# Introduction to Finite Element Method

• Maria Augusta Neto
• Ana Amaro
• Luis Roseiro
• José Cirne
• Rogério Leal
Chapter

## Abstract

As discussed in Chap. , mechanic problems are governed by a set of partial differential equations that are valid in a certain domain and they needed to be solved for evaluating the stress condition of mechanical components. Although analytic methods can be employed to solve linear problems involving partial differential equations, its use to analyze complex structures may be a difficult or, even, an impossible task. Thus, in this chapter, Hamilton’s principle, which one of the most powerful energy principle, is introduced for the FEM formulation of problems of mechanics of solids and structures. The approach adopted in this chapter is to directly work out the dynamic system equations, after which the static dynamic equations can be easily obtained by simply dropping out the dynamic terms

## Keywords

Shape Function Local Coordinate System Nodal Displacement Direct Integration Global Coordinate System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Maria Augusta Neto
• 1
• Ana Amaro
• 1
• Luis Roseiro
• 2
• José Cirne
• 3
• Rogério Leal
• 3
1. 1.CEMUC - Centre for Mechanical EngineeringUniversity of CoimbraCoimbraPortugal
2. 2.Department of Mechanical EngineeringPolytechnic Institute of CoimbraCoimbraPortugal
3. 3.Department of Mechanical EngineeringUniversity of CoimbraCoimbraPortugal