Buckling and wrinkling of prestressed membranes

This paper deals with the numerical computation of buckles and wrinkles appearing in membrane structures by means of the total Lagrangian formulation, using genuine membrane finite elements (with zero bending stiffness) and a prestressed hyperelastic constitutive law. The bifurcation analysis is carried out without assuming any imperfections in the structure. The standard arclength method is modified by means of a specific solution procedure to cope with the occurrence of complex roots when solving the quadratic constraint equation. Applying the proposed formulation to a set of typical numerical examples shows its ability to correctly predict the wrinkling and buckling behaviour in membrane structures.

[1]  M. Crisfield.  Non-Linear Finite Element Analysis of Solids and Structures, Essentials , 1997 .

[2]  C. T. Morley,et al.  Arc-Length Method for Passing Limit Points in Structural Calculation , 1992 .

[3]  S. Pellegrino,et al.  Computation of Wrinkle Amplitudes in Thin Membranes , 2002 .

[4]  Peter Wriggers,et al.  A simple method for the calculation of postcritical branches , 1988 .

[5]  Bernhard A. Schrefler,et al.  A geometrically nonlinear finite element analysis of wrinkled membrane surfaces by a no‐compression material model , 1988 .

[6]  Eugenio Oñate,et al.  Textile composites and inflatable structures , 2005 .

[7]  Sergio Pellegrino,et al.  Analysis of Wrinkle Patterns in Prestressed Membrane Structures , 2000 .

[8]  D. Steigmann,et al.  Point loads on a hemispherical elastic membrane , 1995 .

[9]  Aaron Lee Adler,et al.  Finite element approaches for static and dynamic analysis of partially wrinkled membrane structures , 2000 .

[10]  Alexander Tessler,et al.  Nonlinear Shell Modeling of Thin Membranes with Emphasis on Structural Wrinkling , 2003 .

[11]  Frank Abdi,et al.  Wrinkling Analysis of A Kapton Square Membrane under Tensile Loading , 2003 .

[12]  W. Szyszkowski,et al.  Spherical membranes subjected to vertical concentrated loads: an experimental study , 1987 .

[13]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[14]  D. Steigmann,et al.  Finite deformation of a pressurized toroidal membrane , 1995 .

[15]  Fujikake Masahisa,et al.  Analysis of fabric tension structures , 1989 .

[16]  Tomoshi Miyamura,et al.  Wrinkling on stretched circular membrane under in-plane torsion: , 2000 .

[17]  M. Stanuszek,et al.  FE analysis of large deformations of membranes with wrinkling , 2003 .

[18]  W. Szyszkowski,et al.  Finite deformation and stability behaviour of spherical inflatables under axi-symmetric concentrated loads , 1984 .

[19]  S. Im,et al.  Finite element analysis of dynamic response of wrinkling membranes , 1999 .

[20]  Sergio Pellegrino,et al.  Amplitude of Wrinkles in Thin Membranes , 2002 .

[21]  John M. Hedgepeth,et al.  Finite element analysis of partly wrinkled membranes , 1985 .

[22]  Riccardo Barsotti,et al.  The web bridge , 2001 .

[23]  P. Bergan,et al.  Solution techniques for non−linear finite element problems , 1978 .

[24]  B. Tabarrok,et al.  Nonlinear analysis of tension structures , 1992 .

[25]  J. Hedgepeth,et al.  ANALYSIS OF PARTLY WRINKLED MEMBRANES , 1961 .

[26]  G. F. Moita,et al.  The post-critical analysis of axisymmetric hyper-elastic membranes by the finite element method , 1996 .

[27]  Willi Schur.  Development of a practical tension field material model for thin films , 1994 .

[28]  Seokwoo Kang,et al.  Finite element analysis of wrinkling membranes , 1997 .

[29]  Sergio Pellegrino,et al.  New approaches to structural mechanics, shells and biological structures , 2002 .