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.
