2 1 Introduction

Development of the element matrix for the subdomain (element). Assembly of the element matrices for each subdomain to obtain the global ma-

trix for the entire domain. Imposition of the boundary conditions. Solution of equations. Additional computations (if desired).

There are three main approaches to constructing an approximate solution based on the concept of FEA:

Direct Approach This approach is used for relatively simple problems, and it usu-ally serves as a means to explain the concept of FEA and its important steps (dis-cussed in Sect. 1.4).

Weighted Residuals This is a versatile method, allowing the application of FEA to problems whose functionals cannot be constructed. This approach directly uti-lizes the governing differential equations, such as those of heat transfer and fluid mechanics (discussed in Sect. 6.1).

Variational Approach This approach relies on the calculus of variations, which involves extremizing a functional. This functional corresponds to the potential energy in structural mechanics (discussed in Sect. 6.2).

Fig. 1.1 FEA representation of practical engineering problems