Constrained shell Finite Element Method for thin-walled members, Part 1: constraints for a single band of finite elements

In this paper a novel method for the analysis of thin-walled members is presented: the constrained finite element method. The method is basically a shell finite element analysis, but carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanical criteria, e.g., to force local, global or distortional deformations. The constrained finite element method is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape functions, which-together with longitudinal discretization transforms a finite strip into multiple finite elements. This change in longitudinal interpolation makes the method applicable for a wide range of practical problems not yet handled by other modal decomposition methods. The new shell finite element is briefly presented here, but the main focus of this paper is on how the constraining criteria can be applied for a thin-walled member. More specifically, in this paper a band of finite elements is discussed in detail, where 'band' is a segment of the member with multiple elements along the cross-section, but with one single finite element longitudinally. The possible base systems for the various deformation spaces are demonstrated here. Members built up from multiple bands are discussed and presented in a companion paper, where various numerical examples are also provided to illustrate the potential of the proposed constrained finite element method.