The theory of Cosserat points applied to the analyses of wrinkled and slack membranes

Numerical simulations of wrinkling and slacking of geometrically nonlinear membrane structures are considered using planar Cosserat points. The finite element method (FEM) solves the problem by weakly projecting the governing PDEs and thus requires numerical integration. This is contrasted with Cosserat point elements wherein governing equations are solved in an averaged sense at a point. The point is equipped with a few directors and can describe the deformation kinematics of a finite region containing itself. Numerical modeling through the Cosserat point provides freedom from numerical integration and locking. Presently a plane stress quadrilateral Cosserat point element is used to study the wrinkling and slacking of isotropic membranes. The approach by Roddeman et al. (ASME J Appl Mech 54:884–892, 1987) is exploited to detect wrinkled/slack elements in the membrane structure. Here stretching parameters are employed to modify the deformation tensor to represent a fictive non-wrinkled surface. A variation of the algorithm to detect spatial variations of the stretching parameters within a point element is also described. Several numerical examples on static deformations of wrinkled/slack membranes are presented. Limited comparisons with a reported experiment and with results via the FEM as well as a mesh-free approach are provided to assess the performance of the approach.     

Concomitant wrinkling and buckle-delamination of elastic thin films on compliant substrates

Compressing a thin elastic film attached to a thick compliant substrate can lead to buckling instability. Two commonly observed buckling modes, buckle-delamination and wrinkling, have each been analyzed separately in previous studies. Recent experiments have observed that the two modes can co-exist and co-evolve. In this paper, by analytical and finite element methods, we present a study on concomitant wrinkling and buckle-delamination for an elastic film on a highly compliant substrate. First, without delamination, we present an analytical solution for wrinkling that takes into account the effect of Poisson’s ratio of the substrate. In comparison with a nonlinear finite element analysis, an approximate formula is derived to estimate the normal traction at the interface and to predict initiation of wrinkle-induced delamination. Next, with a pre-existing delamination crack, the critical strain for the onset of buckling instability is predicted by finite element eigenvalue analysis. For an intermediate delamination size, a mixed buckling mode is predicted with the critical compressive strain lower than previous solutions for both wrinkling and buckle-delamination. Post-buckling analyses show a significant shear-lag effect with an effective load transfer length three orders of magnitude greater than the film thickness. Finally, concomitant wrinkling and buckle-delamination is simulated to illustrate the interaction between the two buckling modes, and the results are discussed in view of failure mechanisms and applications in thin film metrology.     

3D numerical study on wrinkling characteristics in NC bending of aluminum alloy thin-walled tubes with large diameters under multi-die constraints

With an increase in the diameters of aluminum alloy thin-walled tubes (AATTs) and a decrease in their bending radii, wrinkling characteristics and its prediction under multi-die constraints have become a key problem urgently to be solved for improving the forming quality in numerical control (NC) bending of AATTs with large diameters. Thus in this paper, considering the characteristics of the bending processes, based on the ABAQUS software environment, a 3D elastic–plastic finite element model and a wrinkling energy prediction model under multi-die constraints are established and their reliabilities are validated, respectively, in which, the appropriate choosing of forming parameters is achieved to guarantee no excessive thinning and flattening in the processes even if wrinkling borders on occurring. By combining the two models, variation relationships of the maximum wrinkling factor with different compressed deformation zones and forming ratios, and effects of clearances and friction between different dies and tubes on the maximum wrinkling factor are obtained, and then an investigation into the wrinkling characteristics is carried out for the processes. It is found that the larger the diameters of AATTs, the larger the wrinkling sensitive zones (WSZs), and there is a larger possibility of wrinkling in the bending segments of WSZs than in the straight ones; the larger the effects of clearances and friction between different dies and tubes on wrinkling.     

Finite element analysis of membrane wrinkling

New results are presented for the finite element analysis of wrinkling in curved elastic membranes under‐going large deformation. Concise continuum level governing equations are derived in which singularities are eliminated. A simple and efficient algorithm with robust convergence properties is established to find the real strain and stress of the wrinkled membrane for Hookean materials. The continuum theory is implemented into a finite element code. Explicit formulas for the internal forces and the tangent stiffness matrix are derived. Numerical examples are presented that demonstrate the effectiveness of the new theory for predicting wrinkling in membranes undergoing large deformation. Copyright © 2001 John Wiley & Sons, Ltd.     

