The book by I.S.Sokolnikoff, "Mathematical theory of elasticity", McGraw-Hill, is recommended for the study of the topics addressed in the first part of the course, dealing with continuum mechanics. Students unable to attend lectures can use this book.
A broad discussion of two dimensional problems in elasticity is reported in S. Timoshenko, J.N. Goodier, "Theory of elasticity", McGraw-Hill.
A survey on the beam theory can be found in S. Timoshenko "Strength of materials. Part I", Van Nostrand Company.
For what concerns Plasticity and Limit analysis, M. Lucchesi, N. Zani "Notes on the plasticity theory" are available on the e-learning platform.
Student should acquire knowledge, skills and competencies on the methods of analysis of continuum bodies, both in elastic and elastic-plastic fields; knowledge, skills and competencies on the methods of limit analysis applied to soil mechanics, steel structures and masonry structures. The course provides the necessary skills to attend the successive course of "Structural Mechanics and Engineering II".
The curricular requirements established by the didactic regulation of the Master Programme.
Type of Assessment
Stress and Strain
Strain analysis. Displacement, deformation, infinitesimal strain tensor; spherical and deviatoric parts of the strain tensor; principal strains and principal strain directions; plane strain state; internal compatibility equations.
Stress analysis. Mass density, contact and body forces, stress vector, stress tensor; spherical and deviatoric parts of stress tensor; principal stresses and principal stress directions; plane stress states and Mohr circle; differential equilibrium equations. Theorem of virtual work.
Constitutive equations. Linear elastic materials; elasticity tensor and specific strain energy. The symmetries and the isotropy of the material; Lamé constants; Young modulus and Poisson ratio.
Two dimensional problems in elasticity. The problems addressed will be defined during the semester.
Theory of structures
Beam theory. Differential equation of the elastic curve. Application of the theorem of virtual works to the analysis of statically indeterminate beam structures.
General theory. Experimental results. Histories and constitutive functional. Stress range and yield surface. Plastic histories. The Drucker postulate. Yield criteria for ductile materials (Tresca and v. Mises criteria). Yield criteria for granular materials (Mohr-Coulomb and Drucker-Prager criteria)
Limit analysis. Weak form of the equilibrium equation. Characterization of the collapse. The static and kinematic theorems. Discontinuous stress fields. Discontinuous displacement fields. Applications.