. A significance-based optimization method of the parameters was proposed based on the finite element （FE） simulation, and the significance analysis of the processing parameters on the forming quality in terms of the maximum wall thinning ratio and the maximum cross section distortion degree was implemented using the fractional factorial design. The optimum value of the significant parameter, the clearance between the tube and the wiper die, was obtained, and the values of the other parameters, including the friction coefficients and the clearances between the tube and the dies, the mandrel extension length and the boost velocity were estimated. The results are applied to aluminum alloy tube NC bending d50 mm×1 mm×75 mm and d70 mm×1.5 mm×105 mm （initial tube outside diameter D0 × initial tube wall thickness t0 × bending radius R）, and qualified tubes are produced.

Rough interfaces and ultrasonic imaging logging behind casing

Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the early- arrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.

Defects detection in typical positions of bend pipes using low-frequency ultrasonic guided wave

In order to analyze the possibility of detecting defects in bend pipe using low-frequency ultrasonic guided wave, the propagation of T(0,1) mode and L(0,2) mode through straight-curved-straight pipe sections was studied. FE(finite element) models of bend pipe without defects and those with defects were introduced to analyze energy distribution, mode transition and defect detection of ultrasonic guided wave. FE simulation results were validated by experiments of four different bend pipes with circumferential defects in different positions. It is shown that most energy of T(0,1) mode or L(0,2) mode focuses on extrados of bend but little passes through intrados of bend, and T(0,1) mode or L(0,2) mode is converted to other possible non-axisymmetric modes when propagating through the bend and the defect after bend respectively. Furthermore, L(0,2) mode is more sensitive to circumferential notch than T(0,1) mode. The results of this work are beneficial for practical testing of pipes.

Catenary action of restrained steel beam against progressive collapse of steel frameworks

The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal force relationship of five stages were proposed. Then, the formulas for determining the midspan deflection of the steel beam under distributed load, which was restrained both in rotational and axial directions, were obtained using restraint coefficient method and rigid-plastic mechanism, thereby the deformation development process was expressed accurately in a quantified way. Priority was given to the analysis of the process from bending to tension-bending, then the final state totally depends on tension to resist the external loads, that is the problem of catenary action of the restrained beam under distributed load. Additionally, finite element analysis was carried out with soitware ABAQUS6.7 on a restrained steel beam under distributed load with different axial and rotational restraint coefficients. The accuracy of the formulas presented was verified by the results of the behavior of the restrained beams. Finally, error analysis was conducted and some formulas were corrected according to the reasons of errors. The calculated results of corrected formulas match the FEM analysis results better, thus the accuracy of these formulas is improve .

FEM simulation and experimental verification of roll forming and springback process under complex contact conditions

The application of advanced high strength steel （AHSS） has an important significance in the development of the lightweight of automobile, but the parts made of AHSS usually have defects, such as fracture and large amount of springback, etc. In this paper, a model of multi-pass roll form- ing and springback process of AHSS is established with finite element software ABAQUS. Then a roll forming experiment is performed, and simulation and experimental results have been compared and analyzed. The model is established under complex contact conditions, including self-contact condi- tion. The results shows that during the process of sheet bending, large Mises stresses appear at ben- ding corners. The smaller the bending radius is, the larger the Mises stress and strain are. Thick- ness of sheet metal changes exceeds a certain limit, the differently if the bending radius is different. When the bending radius change tendency of the sheet thickness turns from increase to decrease.

Optimal design of automotive body B-pillar using simplified finite element model of body-in-prime combined with an optimization procedure

Optimization of an automotive body structure faces the difficulty of having too many design variables and a too large design search space. A simplified model of body-in-prime(BIP) can solve this difficulty by reducing the number of design variables. In this study, to achieve lighter weight and higher stiffness, the simplified model of BIP was developed and combined with an optimization procedure;consequently, optimal designs of automotive body B-pillar were produced. B-pillar was divided into four quarters and each quarter was modelled by one simplified beam. In the optimization procedure, depth, width, and thickness of the simplified beams were considered as the design variables.Weight, bending and torsional stiffness were also considered as objective functions. The optimization procedure is composed of six stages: designing the experiments, calculating grey relational grade, calculating signal-to noise ratio,finding an optimum design using Taguchi grey relational analysis, performing sensitivity analysis using analysis of variance(ANOVA) and performing non-dominated sorting and multi-criteria decision making. The results show that the width of lower B-pillar has the highest effect(about 55%) and the obtained optimum design point could reduce the weight of B-pillar by about 40% without reducing the BIP stiffness by more than 1.47%.

