Impact of basis, orthogonalization, and normalization on the constrained Finite Strip Method for stability solutions of open thin-walled members

The objective of this paper is to explain and establish the sensitivity of the modal decomposition and modal identification capabilities of the constrained Finite Strip Method to choice of basis, orthogonalization, and normalization. The constrained Finite Strip Method provides a mechanical means to separate the deformations of a thin-walled member into those consistent with global, distortional, local, and other (e.g., shear and transverse extension) modes. For eigen-buckling analysis of thin-walled members this enables isolation of any given mode (modal decomposition) or quantitative measures of the interactions within a given general eigenmode (modal identification). Automated strength prediction of thin-walled members, as well as deeper studies of modal interactions are greatly enabled by establishing agreed upon methods for modal identification and decomposition, as such, the sensitivity of the solution to choice of basis, orthogonalization, and normalization is important for advancing understanding of thin-walled members. As shown herein, the mechanical definitions used to separate the deformations lead to unique vector spaces for global, distortional, and local deformations – but not for other (shear and transverse extension) deformations. Further, although the vector spaces are generally unique the choice of basis and its normalization within the space are not, and have an impact on modal decomposition and identification solutions. A series of illustrative examples are provided to demonstrate the impact of basis, orthogonalization, and normalization. Based on these studies recommendations are made for choice of basis, orthogonalization, and normalization when employing the constrained Finite Strip Method.