Finite deformations of cylindrical membrane under internal pressure

This paper investigates the large deformations of an extended cylindrical membrane under internal pressure. A detailed experimental analysis is carried out involving different traction forces and/or geometries and the influence of the axial force and the internal pressure in the stability. The membrane used experimentally consisted of an isotropic, homogeneous, incompressible and hyperelastic rubber-like material, which is modeled as Mooney–Rivlin, described by two elastic constants. The comparison between the experimental and numerical results for the membrane under traction is used to identify the material parameters of the model. The numerical analysis of the membrane is done using finite elements by the software ABAQUS. When the extended membrane is filled with air, it is observed that the pressure in the membrane initially increases as the volume of air inside the membrane increases until a certain critical limit pressure is reached, after which it decreases steadily with increasing volume. A parametric analysis is carried out to study the influence of the geometric and load parameter on the overall behavior and stability of the membrane. These experimental results are, as shown in the paper, in satisfactory agreement with the numerical ones.     

Postbuckling of shear deformable cross-ply laminated cylindrical shells under combined external pressure and axial compression

A postbuckling analysis is presented for a shear deformable cross-ply laminated cylindrical shell of finite length subjected to combined loading of external pressure and axial compression. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, antisymmetric and symmetric cross-ply laminated cylindrical shells for different values of load-proportional parameters.     

Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium

This paper presents a study on the postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for FGM shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling responses of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large.     

Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions

A postbuckling analysis is presented for a cross-ply laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E_z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators subjected to combined mechanical loading of external pressure and axial compression, and under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

薄壁管液压胀形加载路径研究

采用塑性变形理论研究了薄壁管液压胀形过程中轴向载荷与内压力的变化情况。在两种不同变形方式下对薄壁管胀形过程进行分析，分别就两种变形方式提出了薄壁管胀形过程中轴压与内压的理论计算方法，获得了管材在不同应变比下变形时的载荷变化曲线，探讨了薄壁管胀形工艺中确定加载路径的变化范围。     

NONLINEAR ANALYSIS OF PNEUMATIC RADIAL TIRES VIA PIECEWISE RAYLEIGH－RITZ TECHNIQUE

Based on the Sanders thin shell theory and Reddy's higher order shell theory, a general refined shell theory is developed for the analysis of stresses and deformations of pneumatic radial tires of composite construction. For easy and efficient simulation of the tire a piecewise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to the nonlinear structural problem. Bezier polynomials are used to approximate both the geometry of the surface of reference and displacement fields of the tires. Stress distributions and deformations of the tires subjected to uniform inflation pressure are computed and discussed in details. From comparison of the present results with the numerical predictions by 3D finite element method, it has been shown that the present solution procedure is accurate and applicable to much complicated time-consuming nonlinear analysis for the high quality tire.     

Indentation of tubes under combined loading

A theoretical analysis is presented of the problem of large plastic deformations of tubes subjected to combined loading in the form of lateral indentation, bending moment and axial force. A model of the shell is proposed, describing local damage of tubes subjected to large strain, rotation and shape distortion. The model is effectively decoupling the 2-D problem into a set of 1-D problems. The force-deflection characteristics of tubes were shown to depend strongly on the magnitude of the bending moment and/or axial force applied to the tube ends. The calculations revealed that the resistance of the tube to lateral indentation and thereby the energy that the tube can absorb sharply diminishes as the direction of axial force changes from pre-tension to pre-compression. The present results were shown to give good correlation with existing experimental data.     

Flat-topped conical shell under axial compression

Based on experimental observations of a grid-domed textile composite under axial compression, the large deformation mechanisms of a flat-topped conical shell are identified. Accordingly, both elastic model and rigid-plastic model are proposed to describe the collapse process and predict the load–displacement characteristics. In the rigid-plastic analysis, the energies dissipated in bending along plastic hinge lines and in stretching of the thin-wall segments between the plastic hinge lines are taken into account. Analytical expressions describing the load–displacement and energy–displacement relationships during the large deformation process are derived. Illustrated by typical numerical examples, the effects of apical angle of a flat-topped conical shell on its energy absorption capacity are revealed. The respective strain distributions on the conical shell resulted from bending deformation and membrane deformation are presented. A good agreement is shown between the theoretical predictions and experimental results.     