Bundled Hybrid Offset Riser Global Strength Analysis

Bundled hybrid offset riser (BHOR) global strength analysis, which is more complex than single line offset riser global strength analysis, was carried out in this paper. At first, the equivalent theory is used to deal with BHOR, and then its global strength in manifold cases was analyzed, along with the use of a three-dimensional nonlinear time domain finite element program. So the max bending stress, max circumferential stress, and max axial stress in the BHOR bundle main section (BMS) were obtained, and the values of these three stresses in each riser were obtained through the "stress distribution method". Finally, the Max Von Mises stress in each riser was given and a check was made whether or not they met the demand. This paper provides a reference for strength analysis of the bundled hybrid offset riser and some other bundled pipelines.

Flexural response of reinforced concrete beams strengthened with post-poured ultra high toughness cementitious composites layer

Four-point bending tests were conducted up to failure on eleven reinforced concrete (RC) beams and strengthening beams to study the effectiveness of externally pouring ultra high toughness cementitious composites (UHTCC) on improving the flexural behavior of existing RC beams.The strengthening materials included UHTCC and high strength grade concrete.The parameters,such as thickness and length of strengthening layer and reinforcement in post-poured layer,were analyzed.The flexural behavior,failure mode and crack propagation of composite beams were investigated.The test results show that the strengthening layer improves the cracking and ultimate load by increasing the cross section area.Introducing UHTCC material into strengthening not only improves the bearing capacity of the original specimens,but also disperses larger cracks in upper concrete into multiple tightly-spaced fine cracks,thus prolonging the appearance of harm surface cracks and increasing the durability of existing structures.Compared with post-poured concrete,UHTCC is more suitable for working together with reinforcement.The load?deflection plots obtained from three-dimensional finite-element model (FEM) analyses are compared with those obtained from the experimental results,and show close correlation.

Bending tests and finite element analysis of lipped channels with complex edge stiffeners and web stiffeners

In order to study the bearing capacity and stability behavior of cold-formed steel flexural members with complicated sections,a total of 12 specimens divided into 6 groups were tested,including 3 groups of pure bending tests and non-pure bending tests each.There were three types of sections considered in this investigation,including channels with complex edge stiffeners(called B1-section),Σsection with complex edge stiffeners(called B2-section),and channels with complex edge stiffeners and V-type web stiffeners(called B3-section).Local buckling,distortional buckling and interaction buckling between them were observed in tests.The experimental results indicate that the bending strengths of B2-section specimens were the largest of these three types of specimens under the same conditions.It is found that the bending strength of B2-section specimens was increased by 6.47%for pure bending state and 8.12%for non-pure bending state,compared with that of B1-section specimens.Bending strength of B3-section specimens was almost the same with that of B1-section specimens under pure bending,but a little smaller than that of B1-section under non-pure bending state.It is also shown that B2-section specimens have better plastic deformation behavior than the other two sections.In addition,a non-linear finite element model was presented and verified against tests.The finite element analysis results agree well with experimental bending strength and failure modes.

Finite element analysis of couple effect of soil displacement and axial load on single inclined pile

The couple effect of soil displacement and axial load on the single inclined pile in cases of surcharge load and uniform soil movement is discussed in detail with the methods of full-scale field tests and finite element method. Parametric analyses including the degree of inclination and the distance between soil and pile are carried out herein. When the displacement of soil on the left side and right side of a pile is identical, deformation of a vertical pile and an inclined pile is highly close in both cases of surcharge load and uniform soil movement. When the couple effect of soil displacement and axial load occurs, settlement of an inclined pile is greater than that of a vertical pile under the same axial load, and bearing capacity of an inclined pile is smaller than that of a vertical pile. This is quite different from the case when the inclined pile is not affected by soil displacement. For inclined piles, P-Δ effect of axial load would lead to a large increase in bending moment, however, for the vertical pile, P-Δ effect of axial load can be neglected. Although the direction of inclination of piles is reverse, deformation of piles caused by uniform soil movement is totally the same. For the inclined piles discussed herein, bending moment(-8 m to-17 m under the ground) relies heavily on uniform soil movement and does not change during the process of applying axial load. When the thickness of soil is less than the pile length, the greater the thickness of soil, the larger the bending moment at lower part of the inclined pile. When the thickness of soil is larger than the pile length, bending moment at lower part of the inclined pile is zero.

