一种带有沙漏控制的新型EAS实体壳单元

基于 Hu-Washizu 变分原理推导了一种带有沙漏控制的实体壳单元的显式有限元列式;采用面内单点积分方案,提高了计算效率;同时引入沙漏控制力,抑制了沙漏现象.基于缩减积分方案,采用 B-bar 法消除体积自锁,并通过添加七个改善拟应变参数解决了泊松自锁和剪切自锁.采用改善拟应变法消除剪切自锁,使得表达式简洁.利用这种显式实体壳单元模型对3个非线性变形的标准算例进行了计算,并与相关参考文献和有限元软件 ABAQUS 的计算结果进行了比较.结果表明:该实体壳单元具有较高的计算精度,可有效地解决板壳非线性大变形分析问题,具有很好的工程应用前景.     

Three dimensional degenerated shell theory and assumed strain shell elements

In this paper Reissner-Mindlin plate theory is extended to cater for curved shell structures. It can be considered as Reissner-Mindlin type shell theory. From this theory, the C(O) continuity formulation of shell elements of taking account the transverse shear deformation could be derived directly. These degenerated shell elements have been widely employed. To overcome the locking of shear and membrane and avoid zero energy modes the author proposed the formulation of the new elements with assumed strains. A wide range of numerical tests was conducted and the results illustrate that the assumed strain elements possess high accuracy and good performance.     

三维退化的壳理论和假定应变的壳单元

本文将Reissner-Mindlin板理论推广到空间曲壳结构,可称为Reissner-Mindlin型壳理论。从这种理论出发,可直接导出C(0)连续的壳体单元,即考虑横向剪切变型的影向的壳体单元,这种单元在国外已被广泛地采用,为克服这种单元在应用中所出现的剪切和膜的锁制现象同时又防止出现任何零能模式,作者提出了一种采用假定应变的新的壳单元公式,并对这种单元进行了广泛的数值试验,结果表明这种单元具有较高的精度和良好的性能。     

用于超弹性分析的高效杂交应变--EAS固体壳单元的研究

提出了一个用于橡胶材料分析的弱变分方程，基于一个可压缩Neo—Hookean模型，将EAS模式和杂交元法有机地结合起来，推导了一个高效、稳定的杂交应变——EAS固体壳单元，通过巧妙地选择应交插值函数和本文中提出的一个精化措施，克服了橡胶材料所表现出的大应变超弹性本构为杂交元正交化法的实施所带来的困难，保证了整个单元列式都仅采用低阶高斯积分，显著提高了计算效率，确保橡胶材料不可压缩性计算的顺利进行，并克服了固体壳元的厚度自锁问题。     

带有沙漏控制的相对自由度壳元非线性动力分析

针对八节点相对自由度壳单元,给出了单元内坐标和位移的插值公式,利用Hu-Washinzu变分原理,基于拟应变法,在大变形情况下推导了拟应变的表达式,构造了带有沙漏控制的动力问题的有限元求解格式.通过算例表明该文提出的基于相对自由度壳元的沙漏控制算法能够很好地解决非线性动力问题,可改善计算精度和计算效率.     

On Computational Issues in Large Deformation Analysis of Rubber Bushings*

ABSTRACT

Accurate bushing analysis requires a locking free finite element formulation, an appropriate selection of the strain energy density function, and an adequate use of bulk modulus to assure numerical stability and accuracy. In this paper, the pressure projection finite element method is employed. The method projects displacement-calculated pressure onto a lower order pressure field, based on the Babuska-Brezzi condition, to avoid volumetric locking and pressure oscillation. Mooney-Rivlin and Cubic strain energy density functions are used to study the material effect on the predicted rubber behavior in tension-compression and shear deformation modes, and the need to use a higher order strain energy density function for bushing analysis is identified. The effect of bulk modulus on bonded rubber behavior in bushings with respect to bushing shape factor is studied, and the minimum allowable bulk modulus to impose incompressibility in bushing analysis is characterized. The load-deflection response of annular bushings subjected to axial, torsional, and radial deformations are analyzed and results are compared to linear approximations. An effort is made to demonstrate how a Mooney-Rivlin model cannot capture load-displacement nonlinearities in bushing axial and torsional deformations. Two- and three-dimensional results are compared and the applicability of two-dimensional analysis is discussed.     

