Università di Pavia - Offerta formativa

ADVANCED SOLID AND STRUCTURAL MECHANICS

Anno immatricolazione

2021/2022

Anno offerta

2021/2022

Normativa

DM270

SSD

ICAR/08 (SCIENZA DELLE COSTRUZIONI)

Dipartimento

DIPARTIMENTO DI INGEGNERIA CIVILE E ARCHITETTURA

Corso di studio

INGEGNERIA CIVILE

Curriculum

Strutturistico

Anno di corso

1°

Periodo didattico

Primo Semestre (27/09/2021 - 21/01/2022)

Crediti

6

Ore

45 ore di attività frontale

Lingua insegnamento

INGLESE

Tipo esame

SCRITTO E ORALE CONGIUNTI

Docente

Prerequisiti

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

Obiettivi formativi

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.

Programma e contenuti

• An introduction

o Mechanics of deformable solids: definition

o Model construction vs physical reality

o Mechanical modeling basic ingredients: kinematics, equilibrium, constitutive equations

• 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

o Mechanics of deformable solids: definition

o Model construction vs physical reality

o Mechanical modeling basic ingredients: kinematics, equilibrium, constitutive equations

• 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

Metodi didattici

Blackboard lectures, slide lectures, Mathematica-based hands-on tutorials. The course will be held in English if the percentage of non-native Italian students is greater than 25%.

Testi di riferimento

- 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.

- 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.

Modalità verifica apprendimento

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

Altre informazioni

Obiettivi Agenda 2030 per lo sviluppo sostenibile