Application of Pattern Recognition to the Identification of Cross-Section Deformation Modes of Thin-Walled Structures

Abstract

This paper presents a novel procedure to identify cross-section deformation modes of thin-walled structures with the application of pattern recognition. Initially, a higher order model is derived by considering an approximation of cross-section deformation by a set of basis functions, which are integrated in the governing equations and decoupled through the solution of the associated generalized eigenvalue problem. The eigenvectors obtained are deemed to inherit the attributes of structural behaviors, and thus can serve as the basis to identify deformation modes. Accordingly, these eigenvectors are further handled employing the singular value decomposition, in order to recognize the axial variation patterns of the basis functions. Next, each eigenvector is orthogonally decomposed into components corresponding to the variation patterns, with their proportional relationship, which is really pursued, being obtained and used as the weights to “assemble” basis functions to generate deformation modes. Moreover, a numbering system is proposed to hierarchically organize these deformation modes. Finally, a reduced higher order model can be obtained by updating the initial governing equations with a selective set of cross-section deformation modes. The main features lie in the capability to be numerically implemented in a simple and intuitive way and the nature to give identified deformation modes mechanical interpretation inherited from actual dynamic behaviors of thin-walled structures. The versatility of the procedure as well as the resulting beam model has been validated through both numerical examples and comparisons with other theories.