Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS

This paper highlights the problem of obtaining accurate modal stress-resultants, in particular twisting moments and shear forces, for thin vibrating plates that model Very Large Floating Structures (VLFS) when using the Ritz method in conjunction with mathematically complete two-dimensional polynomials as Ritz functions. The twisting moments and shear forces are observed to violate the natural boundary conditions and contain "oscillations". The use of Chebyshev polynomials and trigonometric series as Ritz functions do not solve the problem. Penalty functionals enable the stress-resultants to satisfy the natural boundary conditions but they magnify the oscillations. Based on existing exact solutions of rectangular plates with simply supported and free edges, it was found that the aforementioned problem can be remedied by a post-processing step involving the curve fitting of the "oscillating" results computed from the Ritz method with penalty functionals.