Theory of Elasticity (18 hours).
The stability of elastic equilibrium (12 hours).
Theory of plasticity (18 hours).
Learning Objectives
The main goal of the course are to furnish theoretical and practical tools for:
1. solving some simple plane elasticity problems;
2. determining the buckling load for elastic rectilinear beams, with different restraint conditions;
3. solving the equilibrium problem for ideally-plastic solids and structures.
4. Formulate and prove the static and kinematic theorems of limit analysis. The use these theorems for determining lower and upper bounds of the collapse load for ideally-plastic solids and structures.
Teaching Methods
Lessons and application exercises.
Type of Assessment
Student insight about the argument of the course are tested by means of an oral examination.
Course program
1) Theory of elasticity (18 hours). Plane stress and plain strain. Beltrami-Michell compatibility equations; Airy stress function; bending of a cantilever loaded at the end; bending of a uniformly loaded beam; two-dimensional problems in polar coordinates; axisymmetric problems. The effect of circular holes on stress distribution in plates.
2) The stability of elastic equilibrium (12 hours). Finite degree of freedom systems, loss of stability for stable and unstable brunching or snap-through. Differential equation for determining the buckling load for beams and simple structures.
3) Theory of plasticity (18 hours). Experimental results, strain processes and constitutive functional; elastic range, admissible stress range and yield surface; mechanical work, Drucker’s Postulate and its implication; Tresca and v. Mises criteria; flow rule; the effect of circular holes on collapse load and residual stress in uniformly loaded plates. Elasto-plastic bending. Static and kinematic theorems of limit analysis; collapse load for plane plate with circular notch, subject to tensile loads; Limit analysis of elasto-plastic structures.