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A semianalytical approach for the variational asymptotic sectional analysis of a beam with high values of initial twist and curvatures

Ali Siami and Fred Nitzsche

Vol. 18 (2023), No. 2, 219–245
Abstract

The paper presents a semianalytical method including a perturbation solution combined with a numerical method for solving the set of nonlinear equations associated to the two-dimensional Timoshenko beam cross-sectional analysis. The common solution for this problem included in the variational asymptotic beam sectional analysis (VABS) package is based on an analytical perturbation method. The analytical solution neglects some terms, and it approximates the stiffness matrix with an accuracy up to second order on small parameters based on the initial twist and curvatures of the beam. Despite the computational cost advantages of this method, the accuracy of the approximated stiffness matrix is reduced in the presence of higher values of the initial twist and curvatures. On the other hand, using iterative solution methods for the cross-sectional nonlinear equations shows the sensitivity of the current algorithms to the initial guess. In this work, the firefly algorithm (a nature-inspired iterative solution method) is used to solve the nonlinear equations where the perturbation solution is used as the initial guess for the algorithm. The proposed semianalytical method searches for the stiffness matrix in a limited solution range around the analytical perturbation solution. This allows for both taking into consideration any loss of accuracy due to the neglected terms in the perturbation solution and improved computational efficiency. It has been shown that the solution using the developed semianalytical method minimizes the target function of the problem better than the common analytical approach. Finally, the accuracy of the new developed tool for the structural dynamic analysis of rotating blades is examined by comparing the eigenfrequencies of modal analysis of a blade with high values of initial twist and curvature with the results of the three-dimensional finite element analysis in ANSYS. In addition, Campbell diagrams of a rotating blade with flexible joints are obtained using the developed package and the results are evaluated by the outputs of FLIGHTLAB for the 3D model of the blade.

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Keywords
cross-sectional analysis, semianalytical approach, curved blades, composite beams, Campbell diagram
Milestones
Received: 13 May 2022
Revised: 8 December 2022
Accepted: 18 December 2022
Published: 18 April 2023
Authors
Ali Siami
Department of Mechanical and Aerospace Engineering
Carleton University
Ottawa
Canada
Fred Nitzsche
Department of Mechanical and Aerospace Engineering
Carleton University
Ottawa
Canada