Linear elasticity and FEM

- Introduction: motivation, physical quantities, fields of displacements/deformations/stresses, Hooke’s law,
- Classical formulation: equilibrium equations, constitutive relations, boundary conditions; examples of problems with analytical solutions and dimensional reduction,
- Weak (variational) formulation: conversion of the problem to an integral equation using Green’s theorem, completion of the space of admissible displacements using properties of Sobolev function spaces, solvability analysis using the Lax-Milgram lemma,
- Minimization formulation: equivalence with the weak formulation, discretization using the Ritz method, convergence analysis,
- Lagrangian-type FEM in 2D: reference Lagrangian element, isoparametric transformation, numerical integration, assembly of local and global stiffness matrices and load vectors,
- Implementation aspects: code structure (element data, triangulation, integration), correctness and convergence tests; overview of 2D/3D,
- Projects: problem statement, validation against analytical/known solutions, presentation of results.