A six-node curved membrane ¯nite element with Loof curvatures

Two ¯nite element methods for the analysis of membrane structures are presented in this paper- a 3-node constant strain trianglar element(CST) with large strains and 6-node linear strain triangle elements(LST) with large deformation. For the CST el-ement, the cable analogy method linked with the dynamic relaxation. The signi¯cant error caused by ignoring second order('large') strains in membrane structure analysis will be demonstrated mathematically and numerically through a proposed enhanced nonlin-ear cable analogy formulation.Case studies comparing these two CST formulations will conclude this section of the paper. In LST approach,a new curved 6-node triangular element coupled with the Newton-Raphson algorithm will be introduced with Loof curvatures. The introduction of cur-vatures in the numerical representations of membrane surfaces are demonstrated to be important terms which a®ect the relationship between the membrane strains and nodal displacements and in some special cases,the out-of-balance forces. Having summarised the formulation,numerical examples will be given in both the shape ¯nding and load analysis procedures. Finally, results of the numerical case studies analysed using the CST and LST will be compared and discussed to domonstrate the accuracies and limitations of these two ¯nite element methodologies