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Lecturer:
Ferdinando Auricchio
Armando Gobetti
Course name: Structural dynamics and introductory computational mechanics
Course code: 502859
Degree course: Ingegneria Civile
Disciplinary field of science: ICAR/08
L'insegnamento è caratterizzante per: Ingegneria Civile
University credits: CFU 12
Course website: n.d.
Specific course objectives
Part A. Structural dynamics
(D.Gobetti)
Part B. Introductory computational mechanics
(F. Auricchio)
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
Part A. Structural dynamics
(D.Gobetti)
Part B. Introductory computational mechanics
(F. Auricchio)
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Review of standard displacement method for planar frames
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Development of a finite element scheme for Euler-Bernoulli beam, starting from elastica differential equativo
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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.
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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.
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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
Part B. Introductory computational mechanics
(F. Auricchio)
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): 72
Practical class (hours/year in lecture theatre): 40
Practicals / Workshops (hours/year in lecture theatre): 0
Suggested reading materials
Part A. Structural dynamics
(D.Gobetti)
Part B. Introductory computational mechanics
(F. Auricchio)
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Notes provided by the teacher
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Matlab codes provided by the teacher
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Zienkiewicz, O. and R. Taylor (1991). The finite element method (fourth ed.), Volume I. New York: McGraw Hill.
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Taylor, R. (2000). A finite-element analysis program. Technical report, University of California at Berkeley. http://www.ce.berkeley.edu/rlt.
Testing and exams
Part B. Introductory computational mechanics
(F. Auricchio)
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.
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