This class introduces the fundamentals of the Finite Element Method (FEM) to handle the numerical solution of general mechanical problems, with special reference to the structural framework. As the most commonly used numerical codes rely on the classical displacement-based formulation, this is illustrated in detail. Also, two- and three-field mixed FE approaches are briefly introduced. The main FE families adopted to solve 1D, 2D and 3D continuum problems are dealt with, that is truss, frame, solid, plate and shell FEs are described. Some hints concerning numerical pathological issues and solution strategies are finally given.
February 14-16-17-18, 2022 - 11am-2pm
Monday, February 14, 2022, 11am-2pm, FEM: displacement-based formulation; multi-field mixed formulations derived from extended variational functionals. FEs for Euler-Bernoulli and Timoshenko beams: forced-based approach.
Wednesday, February 16, 2022, 11am-2pm, Lagrangian, Isoparametric, Serendipity FE families. Convergence issues, stress recovery, reduced integration.
Thursday, February 17, 2022, 11am-2pm, Plate and shell FE formulations for thin and thick plates. Shear locking problems. Discrete Kirchhoff Quadrilateral (DKQ) FE.
Friday, February 18, 2022, 11am-2pm, Implementation of a 2D solid FE in MATLAB code. Examples and applications on simple problems.