Finite rotations in non-linear analysis and design of elastic shells

Finite element computations are a widely accepted basis in structural design and optimization of shells, Large deformations. buckling and post-buckling: are governing phenomena for a safe design and for realistic approximations of the optimal layout of shell structures. Even within the framework of the infinitesimal strain theory, large (finite) rotations may appear. Therefore, the description of finite rotations plays an essential role ill finite element computations based on non-linear shell theory A widely accepted parametrization and procedure for updating finite rotations nas suggested by Simo et al. [1, 2, 3, 4]. It was applied to finite element analysis, to refined shear-deformation models and to mixed finite element approximations [5, 6, 7], The fixed asis of reference used in the updating procedure causes a singular point, in the rotation matrix formed by two unit vectors [8]. In a non-linear incremental analysis of general shells and even more ill a layout optimization of shells 1 this singularity requires special provisions which cain influence the iteration history and the quality of the final approximate solution. In our presentation two modifications for the finite rotation formulation and for the rotation update procedure are proposed; both avoid the singularity of the rotation matrix and improve the convergence of non-linear finite element computations considerably. Compared with the results in reference [7], effectiveness of these modifications is demonstrated br the numerical examples.