NURBS-based optimization of natural frequencies for bidirectional functionally graded beams

In this study, the nurbs-based isogeometric analysis is developed to optimize natural frequencies of bidirectional functionally graded (BFG) beams by tailoring their material distribution. One-dimensional Non-Uniform Rational B-Spline (NURBS) basis functions are utilized to construct the geometry of beam as well as approximate solutions, whereas the gradation of material property is represented by two-dimensional basis functions. To optimize the material composition, the spatial distribution of volume fractions of material constituents is defined using the higher order interpolation of volume fraction values that are specified at a finite number of control points. As an optimization algorithm, the differential evolution (DE) algorithm is employed to optimize the volume fraction distribution that maximizes each of the first three natural frequencies of BFG beams. A numerical analysis is performed on the examples of BFG beams with various boundary conditions and slenderness ratios. The obtained results are compared with the previously published results in order to show the accuracy and effectiveness of the present approach. The effects of number of elements, boundary conditions and slenderness ratios on the optimized natural frequencies of BFG beams are investigated.

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