Flexibility of the Lumbar Intervertebral Disc in Bending and Torsion： Experimental and Finite Element Study

Intervertebral disc flexibility is influenced by lifestyle, loading history, trauma, preexisting conditions, age and degeneration. With regard to degeneration, intervertebral discs become less flexible and stiffer. In this study, a testing protocol using bending and torsion loading was developed to gain the flexibility curves and stiffness often cadaveric lumbar discs. Measurements of rotation in the sagittal plane （flexion-extension）, coronal plane （right-lefl lateral bending） and transverse plane （torsion） due to a 5 N-m load are reported. Results show that overall normal discs are more flexible and behave in a nonlinear fashion. The testing results were used in a develop t＇mite element model of an intervertebral disc to investigate the stresses and strains in the disc components： annulus fibrosus and nucleus pulposus with regard to degeneration. Simulation of bending and torsion loadings show large strains in the annulus and nucleus from a normal disc, in contrast higher stresses develop in the annulus from a degenerated disc. The proposed methodology is novel, versatile, functional and economic with implications in bioengineering, medical sciences and the clinical field.

Cell Area and Strut Distribution Changes of Bent Coronary Stents:A Finite Element Analysis

Coronary stents are metal coils or mesh tubes delivered to blocked vessels through catheters, whic Recently, special drugs h are expanded by balloons to reopen and scaffold target vessels. are carried by stents （drug-eluting stents） to further reduce instent restenosis rate after stenting procedure. However, continual study on biomechanical characteristics of stents is necessary provide a more suitable drug loading for better interactions between stents and tissue, or to platform for drug-eluting stents. The purpose of this paper is to show how finite element methods can be used to study cell area and strut distribution changes of bent coronary stents. A same bending deformation was applied to two commercial coronary stent models by a rigid curved vessel. Results show that the stent design influenced the changes of cell area and strut distribution under bending situation. The stent with links had more cell area changes at outer curvature, and the stent with peak-peak （ 〉 〈 ） strut design could have strut contact and overlapping at inner curvature. In conclusion, this finite element method can be used to study and compare cell area and strut distribution changes of bent stents, and to provide a convenient tool for designers in testing and improving biomechanical characteristics of new stents.

Fabrication of lightweight 3D interpenetrated NiTi@Mg composite with superior bending properties

A NiTi@Mg interpenetrating phase composite with high strength and lightweight was prepared by additive manufacturing(AM)and infiltration technology,and the interface bonding,three-point bending properties and cyclic compressive properties of NiTi@Mg composites were investigated.The results show that the metallurgically bonded interface is formed at the NiTi/Mg interfaces.The bending strength and compressive strength of the NiTi@Mg composite are 2.5 and 1.7 times higher than those of the NiTi scaffold,respectively.During the bending deformation process,a large number of dislocations are observed to accumulate in the soft Mg area at the interface.Furthermore,the finite element model showed that the stress accumulation area,where the bending crack is initiated,is located at the interface of NiTi and Mg.The strengthening mechanism of NiTi@Mg composites is attributed to the twinning strengthening of Mg and heterogeneous structure strengthening.

SOME SEMI-BENT FUNCTIONS WITH POLYNOMIAL TRACE FORM

This paper is devoted to the study of semi-bent functions with several parameters flexible on the finite field F2n.Boolean functions defined on F2n of the form f（r）ab（x） =Trn1（axr（2m-1））＋Tr41（bx（2n-1）/5） and the form g（rs）abcd（x）=Trn1（axr（2m-1））＋Tr41（bx（2n-1）/5）＋Trn1（cx（2m-1）1/2＋1）＋Trn1（dx（2m-1）s＋1） where n = 2m,m = 2（mod 4）,a,c ∈ F2n,and b ∈ F（16）,d ∈ F2,are investigated in constructing new classes of semi-bent functions.Some characteristic sums such as Kloosterman sums and Weil sums are employed to determine whether the above functions are semi-bent or not.