Periodic trim solutions with hp-version finite elements in time

We have studied finite elements in time as an alternative strategy for rotorcraft trim problems. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic problems is also examined. It is shown that Fourier series is a special case of space-time finite elements for which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety of parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and optimum polynomial order for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for certain given error criteria. The mixed method provides better results than does the displacement method.