2022/2023

2022/2023

DM270

ICAR/08 (CONSTRUCTION SCIENCE)

DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE

CIVIL ENGINEERING

Strutturistico

1°

1st semester (03/10/2022 - 20/01/2023)

6

70 lesson hours

Italian

WRITTEN AND ORAL TEST

AURICCHIO FERDINANDO (titolare) - 4 ECTS
SCALET GIULIA - 2 ECTS

Knowledge of the concepts given within the courses of Rational
Mechanics and Structural Mechanics.

The course aims to advance the knowledge and understanding of the mathematical and physical foundations of continuum mechanics of solids and to enhance the ability to apply its principles to solve structural
engineering problems.

• An introduction
o Mechanics of deformable solids: definition
o Model construction vs physical reality
o Mechanical modeling basic ingredients: kinematics, equilibrium,
constitutive equation

• Review on vector and tensors
o Vectors and tensors: an introduction
o Compact, indicial, engineering/Voigt notations
o Operations between vectors and tensors
o Vector and tensor calculus

• Review of solid mechanics (and notation) from basic courses (I)
o Kinematics
change of configuration, reference & current configuration; reference
configuration as a natural one for kinematics
displacement field, gradient of change of configuration, Cauchy-Green
deformation tensor, Green-Lagrange strain tensor
Fundamental assumptions: small displacement gradient; interpretation
of displacement fields in terms of rigid body and strain quotas
o Equilibrium
current configuration as a natural one to study equilibrium
external & internal actions, equilibrium for a deformable body in a
integral format
Principle of action/reaction, Cauchy stress tensor
o Principle of virtual work

• Review of solid mechanics (and notation) from basic courses (II)
o Material response and constitutive relations
o Green elasticity
o Isotropy

• Variational & energy-based formulations for 3D problems
o Minimum of free energy
o Minimum of complementary free energy
o Hellinger-Reissner and Hu-Washizu principles

• Plane beam model (1D structural model)
o Kinematic assumptions and beam-like strains
o Equilibrium from principle of virtual work and beam resultants
o Beam constitutive equations
o Euler-Bernoulli beam model
o Timoshenko beam model

• Plate model (2D structural model)
o Kinematic assumptions and plate-like strains
o Equilibrium from principle of virtual work and plate resultants
o Plate constitutive equations
o Kirchhoff-Love plate model
o Reissner-Mindlin plate model

• Principle of virtual work for (planar) beam
o PVW of planar beam problems
o Use of PVW to solve simple beam problems
o Use of PVW to solve over-constrained beam problems

• Energy-based formulations for 1D and 2D problems
o Derivation of Timoshenko plane beam model
o Derivation of Reissner-Mindlin plate model
o Elasticity vs inelastic material response in terms of energy and
dissipation

• Limit analysis basic concepts and applications to beam problems
o Simple truss structures: limit analysis
o Kinematic theorems
o Equilibrium theorems
o Simple beam structures: limit analysis

• Solid mechanics: finite strain extension
o Kinematics
Strain measure in the current configuration
Push-forward and pull-back concept
o Equilibrium
First and second Piola-Kirchhoff stress tensor

• Simple 1D structural theories: finite strain extension

• Basic concepts of instability of structures

Blackboard lectures, slide lectures, Mathematica-based hands-on
tutorials.

- Lecture notes;
- K.D. Hjelmstad, Fundamentals of Structural Mechanics, Second Edition,
Springer;
- L. Corradi dell’Acqua, La meccanica delle strutture, vol. 3, McGraw Hill
(in particular, chap. 13 for limit analysis);
- O. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its
Basis and Fundamentals, Butterworth-Heinemann, 2013.

The exam consists in a written evaluation, an oral discussion, and the
assignment of Mathematica-based homework.