Answer Happy

Problem 8: Rayleigh-Ritz Method Consider the transversely loaded beam shown in the figure below. The bar is of stiffness E, length L, inertia I and cross-section A. It is subjected to a uniformly distributed transverse load po. Z Po (a) Derive the expression for the total potential energy for this structural system (b) What are the essential (geometric) and natural (force) boundary conditions for this problem? (c) Consider the four basis functions below from the Fourier series sin(x/L), cos(x/L), sin(2x/L), cos(2xX/L) Are any of these basis functions admissible? Explain why, and comment on the suitability of the Fourier series in solving this problem. (d) Determine the simplest polynomial basis function, and use this basis function to determine an approximate solution for the transverse displacement.