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Single discipline educational activity
Course Sheet Academic Year of enrolment:
Professor and Collaborators:
Hours of classroom activity:
Objectives
Contents Computational mechanics relies on numerical methods that allow the solution of complex problems in all fields of Engineering and Applied Sciences, including mechanical applications of Biomedical Engineering. It is therefore fundamental to master the basics of the Finite Element Method, the central method of computational mechanics, to be aware of the errors and simplifications that are introduced in the finite element computations.
Extended Syllabus Linear Finite Element Analysis - basic concepts:
- Basic equations of continuum mechanics (equilibrium, compatibility, material constitutive law)
- Review of energy principles
- Bars and Beams (Euler-Bernoulli and Timoshenko) – 1D Elements
- Displacement formulations for bar and beam elements (shape functions). Element stiffness matrix and its physical meaning
- Assembly of stiffness matrix and external force vector
- Boundary conditions
- Solution of the system of linear equations
- Force recovery
- Convergence to the exact solution (h- and p- convergence)
- Finite Element formulations
- Interpolation functions and approximations
- Integration rules
- Basics of 2D and 3D elements
- Isoparametric formulation
- Examples
Recommended Bibliography Class notes by Instructor
Suggested textbooks (not required):
- Carlos A. Felippa, INTRODUCTION TO FINITE ELEMENT METHODS, Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado Boulder, Colorado 80309-0429, USA http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/Home.html
- Zienkiewicz, O. and R. Taylor (1991). The finite element method (fourth ed.), Volume I. New York: McGraw Hill
- Robert D. Cook, Davis S. Malkus, Michael E. Plesha, Robert J. Witt, CONCEPTS AND APPLICATIONS OF FINITE ELEMENT ANALYSIS, University of Wisconsin – Madison, John Wiley & Sons Inc. 2002
- O. C., Taylor, R. E., THE FINITE ELEMENT METHOD, 4th ed., McGraw-Hill, London, Vol. I: 1988, Vol II: 1993
Methods of Provision
Teaching Methods The teaching activity includes a theoretical part with lectures and exercises carried out by the teacher in the classroom and an applicative part with the assignment of a final project that will be developed by the student under the supervision of the teacher, according to weekly review cycles
Evaluation methods Verification of learning:
The exam consists in:
1) a midterm written examination that can be made up during the regular exam dates (mainly exercises)
2) a final oral examination focused on the topics covered during the lessons and on the discussion of a finite element modelling project that will be assigned during the course