Postbuckling analysis of laminated composite plates subjected to the combination of in-plane shear,compression and lateral loading

This study deals with postbuckling behavior of laminated composite plates under the combination of in-plane shear, compression and lateral loading using an Element-based Lagrangian formulation. Natural co-ordinate-based strains, stresses and constitutive equations are used in the present shell element. The Element-based Lagrangian formulation described in this paper, in comparison with the traditional approaches, is more attractive not only because it uses only single mapping but also it converges faster. In addition, the finite element (FE) formulation based on the assumed natural strain method for composite structures shows excellence from the standpoints of computational efficiency as well as its ability to avoid both membrane and shear locking behavior. The numerical results obtained are in good agreement with those reported by other investigators. In particular, new results reported in this paper show the influence of various types of loading, materials and number of layers on postbuckling behavior.     

近似不可压软材料动力分析的完全拉格朗日物质点法

物质点法(MPM)在模拟非线性动力问题时具有很好的效果,其已被广泛应用于许多大变形动力问题的分析中.然而传统的MPM在模拟不可压或近似不可压材料的动力学行为时会产生体积自锁,极大地影响模拟精度和收敛性.本文针对近似不可压软材料的大变形动力学行为,提出一种混合格式的显式完全拉格朗日物质点法(TLMPM).首先基于近似不可压软材料的体积部分应变能密度,引入关于静水压力的方程;之后将该方程与动量方程基于显式物质点法框架进行离散,并采用完全拉格朗日格式消除物质点跨网格产生的误差,提升大变形问题的模拟精度;对位移和压强场采用不同阶次的B样条插值函数并通过引入针对体积变形的重映射技术改进了算法,提升算法的准确性.此外,算法通过实施一种交错求解格式在每个时间步对位移场和压强场依次进行求解.最后,给出几个典型数值算例来验证本文所提出的混合格式TLMPM的有效性和准确性,计算结果表明该方法可以有效处理体积自锁,准确地模拟近似不可压软材料的大变形动力学行为.     

两类基于局部标架梁单元的闭锁缓解方法

对于大转动、大变形柔性体的刚柔耦合动力学问题,基于李群SE(3)局部标架(local frame formulation,LFF)的建模方法能够规避刚体运动带来的几何非线性问题,离散数值模型中广义质量矩阵与切线刚度矩阵满足刚体变换的不变性,可明显地提高柔性多体系统动力学问题的计算效率.有限元方法中,闭锁问题是导致单元收...     

A new formulation for the analysis of elastic layers bonded to rigid surfaces

Elastic layers bonded to rigid surfaces have widely been used in many engineering applications. It is commonly accepted that while the bonded surfaces slightly influence the shear behavior of the layer, they can cause drastic changes on its compressive and bending behavior. Most of the earlier studies on this subject have been based on assumed displacement fields with assumed stress distributions, which usually lead to “average” solutions. These assumptions have somehow hindered the comprehensive study of stress/displacement distributions over the entire layer. In addition, the effects of geometric and material properties on the layer behavior could not be investigated thoroughly. In this study, a new formulation based on a modified Galerkin method developed by Mengi [Mengi, Y., 1980. A new approach for developing dynamic theories for structural elements. Part 1: Application to thermoelastic plates. International Journal of Solids and Structures 16, 1155–1168] is presented for the analysis of bonded elastic layers under their three basic deformation modes; namely, uniform compression, pure bending and apparent shear. For each mode, reduced governing equations are derived for a layer of arbitrary shape. The applications of the formulation are then exemplified by solving the governing equations for an infinite-strip-shaped layer. Closed form expressions are obtained for displacement/stress distributions and effective compression, bending and apparent shear moduli. The effects of shape factor and Poisson’s ratio on the layer behavior are also investigated.     

Large displacement analysis of shear deformable composite beams with interlayer slips

This paper presents a novel geometric non-linear finite element formulation for the analysis of shear deformable two-layer beams with interlayer slips. We adopt the co-rotational approach where the motion of the element is decomposed into two parts: a rigid body motion which defines a local coordinate system and a small deformational motion of the element relative to this local coordinate system. The main advantage of this approach is that the transformation matrices relating local and global quantities are independent to the choice of the geometrical linear local element. The effect of transverse shear deformation of the layers is taken into account by assuming that each layer behaves as a Timoshenko beam element. The layers are assumed to be continuously connected and partial interaction is considered by considering a continuous relationship between the interface shear flow and the corresponding slip. In order to avoid curvature and shear locking phenomena, the local linear element is formulated using “exact” displacement shape functions derived from the closed-form solution of the governing equations of a two-layer beam element. Finally, three numerical applications are presented in order to assess the performance of the proposed formulation.     

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

This paper proposes an extension of the SHB8PS solid–shell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the “thickness” direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications—both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems.     

Simulation of fabric drape using a thin plate element with finite rotation

The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated.     

Locking-Free Degenerated Isoparametric Shell Element

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A polygonal finite element formulation for modeling nearly incompressible materials

The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements.