Investigation into the wrinkling behaviour of thin sheets in the cylindrical cup deep drawing process using bifurcation theory

The initiation and growth of wrinkles are influenced by many factors such as stress ratios, the mechanical properties of the sheet material, the geometry of the workpiece, and contact condition. It is difficult to analyse wrinkling initiation and growth while considering all the factors because the effects of the factors are very complex and studies of wrinkling behaviour may show a wide scattering of data even for small deviations in factors. In the present study, the bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above mentioned factors are conveniently considered by the finite element method. Wrinkling initiation is found by checking the determinant of the stiffness matrix and wrinkling behaviour is analysed by successive iteration with the perturbed guess along the eigenvector. Wrinkling initiation and growth in the cylindrical cup deep drawing process are analysed by using the proposed bifurcation algorithm. The mechanism of wrinkling initiation and growth in the cylindrical cup deep drawing process is investigated in detail. The results of the finite element analysis are compared with the experimental results. Through the finite element analyses of wrinkling growth for various material constants, the effects of plastic anisotropy and the strain hardening coefficient on the wrinkling behaviour of sheet metal are investigated. Copyright © 2003 John Wiley & Sons, Ltd.     

Wrinkling on irreversibly deforming foundations

Wrinkling is a mechanical instability occurring in multi-layer structures comprising a thin and stiff layer resting on a supporting underlying compliant layer. The present study is motivated by experimental observations of wrinkling leading to irreversible deformation and to the initiation of defects. An incremental Spectral Method is employed to solve the governing differential equations. This approach enables the analysis of wrinkling processes non-linear foundations and under cyclic loading. Numerical simulation results are compared to a set of analytical solutions describing wrinkling events on nonlinear foundations. Wrinkling is analyzed for cases of elastic, elastic damageable, and elastic plastic foundations. The behavior of homogeneous foundation properties is contrasted to situations where local defects are present.     

Characterising the shear–tension coupling and wrinkling behaviour of woven engineering fabrics

Modelling the forming process for engineering fabrics and textile composites using a mechanical approach, such as the finite element method, requires characterisation of the material’s behaviour under large shear deformation. For woven engineering fabrics, a coupling between in-plane tension and both shear compliance and the onset of wrinkling is to be expected. This paper focuses on a novel testing technique, the biaxial bias extension test, as a means to investigate this shear–tension coupling and fabric wrinkling. Novel methods of determining the wrinkling behaviour are demonstrated. The main difficulty with the technique lies in extracting the material contribution to the recorded signal. To do this, an experimental method is proposed and demonstrated using a plain weave glass fabric. Biaxial bias extension test results are compared against picture frame and uniaxial bias extension results.     

薄壁筒形件粘性介质外压缩径失稳起皱分析

缩径成形受筒坯稳定性的影响,容易产生失稳起皱,很难成形出缩径量较大的零件.提出了采用粘性介质外压缩径工艺成形直径变化量较大的薄壁异形曲面筒形零件新方法.针对坯料端部约束和自由条件下的失稳起皱问题进行了试验和有限元模拟,分析了试件失稳起皱过程中几何形状和应力的变化规律.研究表明,约束坯料端部可以改善试件失稳起皱后的应力分布规律,有利于消除褶皱,在较高粘性介质压力条件下可以直接成形出缩径量为15%的试件.     