初始缺陷和比例加载路径对圆柱壳弹塑性稳定性的影响

应用非线性弹塑性稳定性理论研究圆柱壳在轴向力和内压联合作用下的弹塑性稳定性问题,得到了不同比例加载路径、初始缺陷和塑性变形发展程度对弹塑性失稳的影响规律曲线。结果表明,在内压的作用下,柱壳的临界轴向压应力在初始阶段有所提高,但从某一内压值开始将会有所下降。对于同一比例加载路径,随着缺陷因子的增加,临界屈曲轴向压应力随着相应地递减。而对于同样的缺陷因子,比例加载参数小于1.0时,临界屈曲轴向压应力随着比例加载参数的增大而增大;比例加载参数大于1.0时,临界屈曲轴向压应力随着比例加载参数的增大而减小;比例加载参数等于1.0为理想加载比例参数值。该研究丰富了内高压成形工艺的理论基础。     

Analytical and numerical approach to prediction of forming limit in tube hydroforming

Analytical and numerical analyses of forming limit in tube hydroforming under combined internal pressure and independent axial feeding are discussed in this paper. To predict the initiation of necking, Swift's criterion for diffuse plastic instability is adopted based on Hill's general theory for the uniqueness to the boundary value problem. In addition, in order to predict fracture initiation, Oyane's ductile fracture criterion is introduced and evaluated from the histories of stress and strain calculated by means of finite element analysis. From the comparison with a series of tube bulge tests, the prediction of the bursting failure based on the plastic instability and the ductile fracture criterion demonstrates to be reasonable so that these approaches can be extended to a wide range of practical tube hydroforming processes.     

基于DASYLab的管材轴压胀形的加载控制

内压与轴向压力的合理匹配是管材轴压胀形成败的关键因素。本文利用数据采集与处理软件 DASYL ab实现了轴向压力基于内压的线性加载控制 ,为进一步研究更为复杂的管材轴压胀形的加载控制关系奠定了实验基础     

内补液增压式THF性能测试装置开发及试验研究

材料性能对液压胀形工艺(THF)及产品质量有重大影响,传统单向拉伸试验所得材料性能不能很好反映管材液压胀形性能。开发了一种简单实用可在单动压力机上使用的试验装置,可用于不同材料及尺寸管材的液压胀形试验,以确定管材胀形性能。该装置不需要复杂的外部供液系统,而是利用其内部的补液腔自动、同步地建立起胀形所需液压力及轴向载荷,两载荷比值可通过合理设计补液腔直径得到。可以实现管材自然胀形、轴向压缩胀形、两端不同约束下的胀形和一定程度的比例加载胀形。一系列胀形对比试验表明：管端约束方式对自然胀形有较大影响,而对轴向压缩胀形影响较小;液压力、轴向载荷及其比值对轴向压缩胀形有较大影响。     

Study on experimental approaches of forming limit curve for tube hydroforming

This paper proposes a set of experimental approaches to establish the forming limit curve (FLC) in different forming modes for tube hydroforming. In tension–compression strain state, analytical models are constructed to determine the linear strain paths at the pole of the hydroformed tube, and a self-designed free hydroforming apparatus with axial feeding and internal pressure are used to carry out the bulge tests. In plane strain state, the difference is that both ends of the tube are fixed with different punches. In tension–tension strain state, a novel hydroforming apparatus are designed. The novel device requires the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. The linear strain paths for the right hand side of FLC by finite element method simulation are calculated. The linear strain paths in different strain states are verified and the FLC of roll-formed QSTE340 seamed tube is constructed through the proposed experimental approaches. Comparison between simulation and experimental results for hydroforming process of front crossmember shows that the experimental FLC is accurate and valid for tube hydroforming.     

含有初始凹陷圆柱壳的稳定承载能力的研究

对含有轴对称凹陷的圆柱壳在受到轴力作用下的稳定承载能力进行了实验研究,同时利用ANSYS软件对相同条件下的圆柱壳的承载能力进行了数值分析,实验研究与数值分析结果表现出较好的一致性。研究表明,含有初始轴对称凹陷圆柱壳的承载能力随参数,如凹陷的幅值、长度以及圆柱壳自身的长度的变化而改变,其中对凹陷的幅值变化最敏感,凹陷长度次之,圆柱壳自身长度最不敏感。     

Analytical and numerical study on plastic instabilities for axisymmetric tube bulging

In this paper, plastic instabilities of elasto–plastic tubes subject to internal pressure are discussed. For diffuse necking prediction, the classical intrinsic criteria for diffuse necking are accurate for long cylindrical tubes. However, for short tubes, geometric changes are important, and the intrinsic criteria become insufficient. For this purpose, a new diffuse necking criteria is proposed including geometric effects in the prediction.On the other hand, for the local necking prediction, the Hill's criterion is not accurate for short tubes, due to the biaxial stretching. As an alternative, a local necking criterion based on a modified Hill's assumption for localized necking is proposed. The numerical calculations carried out for different tube dimensions, explains the geometrical effects on the localization of deformations for pressurized tubes, and improves the accuracy of the proposed criteria.     

Postbuckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and thermal loading

A postbuckling analysis is presented for a stiffened laminated cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulation is based on a boundary layer theory of shell buckling which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The “smeared stiffener” approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples are presented that relate to the performance of perfect and imperfect, stiffened and unstiffened cross-ply laminated cylindrical shells. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.     

基于断裂力学的射孔套管孔边开裂行为分析

针对内压作用下的射孔套管的孔边开裂行为,应用断裂力学分别对线弹性条件和弹塑性条件下的孔边开裂进行分析,给出线弹性条件下圆柱壳体孔边裂纹应力强度因子和临界开裂内压公式,以及弹塑性条件下含孔边裂纹管道的临界开裂内压公式;通过MATLAB对两种条件下的力学模型进行解析,首先从线弹性条件下内压、裂纹长度以及孔径对应力强度因子的影响展开分析;然后从弹塑性条件下孔径和裂纹长度对临界开裂内压的影响进行分析;最后对小范围屈服情况下的两种断裂判据的套管临界开裂内压进行了对比。     

Bursting failure prediction in tube hydroforming using FLSD

In tube hydroforming, circular components are hydrobulged or hydroformed from tubular blanks with internal pressure and simultaneous axial loading. Thus the tube can be fed into the deformation zone during the bulge operation allowing more expansion and less thinning without any defects such as wrinkling, buckling, and bursting. By contrast with the buckling and the wrinkling, the bursting is generally classified as an irrecoverable failure mode. Hence in order to obtain the sound hydroformed products, it is necessary to predict the bursting behavior and to analyze the effects of process parameters on this failure condition in hydroforming processes. In this study, a forming limit stress diagram (FLSD) is constructed by plotting the calculated principal stresses based on the local necking criterion. Using the theoretical FLSD, we carry out the numerical prediction of bursting failure in a hydroforming process, which usually has non-linear strain path. Finite element analyses are carried out to find out the state of stresses during simple hydroforming operation, in which the FLSD is utilized as the forming limit criterion for assessment of the initiation of necking, and influences of the material parameters on the formability are investigated. In addition, the numerical results obtained from the FEM combined with the FLSD are confirmed with a series of bulge tests in view of bursting pressure and show a good agreement. Consequently, it is shown that the theoretical and numerical approach to bursting failure prediction proposed in this paper will provide a feasible method to satisfy the increasing practical demands for assessment of the forming severity in hydroforming processes.     

管板间隙对管壳式换热器流动与传热的影响研究

管壳式换热器中,由管板间隙引起的漏流不利于换热器的传热。通过一种新型网格生成方法,对所建立的三维实体模型进行网格划分,并利用CFD软件Fluent进行数值模拟,研究不同情况下壳程与管程的流动与传热特性。计算中采用标准k—ε模型,SIMPLE算法,压力方程为标准格式。将模拟结果引入换热器评价指标,全面分析管板间隙对管壳式换热器流动与传热的影响。     

A prediction of bursting failure in tube hydroforming process based on plastic instability

Based on plastic instability, an analytical prediction of bursting failure on tube hydroforming processes under combined internal pressure and independent axial feeding is carried out. Bursting is an irrecoverable phenomenon due to local instability under excessive tensile stresses. In order to predict the bursting failure, three different classical necking criteria – diffuse necking criteria for a sheet, and a tube, and a local necking criterion for a sheet – are introduced. The incremental theory of plasticity for an anisotropic material is adopted and the hydroforming limit, as well as a diagram of bursting failure with respect to axial feeding and hydraulic pressure are presented. In addition, the influences of material properties such as anisotropy parameter, strain hardening exponent and strength coefficient on plastic instability and bursting pressure are investigated. As a result of the above approach, the hydroforming limit with respect to bursting failure is verified with experimental results.