512120 - SOLIDS AND STRUCTURAL MECHANICS

insegnamento

ID:

512120

Durata (ore):

45

CFU:

SSD:

Scienza delle costruzioni

Anno:

2026

Periodo di attività

Primo Semestre (28/09/2026 - 15/01/2027)

Obiettivi Formativi

The course provides a unified and rigorous treatment of solid and structural mechanics, based on the fundamental triad: Kinematics, Equilibrium, and Constitutive Law.

Prerequisiti

Mathematical Analysis (differential/integral calculus, differential equations, linear algebra).
Experimental Physics and Rational Mechanics / Statics.

Metodi didattici

Front lecture with resolved exercises

Verifica Apprendimento

Written Examination (2 hours): Solving application problems without supporting materials.
Oral Examination: Discussion of the written exam, theory assessment, and review of course assignments/exercises.

Testi

K.D. Hjelmstad, Fundamentals of Structural Mechanics, 2nd Ed., Springer (2005).
L. Anand, S. Govindjee, Continuum Mechanics of Solids, Oxford University Press (2020).
L. Corradi dell'Acqua, La meccanica delle strutture, Vol. 3, McGraw-Hill.
J. Bonet, A.J. Gil, R.D. Wood, Nonlinear Solid Mechanics for Finite Element Analysis, Cambridge University Press (2021).

Contenuti

Introduction and Tensor Review: Modeling of deformable solids; indicial notation (Einstein convention) and algebraic notation for vectors and tensors; divergence theorem.
Continuum Kinematics: Reference and current configurations; deformation gradient, Cauchy-Green and Green-Lagrange tensors; small deformations and Saint-Venant compatibility conditions.
Continuum Equilibrium: Internal and external forces; Cauchy stress tensor; balance equations and Principle of Virtual Work (PVW).
Constitutive Equations and Linear Elasticity: Green elasticity, generalized Hooke's law, isotropy, Lamé parameters, Young's modulus, and Poisson's ratio; Navier equations.
Variational and Energy-Based Formulations: Minimum of total potential energy and complementary energy; mixed principles of Hellinger-Reissner and Hu-Washizu.
One-Dimensional Structural Models (Planar Beam): Kinematic assumptions; Euler-Bernoulli vs. Timoshenko beam theory; internal force resultants (N, M, V) and stiffnesses.
Two-Dimensional Structural Models (Plate): Reissner-Mindlin and Kirchhoff-Love models; curvatures, stress resultants, and flexural rigidity.
Limit Analysis: Perfectly elastoplastic material behavior, plastic hinges; static and kinematic theorems for ultimate limit load calculation of beams and frames.
Extension to Finite Strain: Non-linear kinematics, first and second Piola-Kirchhoff stress tensors, hyperelasticity.
Classical Elasticity Solutions and Energy Theorems: Bending, Saint-Venant torsion (Prandtl stress function), plane stress/strain (Airy stress function), Castigliano's theorems.