Finite Element Method


The finite element method is one of the most important tools used
in structural analysis. The method was introduced in the early
sixties, since then its use has been spread to several scientific
domains, namely in several fields of solid and fluid mechanics.

In this course the finite element method will be discussed and
applied to several civil engineering problems. This will allow the
students to understand its potential and usefulness. It will alert
for its limitations.

General characterization





Responsible teacher

Corneliu Cismasiu


Weekly - 4

Total - 70

Teaching language



Available soon


  • K. J. Bathe. Finite element procedures. Prentice-Hall, 1996. (COTA: TA347.BAT)
  • O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The finite element method. Volume 1: Its Basis and Fundamentals. Butterworth-Heinemann, 2005. (COTA: TA640.2.ZIE)
  • J. N. Reddy. An Introduction to the Finite Element Method. McGraw Hill, 1993. (COTA: TA347.RED)
  • A. F. M. Azevedo. Método dos elementos finitos. FEUP, 2003. (
  • Teaching method

    The several subjects will be presented and discussed in theorical-practical lectures. The several concepts, principles and methods will be presented and applied to simple problems.

    Several problems of practical application of the method under study to current problems in the field of civil engineering will be solved.

    Outside the classes the students are encouraged to study the given bibliography in order to mature and consolidate the acquired knowledge.



    Evaluation method

    Continuous evaluation without examination or final work.

    During the learning period there will be team works which will be classified. These works must be realised during classes, being the performance of the students in the class evaluated. This evaluation will count 30% in the mark.

    The final mark will be calculated using these classifications after an oral examination.

    Still it is demanded that the number of unjustified lackes to the lessons does nor exceed one third of the total.

    Subject matter

    1. Presentation
      1. Objectives and Program
      2. Course structure
      3. Evaluation methods
      4. Access and use of the available information
    2. Introduction
      1. Computational Mechanics
      2. Discretization Methods
      3. Finite Element Method
      4. Physical problems/Mathematical models
    3. Finite Element Method
      1. Governing system
      2. Developpment of the 3 and 4-nodes plain stress finite element
      3. Use of finite elements programs
      4. Errors in the analysis
      5. Convergence of the solution
    4. Applications
      1. Heat flow
      2. Plain stress
      3. Plates