5 Approximate Analysis of Plates

The classical solutions discussed in the previous chapters are cumbersome, if not impractical, to obtain when the geometry, boundary conditions, and load distribution become more complicated. Other approximate methods are more suitable to solve such problems such as the strain energy (Ritz), yield line theory, finite difference, finite element, and finite strip methods. In this chapter, the Ritz, yield line, and finite difference methods are discussed. The finite element method, which is used for solving complicated geometries, boundary conditions, loading, and physical properties is briefly discussed in Chapter 16. The finite strip method (Cheung 1976) consists of dividing the plate into long strips of narrow width. It was developed, as an alternative method to the finite element method for the purpose of reducing solution time in the 1970's when processing time of computers was relatively slow. Its coverage, however, is beyond the scope of this book.