Solid Mechanics

Objectives

Introduction to the classical theory of Solid Mechanics, in particular to the theory of Linear Elasticity, with application to various practical problems of Continuum Mechanics and background to develop more complex theories of material behaviour.

Program

Applied Forces. Stress. Cauchy's formula. Stress Tensor. Equilibrium equations. Principal stresses. Plane states of stress and itsrepresentation by Mohr's circle. Deformation. Homogeneous and non-homogeneous deformations. Stretch. Deformation Tensor. Infinitesimal deformations. Principal deformations. Constitutive relations. Hooke's solid, isotropic and anisotropic. Bar extension bylongitudinal forces and own weight. Bar bending by applied moments. Bar torsion by applied moments with circular and noncircular cross-section. Torsion of thin-walled bars with open and closed cross-sections, uni and multicellulars. Torsion ofanisotropic bars. Torsion of cylinders subjected to lateral forces and torsional moments. Thick cylinders subjected to pressure.Introduction to materials failure.

Teaching Methodologies

Laboratory experiments with reports (20%), 3 mini-tests during classes (30%) and final exam (50%). Minimum grade of 7/20 in the final exam.

Bibliography

Mecânica dos Sólidos – Notas das Aulas e Problemas, Luis Faria, Luís Sousa e Aurélio Araujo, 2018, IST; "A First Course inContinuum Mechanics", Y. C. Fung, 1991, Prentice Hall; "An Introduction to Continuum Mechanics", M. Gurtin,, 1981, AcademicPress; "The Theory of Materials Failure", R. Christensen, 2016, Oxford University Press