J. Eberhardsteiner, H.A. Mang:
"Discrete Orthogonalization of Parameter Lines on Curved Surfaces for Finite-Element Analysis of Thin Shells";
International Journal for Numerical Methods in Engineering, 21 (1985), 837 - 851.
Orthogonal curvilinear co-ordinates represent the logical choice for description of the middle surface of the majority of shells in engineering practice. By means of orthogonalization of orignially skew parameter lines at integration points for shell analysis by the finite element method (FEM), the remaining minority can be treated without having to resort to skew curvilinear co-ordinates. Therefore, it does not seem to be worth while to extend existing computer codes for shell analysis by the FEM, restricted to orthogonal curvilinear co-ordinates, to general curvilinear co-ordinates. Depending on the structure of such a code, this extension may require a substantial amount of recoding. (However, it is advisable to consider general curvilinear co-ordinates of a new computer code for shell analysis by the FEM, based on thin- or thick-shell theory, is written.)
Based on these considerations, the concept of discrete orthogonalization of parameter lines' has been developed. It is presented in this paper and applied to the analysis of a hyperbolic paraboloid groined vault subjected to deal load. In the numerical investigation it is demonstrated that treating skew parameter lines incorrectly as orthogonal has a significant effect on the results for the displacements and the internal forces.