Rayleigh - Ritz Method (Variational Approach)

RAYLEIGH – RITZ METHOD (VARIATIONAL APPROACH)

It is useful for solving complex structural problems. This method is possible only if a suitable functional is available. Otherwise, Galerkin’s method of weighted residual is used.

Problems (I set)

1. A simply supported beam subjected to uniformly distributed load over entire span. Determine the bending moment and deflection at midspan by using Rayleigh – Ritz method and compare with exact solutions.

2. A bar of uniform cross section is clamed at one end and left free at another end and it is subjected to a uniform axial load P. Calculate the displacement and stress in a bar by using two terms polynomial and three terms polynomial. Compare with exact solutions.

ADVANTAGES OF FINITE ELEMENT METHOD

1.    FEM can handle irregular geometry in a convenient manner.

2.    Handles general load conditions without difficulty

3.    Non –homogeneous materials can be handled easily.

4.    Higher order elements may be implemented.

DISADVANTAGES OF FINITE ELEMENT METHOD

5.    It requires a digital computer and fairly extensive

6.    It requires longer execution time compared with FEM.

7.    Output result will vary considerably.

The finite element method constitutes a general tool for the numerical solution of partial differential equations in engineering and applied science.

The finite element method (FEM), or finite element analysis (FEA), is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces. Application of this simple idea can be found everywhere in everyday life as well as in engineering.