Finite Element Method with Applications in Engineering

2.4 RAYLEIGH–RITZ METHOD

Form of the unknown solution is assumed in terms of known functions (trial functions) with unknown adjustable parameters in the Rayleigh–Ritz Method. From the family of trial functions, the function that renders the functional stationary are selected and substituted into the functional, which is a function of the functions. Thus, the functional is expressed in terms of the adjustable parameters. The resulting functional is differentiated with respect to each parameter and the resulting equation is set equal to zero. If there are n unknown parameters in the functional, there will be n simultaneous equations to be solved for the parameters. Thus the best solution is obtained from the family of assumed solutions. Accuracy ...