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ADVANCES IN NON-LINEAR FINITE ELEMENT METHODS
Edited by: B.H.V. Topping and M. Papadrakakis
Finite Element Analysis of Membrane Cable Reinforced Structures at Large Deformations
M. Stanuszek and J. Orkisz
Cracow University of Technology, Poland
M. Stanuszek, J. Orkisz, "Finite Element Analysis of Membrane Cable Reinforced Structures at Large Deformations", in B.H.V. Topping, M. Papadrakakis, (Editors), "Advances in Non-Linear Finite Element Methods", Civil-Comp Press, Edinburgh, UK, pp 67-76, 1994. doi:10.4203/ccp.24.2.6
In the paper we return to the problem of large deformations of membrane cable reinforced structures of arbitrary shape. The membrane theory of large deformations of hyperelastic bodies in total Lagrangian formulation is used. Initial, actual and working configurations of cables and membranes are distinguished.
In the Finite Element Method [FEM] the families of higher order membrane and compatible cable elements are applied. The basic equations for the higher order cable and membrane elements, by means of the natural approach and subelement technique were derived in . Based on them special numerical algorithms are built and examined here. Numerical results are obtained by means of an iterative Newton-Raphson technique incorporating a specially developed FORTRAN computer code NAMS (Nonlinear Analysis of Membrane Shells). Due to a variety of numerical difficulties caused mainly by significant geometrical (large displacement) and physical (hyperelasticity) nonlinearities, as well as by possible stability loss, presence of nonconservative loadings, and very small membrane stiffness in the load direction, a special attention is paid to the effectivenes of numerical analysis (convergence, error analysis), collaboration of membrane and cables and analysis of folded zones.
Detailed calculations are carried out for a variety of membranes and cable reinforced membrane structures of various shape, including examples of folded zones. Numerical results are compared with those obtained by means of the Finite Difference Method [FDM] at arbitrary irregular grids. Moreover in some cases (for folds) experiments are carried out, and results compared with numerical ones.
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