Today the finite element method (FEM) is considered as one of the well established and convenient technique for the computer solution of complex problems in different fields of engineering: civil engineering, mechanical engineering, nuclear engineering, biomedical engineering, hydrodynamics, heat conduction, geo-mechanics, etc. From other side, FEM can be examined as a powerful tool for the approximate solution of differential equations describing different physical processes.
The success of FEM is based largely on the basic finite element procedures used: the formulation of the problem in variational form, the finite element discretization of this formulation and the effective solution of the resulting finite element equations. These basic steps are the same whichever problem is considered and together with the use of the digital computer present a quite natural approach to engineering analysis.
The study course examines each of the above operations of the finite element method, giving a general understanding of the complete solution process. According to three basic areas in which knowledge is required, the study course is divided into three parts. The first part of the study course comprises the formulation of FEM and the numerical procedures used to evaluate the element matrices and the matrices of the complete element assemblage. In the second part, methods for the efficient solution of the finite element equilibrium equations in static analysis will be discussed. In the third part of the study course, some modelling aspects and general features of some Finite Element Programs (ANSYS, NASTRAN, LS-DYNA, ABAQUS) will be briefly examined.