材料参数对高强不锈钢管数控绕弯成形失稳起皱的影响

目的研究材料参数波动对管材数控绕弯成形失稳起皱的影响规律。方法基于ABAQUS有限元平台,建立了21-6-9高强不锈钢管数控绕弯成形过程三维弹塑性有限元模型,并验证了模型的可靠性;采用该模型模拟分析了材料参数波动对其数控绕弯成形过程失稳起皱的影响规律。结果随着厚向异性指数、屈服强度的增大或弹性模量、硬化指数的减小,弯管的起皱趋势增大,泊松比和强度系数对弯管起皱趋势的影响较小。结论材料参数对弯管起皱趋势影响的大小依次为:屈服强度、弹性模量、厚向异性指数、硬化指数、强度系数和泊松比。     

An Experimental Study on Wrinkling Behaviours and Characteristics of Gossamer Space Structures

Abstract:  Ultra-large and ultra-lightweight gossamer space structures have received wide attention because of their small packaging volume and low cost. Wrinkle is the common deformation outcome and the main failure mode of such structures. The experimental test is essential for the wrinkling analysis, as contact test cannot be used to accurately determine wrinkling behaviour because of lightweight and flexibility. A novel non-contact dot-printing photogrammetry (DPP) based on the technology of the printed-dot targets is presented to measure wrinkling characteristics. The characteristics of wrinkle development of gossamer space structures are obtained by incorporating the DPP method and a tension wrinkling (TW) test. Results reveal that wrinkle formation is the predominant form of bifurcation when the membrane is undergoing in-plane displacement. Over-contraction deformation is the special characteristic of the wrinkles, which reflects the degree of wrinkling and region in the wrinkled membrane. The development of wrinkling can be divided into five characteristic phases, and the occurrence of the wrinkles is followed by an abrupt jump variation. DPP measurement and TW test are the effective ways to obtain accurately the wrinkling behaviours and characteristics in small-scale gossamer structures. Finite element results based on nonlinear post-wrinkling analysis are used to validate the experimental test. The numerical predictions agree well with the experimental results.     

薄膜结构褶皱分析的有限元法

褶皱分析是薄膜结构受力分析的重要组成部分,阐述了适用于建筑膜材的主应力-主应变膜材受力状态判别准则和采用修正本构矩阵对褶皱的膜单元进行处理的方法,并给出了有限元公式。在此基础上,以索膜结构分析软件CAFA为平台编制了相应的有限元程序,根据矩形张拉膜受面内弯矩作用的计算结果与理论解的对比证明了程序的正确性,最后还给出了另外三个工程算例的分析结果。     

A hybrid numerical and imaging approach for characterizing defects in composite structures

In this study, a hybrid approach coupling hyperspectral near infrared imaging with a progressive finite element method is proposed for characterization of the elastic and failure response of composites with non-uniform variations of the wrinkles profile through the thickness and across the structure dimensions. In this approach, hyperspectral near infrared spectroscopy is used to create a 3D profile of the surface resin pockets with the capability of measuring resin thickness from approximately 125 to 2500 μm. These resin pockets are directly correlated to underlying ply level wrinkling as confirmed by optical microscopy. The 3D mapped resin plane obtained from the hyperspectral imaging is used to morph a ply-by-ply finite element model of a carbon-fiber/epoxy resin laminated plate using a progressive damage failure methodology. The results show the capability of the hybrid method to predict the structural response in laminated composites containing spatially distributed and non-uniform ply-level wrinkling.     

Thermal postbuckling analysis of laminated composite plates

The thermal postbuckling behavior of graphite/epoxy multi-layered rectangular plates of various boundary conditions is studied using the finite element method. Temperature dependent thermal and elastic properties of the material are used in the analysis. The nonlinear finite element equations are solved as a sequence of linear eigenvalue problems to trace the thermal postbuckling paths of 15-layered symmetric angle-ply plates. The presence of secondary instability with an unsymmetric deformation mode has been identified for symmetric laminates under uniform temperature rise. In the case of linearly varying temperature rise through the thickness of the plate, the nonlinear equilibrium equations are solved by the modified Newton–Raphson technique to get the temperature-displacement curves.     

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.     

