Methods for the discretization of the linear elastic problem.
The FInite Difference Method.
The Ritz Method.
The Finite Element Method.
Parent finite element. Interpolation and shape functions. Transformation from the parent to the real finite element. Isoparametric finite elements. Numerical integration: Gauss-Legendre method. Convergence criteria. Patch test.
Limit Analysis of plane frames.
Introduction to constitutive laws: linear and non linear elastic laws; linear viscoelastic laws; perfectly plastic laws.
The case of beams subjected to axial forces and bending moments. M-N interaction curves. Assumption of plastic hinge. Step-by-step analysis of perfectly plastic plane frames. Plastic collapse. Limit Analysis: calculation of the limit load. Static and kinematic theorem.
Introduction to the stability analysis of plane beams.
Analysis of discrete problems under arbitrarily large displacements and strains. Second order theory. Methods for the analysis of stability of discrete problems. Calculation of the critical load for continuous beams in the elastic range. Hints to more complex problems: analysis of frames; elastic-plastic material; imperfect or transversally loaded beams.