Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells

Abstract

Mixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based on the three-field Hu-Washizu principle are proposed. In the formulation, apart from displacement and rotation fields, both strain and stress resultant fields are treated as independent. The elements are derived in the framework of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells. The novelty of the developed elements stems from the fact that the measures of assumed strains and stress resultants are asymmetric. The original interpolation of drilling and bending components of strains and stress resultants is proposed. In the formulation of new mixed elements, two variants of the interpolation of membrane components are used and interpolation of the independent fields is defined in the natural or skew coordinates. Accuracy and efficiency of the developed elements are tested in several linear and nonlinear numerical examples. It is shown that smaller number of independent parameters in the interpolation of membrane components gives more accurate results. The proposed mixed 4-node elements enable the use of large load steps in nonlinear computations. Moreover, they require significantly less equilibrium iterations than other shell elements formulated in the 6-parameter shell theory. Keywords Shell • Finite element • Mixed element • Cosserat • Asymmetric strains • Drilling rotation 1 Introduction Thin-walled shell structures are widely used in different branches of industry, e.g. aircraft, automotive, civil engineering. However, these structures are very sensitive to loss of stability and local damage, like delamination, cracking, etc. The detailed and comprehensive nonlinear analysis (postbuckling, damage, plasticity) requires an appropriately refined finite element discretization. Hence, accuracy and efficiency of the shell element formulation play both essential roles in fast and correct design process of thin-walled shell structures. Moreover, Communicated by Andreas Öchsner.