On using Legendre polynomials and amended spline transformations in the SFSM for buckling and free vibrations of plates and thin-walled beams

This paper presents two modifications to the spline finite strip method (SFSM) for plate and thin-walled beam buckling and free vibrations; these being augmenting of the flexural buckling displacements with Legendre polynomials which represent additional bubble modes, and a modification of the dedicated amended splines that are conventionally needed to handle boundary conditions. A simple matrix technique to remove the need for amended splines is described, and the efficacy of the method is demonstrated in which it is shown that inclusion of the Legendre polynomials enhances the performance of the SFSM significantly when benchmarked against other techniques.