A wrinkling model based on material modification for isotropic and orthotropic membranes
A wrinkling model based on material modification for isotropic and orthotropic membranes
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DOI：
10.1016/j.cma.2007.09.005
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发表时间：
2008-01
影响因子：
7.2
通讯作者：
A. Jarasjarungkiat;R. Wüchner;K. Bletzinger
中科院分区：
文献类型：
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作者：
A. Jarasjarungkiat;R. Wüchner;K. Bletzinger
膜的固有抗压能力是膜有限元数值模拟中的一个难题。基本上，有两种可能性来处理这个问题。一方面，一旦使用弯曲公式，就可以通过精细化的壳单元网格来检测皱纹。另一方面，这个问题是在一个更粗糙的膜单元网格上计算的，该模型考虑了未解决的变形模式的影响。这一贡献侧重于材料修改方法，该方法被视为后者的成员。在这一范畴内，他在[P.Contri，B.A.Schrefer，一种通过非压缩材料模型对起皱的薄膜表面进行几何非线性有限元分析，Commun。APPL诺默。方法4(1988)5-15；X.H.Jenkins，W.W.Schur，基于罚参数修正材料模型的气动封头大挠度分析，有限元分析。得了。37(2001)233-251；刘晓华，膜起皱的精细分析，国际。J·努默。电脑。英格。SCI。1(2)(2000)1017-1038；R.Rossi，M.Lazzari，R.Vitaliani，E.Onate，用褶皱模型模拟轻质膜结构，Int.J.Numer，方法工程。62(15)(2005)2127-2153；R.Rossi，E.Onate，用于轻质膜结构起皱模拟的修正材料模型的收敛，见：E.Onate，B.Kröpin(编辑)，《纺织复合材料和充气结构(结构膜2003)》，CIMNE，2003；R.Rossi，轻量级结构：结构分析和耦合问题，博洛尼亚大学博士，2005]很有吸引力，因为他们在粗网上的起皱模型简单而直观。该模型的基本思想是：当膜中发生压缩时，在压应力方向上的本构张量的相应分量被惩罚，以削弱膜的压缩刚度。然而，这种突变不可避免地导致了应力重分布的非物理振荡。因此，需要一种算法来稳定这种振荡。本文的第一个目的是通过对起皱和塑性的类比，对基于材料修正方法的起皱模型进行系统的验证。第二种方法是将该模型用于各向同性膜和正交各向异性膜的静态分析。该模型具有以下优点：计算成本低，几乎能够在宏观尺度上再现由褶皱引起的精确应力场。据作者所知，利用正交各向异性材料进行材料改性的方法几乎没有应用。本文通过数值算例验证了该模型的潜力，并与文献中的结果进行了比较。
The intrinsic inability to withstand compression is a challenge in numerical simulation of a membrane with the finite element method. Basically there are two possibilities to deal with this problem. On the one hand wrinkles would be detected in detail by a refined mesh of shell elements once a bending formulation is used. On the other hand this problem is computed on a coarser mesh of membrane elements augmented with a wrinkling model, which considers effects of unresolved deformation patterns. This contribution focuses on the material modification approach, which is considered as a member of the latter. Within this category, works in [P. Contri, B.A. Schrefler, A geometrically nonlinear finite element analysis of wrinkled membrane surfaces by a no-compression material model, Commun. Appl. Numer. Methods 4 (1988) 5–15; X. Liu, C.H. Jenkins, W.W. Schur, Large deflection analysis of pneumatic envelopes using a penalty parameter modified material model, Finite Elements Anal. Des. 37 (2001) 233–251; X. Liu, Fine scale analysis of wrinkled membrane, Int. J. Numer. Comput. Engrg. Sci. 1 (2) (2000) 1017–1038; R. Rossi, M. Lazzari, R. Vitaliani, E. Onate, Simulation of light-weight membrane structures by wrinkling model, Int. J. Numer, Methods Engrg. 62 (15) (2005) 2127–2153; R. Rossi, E. Onate, Convergence of the modified material model for wrinkling simulation of light-weight membrane structures, in: E. Onate, B. Kröpin (Eds.), Textile Composites and Inflatable Structures (Structural Membranes 2003), CIMNE, 2003; R. Rossi, Light Weight Structures: Structural Analysis and Coupling Issues, Ph.D. Diss., The university of Bologna, 2005] are attractive because their wrinkling models on a coarse grid are simple and intuitive. The basic idea of this model is as follows: whenever compression occurs in a membrane, the corresponding components of the constitutive tensor in the direction of the compressive stress are penalized to weaken the compressive stiffness of the membrane. However, such abrupt change causes inevitably an unphysical oscillation of stress redistribution. Therefore, an algorithm to stabilize this oscillation is required. The first objective of this paper is to give a systematic verification of a wrinkling model based on the material modification approach by means of an analogy between wrinkling and plasticity. The second one is to include this model in a static analysis for both isotropic and orthotropic membranes. This model holds following advantages: it is computationally inexpensive and virtually able to reproduce the exact stress field, caused by wrinkling, on a macroscopic scale. To the author’s knowledge applications of a material modification approach with orthotropic materials are scarcely available. This paper demonstrates the potential of the model by means of numerical examples, compared to ones in literature.