Chapter 3 Classical Variational Methods and the Finite ...

44 Chapter 3: Classical Variational Methods and the Finite Element Method Introduction Deriving the governing dynamics of physical processes is a complicated task in itself; finding exact solutions to the governing partial differential equations is usually even more formidable. When trying to solve such equations, approximate Methods of analysis provide a convenient, alternative method for finding solutions. Two such Methods , the Rayleigh-Ritz method and the Galerkin method, are typically used in the literature and are referred to as Classical Variational Methods . According to Reddy (1993), when solving a differential equation by a Variational method, the equation is first put into a weighted-integral form, and then the approximate solution within the domain of interest is assumed to be a linear combination )( iiic of appropriately chosen approximation functions i and undetermined coefficients, ci.

variational methods. Comparisons will be made between the Rayleigh-Ritz, Galerkin, and finite element methods. Such comparisons will be highlighted through representative problems for each. In the end, the benefits of the finite element method will be apparent. 3.2 Defining the Strong, Weak, and Weighted-Integral Forms

Loading..

Tags:

  Methods, Finite

Information

Related search queries