Lecturer: Ferdinando Auricchio   Simone Morganti  

Course name: Introductory computational mechanics
Course code: 502861
Degree course: Bioingegneria
Disciplinary field of science: ICAR/08
University credits: ECTS 6
Course website: n.d.

Specific course objectives

The course is an introduction to classical computational mechanics methods.
In particolar, starting from the standard displacement-based method for planar frames, we will develop the finite-element method for shear-undeformable and shear-deformable beams. We will then approach the development of finite-elements for two-dimensional continuum problems (addressing both triangular and quadrangolar elements). Finally, the course will address the solution of non-linear problems relative to stability issues discussing arclength methods.

Course programme

• Review of standard displacement method for planar frames
• Development of a finite element scheme for Euler-Bernoulli beam, starting from elastica differential equativo
• Development of a finite element scheme for Timoshenko (shear deformable) beam starting from total potential energy. Locking issues and possible solution techniques: linked interpolation, under-integration, Hellinger-Reissner mixed approach.
• Two-dimensional problems. Development of triangular and iso-parametric quadrangolar finite elements. Numerical integration. Locking issues and possible solution techniques: under-integration, enhanced method, mixed approach.
• Rigid frame structures with pointwise elastic joints. Equilibrium stability issues and their non-linearity. Techniques for the solution of non-linear problems, in particular for the case of non-monotonic paths: arc-length methods.

Course entry requirements

Intermediate knowledge of algebra, mechanics of solids (introductory concepts on strain and stress), numerical analysis.

Course structure and teaching

Lectures (hours/year in lecture theatre): 45
Practical class (hours/year in lecture theatre): 0
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

Notes provided by the teacher
Matlab codes provided by the teacher

Zienkiewicz, O. and R. Taylor. The finite element method (fourth ed.), Volume I (1991). New York: McGraw Hill.

Taylor, R.. A finite-element analysis program. Technical report, University of California at Berkeley. http://www.ce.berkeley.edu/rlt.

Testing and exams

Written and oral final exam, with discussion of the proposed homeworks suggested during the course and eventually of a either theoretical or numerical final project.