     

A new super convergent thin walled composite beam element for analysis of box beam structures

In this paper, a new composite thin wall beam element of arbitrary cross-section with open or closed contour is developed. The formulation incorporates the effect of elastic coupling, restrained warping, transverse shear deformation associated with thin walled composite structures. A first order shear deformation theory is considered with the beam deformation expressed in terms of axial, spanwise and chordwise bending, corresponding shears and twist. The formulated locking free element uses higher order interpolating polynomial obtained by solving static part of the coupled governing differential equations. The formulated element has super convergent properties as it gives the exact elemental stiffness matrix. Static and free vibration analyses are performed for various beam configuration and compared with experimental and numerical results available in current literature. Good correlation is observed in all cases with extremely small system size. The formulated element is used to study the wave propagation behavior in box beams subjected to high frequency loading such as impact. Simultaneous existence of various propagating modes are graphically captured. Here the effect of transverse shear on wave propagation characteristics in axial and transverse directions are investigated for different ply layup sequences.     

Determination of hourglass coefficients in the theory of a Cosserat point for nonlinear elastic beams

The theory of a Cosserat point has recently been used [Int. J. Solids Struct. 38 (2001) 4395] to formulate the numerical solution of problems of nonlinear elastic beams. In that theory the constitutive equations for inhomogeneous elastic deformations included undetermined constants associated with hourglass modes which can occur due to nonuniform cross-sectional extension and nonuniform torsion. The objective of this paper is to determine these hourglass coefficients by matching exact solutions of pure bending and pure torsion applied in different directions on each of the surfaces of the element. It is shown that the resulting constitutive equations in the Cosserat theory do not exhibit unphysical stiffness increases due to thinness of the beam, mesh refinement or incompressibility that are present in the associated Bubnov–Galerkin formulation. Also, example problems of a bar hanging under its own weight and a bar attached to a spinning rigid hub are analyzed.     

Geometrically non-linear analysis of arbitrary elastic supported plates and shells using an element-based Lagrangian shell element

In the present paper, the ELF (element-based Lagrangian formulation) 9-node ANS (assumed natural strain) shell element was combined with the spring element for geometrically non-linear analysis of plates and shells sustained by arbitrary elastic edge supports that are subjected to variation in loading.This particular spring element serves as tool for modeling an arbitrary elastic edge support with 6 DOF (degrees of freedom). The elastic edge support was modeled by combining different spring models. The ANS method was used to overcome shear and membrane locking problems inherent in some thin plate and shell problems. In the formulation of the ELF characteristic arrays, the expression of element strains was adopted in the framework of the element natural coordinates. The non-linear analysis results of idealized edge supports were validated against the reference solutions available in the literature. As a result of the numerical test, the combination of the ELF 9-node shell element and spring element shows an exceptional performance for non-linear analysis of plates and shells under elastic edge supports.     

Particle-image velocimetry measurements of flow over interacting barchan dunes

Barchan dunes are crescentic planform-shaped dunes that are present in many natural environments, and may occur either in isolation or in groups. This study uses high-resolution particle-image velocimetry (PIV) experiments using fixed-bed models to examine the effects of barchan dune interaction upon the flow field structure. The barchan dune models were created from an idealized contour map, the shape and dimensions of which were based upon previous empirical studies of dune morphology. The experimental setup comprised two, co-axially aligned, barchan dune models that were spaced at different distances apart. In this paper, two volumetric ratios (V _r, upstream dune: downstream dune) of 1.0 and 0.175 were examined. Models were placed in a boundary-layer wind tunnel and flow quantification was achieved via PIV measurements of the mean and turbulent flow field in the streamwise–wall-normal plane, along the centerline of the barchan(s), at an average flow Reynolds number of 59,000. The presence of an upstream barchan dune induces a “sheltering effect” on the flow. Flow on the stoss side of the downstream dune is controlled by the developing internal boundary layer from the upstream dune, as well as by the turbulent flow structures shed from the free shear layer of the upstream dune leeside. At both volumetric ratios, enhanced turbulence is present over the downstream barchan dune leeside, which is proposed to be caused by the interaction of shear layers from the upstream and downstream dunes. Both the size and magnitude of the shear layer formed in the leeside of the upstream dune control this interaction, together with the proximity of this shear layer to the stoss side of the downstream dune. Proper orthogonal decomposition (POD) analysis shows that the distribution of turbulent kinetic energy is shifted to higher modes (i.e., smaller spatial scales) over interacting barchan dunes, which also reflects the role of the leeside free shear layer in dominating the flow field by generation, or redistribution, of TKE to smaller scales.