The intrinsic inability to withstand compression is a challenge in numericalsimulation of a membrane with the finite element method. Basically thereare two possibilities to deal with this problem. On the one hand wrinkleswould be detected in detail by a refined mesh of shell elements once abending formulation is used. On the other hand this problem is computedon a coarser mesh of membrane elements augmented with a wrinkling model,which considers effects of unresolved deformation patterns. This contributionfocuses on the material modification approach, which is considered as amember of the latter. Within this category, works in [P. Contri, B.A. Schrefler,A geometrically nonlinear finite element analysis of wrinkled membranesurfaces by a no-compression material model, Commun. Appl. Numer. Methods4 (1988) 5–15; X. Liu, C.H. Jenkins, W.W. Schur, Large deflection analysisof pneumatic envelopes using a penalty parameter modified material model,Finite Elements Anal. Des. 37 (2001) 233–251; X. Liu, Fine scale analysisof wrinkled membrane, Int. J. Numer. Comput. Engrg. Sci. 1 (2) (2000) 1017–1038; R. Rossi, M. Lazzari, R. Vitaliani, E. Onate, Simulation of light-weightmembrane structures by wrinkling model, Int. J. Numer, Methods Engrg. 62(15) (2005) 2127–2153; R. Rossi, E. Onate, Convergence of the modifiedmaterial 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 ofBologna, 2005] are attractive because their wrinkling models on a coarsegrid are simple and intuitive. The basic idea of this model is as follows:whenever compression occurs in a membrane, the corresponding componentsof the constitutive tensor in the direction of the compressive stress arepenalized to weaken the compressive stiffness of the membrane. However,such abrupt change causes inevitably an unphysical oscillation of stressredistribution. Therefore, an algorithm to stabilize this oscillation isrequired. The first objective of this paper is to give a systematic verificationof a wrinkling model based on the material modification approach by meansof an analogy between wrinkling and plasticity. The second one is to includethis model in a static analysis for both isotropic and orthotropic membranes.This model holds following advantages: it is computationally inexpensiveand virtually able to reproduce the exact stress field, caused by wrinkling,on a macroscopic scale. To the author’s knowledge applications of a materialmodification approach with orthotropic materials are scarcely available.This paper demonstrates the potential of the model by means of numericalexamples, compared to ones in literature.
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The intrinsic inability to withstand compression is a challenge in numericalsimulation of a membrane with the finite element method. Basically thereare two possibilities to deal with this problem. On the one hand wrinkleswould be detected in detail by a refined mesh of shell elements once abending formulation is used. On the other hand this problem is computedon a coarser mesh of membrane elements augmented with a wrinkling model,which considers effects of unresolved deformation patterns. This c...
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