铝合金薄板冲压成形过程中的侧壁起皱及有限元模拟

针对铝合金薄板的侧壁起皱问题,本文通过有限元软件分析工艺参数对成形质量的影响,提出了一种基于数值模拟与智能算法相结合的优化方法。首先,利用最优拉丁超立方抽样进行实验设计,并依据数值模拟获取实验值;其次,基于BP神经网络拟合工艺参数与成形质量之间的关系,预测结果的平均相对误差为2.69%,建立了准确的预测模型;最后,用遗传算法极值寻优获取了一组最优的工艺参数组合,起皱幅值的预测值和仿真值相对误差仅为4.03%,实验结果与仿真分析结果相近,验证了该优化方法的合理性和有效性。研究表明:以料厚、摩擦系数和压边力作为优化变量,以最大起皱幅值最小化为优化目标,建立几何模型,并利用有限元软件Autoform进行仿真分析;依据起皱轮廓线径向位移的实验和数值模拟对比,验证了有限元模型的正确性,表明利用神经网络和遗传算法极值寻优可以有效解决铝合金侧壁起皱缺陷。     

Wrinkling of sandwich column: comparison between finite element analysis and analytical solutions

Wrinkling analysis of sandwich columns was carried out. Two methods were used, namely finite element methods and analytical solutions. In the finite element methods, shell elements based on Reissner–Mindlin were employed across the beam thickness. A very fine element was used to model both the skin and the core across the beam thickness. The buckling mode was increased up to 100 in order to be able to model the wrinkling mode. The analytical solutions used energy methods and Raleigh–Ritz solutions developed earlier by the author. Finally, comparisons were made with experimental data taken from published results. Good agreements were achieved between the experimental results and both the finite element and analytical solution. The difference was less than 10%. Both finite element and analytical solutions were able to predict both symmetrical and asymmetrical wrinkling.     

Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories

This paper addresses the axisymmetric nonlinear bending analysis of an annular functionally graded plate under mechanical loading based on FSDT and TSDT. Using nonlinear von-Karman theory, the discretized equations are solved using the dynamic relaxation (DR) method combined with the finite difference technique. The effects of the material constant n, boundary conditions, thickness-to-radius ratio and shear deformation are studied. The results show that although, the difference between TSDT and FSDT becomes greater with an increasing thickness-to-external radius ratio, the effects of different types of boundary conditions is also of great importance.     

Studying the Tensile Behaviour of GLARE Laminates: A Finite Element Modelling Approach

Numerical simulations based on finite element modelling are increasingly being developed to accurately evaluate the tensile properties of GLARE (GLAss fibre REinforced aluminium laminates). In this study, nonlinear tensile behaviour of GLARE Fibre Metal Laminates (FML) under in-plane loading conditions has been investigated. An appropriate finite element modelling approach has been developed to predict the stress–strain response and deformation behaviour of GLARE laminates using the ANSYS finite element package. The finite element model supports orthotropic material properties for glass/epoxy layer(s) and isotropic properties with the elastic–plastic behaviour for the aluminium layers. The adhesion between adjacent layers has been also properly simulated using cohesive zone modelling. An acceptable agreement was observed between the model predictions and experimental results available in the literature. The proposed model can be used to analyse GLARE laminates in structural applications such as mechanically fastened joints under different mechanical loading conditions.     

方盒形件混合分块压边拉深工艺研究

目的 提高盒形件拉深成形过程中的成形件质量及成形极限。方法 提出混合分块压边方法,即将法兰区的4个直边区和4个圆角区沿周向分开进行压边,并在每个圆角区分别采用径向分块压边。采用有限元方法,结合正交试验,对压边圈的分块位置及压边力的分配方案进行优化设计,并通过实验比较分别采用混合分块压边方法和整体压边方法时方盒形件拉深成形的抑制起皱效果及成形极限。结果 有限元模拟和实验结果表明,采用混合分块压边方法,成形件皱纹最大幅值及最大减薄率显著减小,板料最小厚度增加,有效降低了成形件的起皱和破裂风险。结论 新方法抑制起皱的效果显著优于普通压边方法,在合理的工艺条件下,板料的成形极限也得到明显的提高。     

受弯充气锥台的褶皱特性分析

充气锥台是空间充气膜结构的主要承载力构件单元之一,膜面褶皱是导致其承载力降低的关键因素。该文基于薄膜理论分析了受弯充气锥台的褶皱特性。借助褶皱的应力判定准则对褶皱特征参数进行了预报,得到了初始起皱位置和起皱力随充气锥台两端半径比的变化规律,并得到了数值分析结果的验证。该文的结果为空间充气薄膜结构的承载能力预报提供重要依...