Skip to main content
\(\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \renewcommand{\vec}[1]{\boldsymbol{#1}} \newcommand{\tens}[1]{\boldsymbol{#1}} \newcommand{\mat}[1]{\left[\boldsymbol{#1}\right]} \newcommand{\matWp}[2]{\left[\boldsymbol{#1}_{#2}\right]} \newcommand{\tensQ}[1]{\pmb{\mathbb{#1}}} \newcommand{\tensQc}[1]{\mathbb{#1}} \newcommand{\transp}[1]{{#1}^{\textrm{T}}} \newcommand{\veczero}{\vec{0}} \newcommand{\body}{\Omega} \newcommand{\calvec}[1]{\boldsymbol{\mathcal{#1}}} \newcommand{\commadiff}[2]{{#1,}_{#2}} \newcommand{\regulardiff}[2]{ \frac{\partial#1}{\partial#2} } \newcommand{\func}[2]{#1\left(#2\right)} \newcommand{\transp}[1]{{#1}^{\text{T}}} \newcommand{\transpm}[1]{{#1}^{-\text{T}}} \newcommand{\trace}[1]{\text{tr}#1} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)
A first course on solid mechanics
Antonio Bilotta
Contents
Prev
Up
Next
Contents
Prev
Up
Next
Front Matter
Colophon
Author Biography
Dedication
Acknowledgements
Preface
using MATLABĀ®
Additional resources
I
continuum mechanics
1
bodies' kinematics
configurations
transformations
deformation gradient
displacement field
determinant of the deformation gradient
polar decomposition
stretch tensor \(\tens{U}\) and principal directions (transformation of line elements)
strain measures
the infinitesimal strain tensor
exercises
answers to selected exercises
references and suggested readings
2
forces, equilibrium and stress
the continuity hypothesis
equilibrium equations
Cauchy stress tensor tensor
analisys of states of stress
principle of virtual work
exercises
answers to some of the proposed exercises
references and suggested readings
3
elasticity
motivation
uniaxial states
multi-axial states
the elastic problem
one-dimensional models: stretched beam
one-dimensional models: bent beam
applications of the stretched beam model
applications of the bent beam model
exercises
answers to selected exercises
references and suggested readings
II
rigid systems
4
kinematics
basic kinematic description
constraints
kinematic analysis
kinematic analysis of simple rigid body systems
references and suggested readings
5
statics
equilibrium equations
2D case
constraints
free body diagrams
static analysis
application of static analysis to systems of bodies
generalized section forces
2D beam equilibrium differential equations
generalized section forces calculation and diagrams
Authored in PreTeXt
Dedication
Dedication
To those who study the solid mechanics
To my grandfather Giovanni