Sumários

AP7 - 2D Problems

28 outubro 2019, 09:30 • Miguel Matos Neves

Prob. 15 - Stiffness and load vector for the reference element.Choice of local numbering in order to have all element matrices and load vectors equal in this case. Assembling entry by entry using the connectivity matrix to obtain the global system before boundary conditions. Robin boundary condition, the boundary integral and the contributions Hij and Pi to stiffness matrix and to load vector, respectively.

AT13 - Saint-Venant torsion and Prandtl torsion

28 outubro 2019, 08:00 • Miguel Matos Neves

 Torsion of a generic shaft (cont.). Non-constrained wrapping and Saint-Venant assumptions. Displacement field and wrapping as function of distortion angle. Equilibrium (Cauchy law) and stress equations.Strong formulation in terms of wrapping function as Neumann problem. Prandtl stress function. Strong formulation in terms of Prandtl stress function as Dirichelet problem. Analogy with the thermal conductivity problem in 2D and solution by finite element method. Post-processing: torsional constant Jsv of the cross section.

AT12 - 2D Problem Heat conduction (Cont.) + Saint-Venant torsion

23 outubro 2019, 09:30 • Miguel Matos Neves

Tensorial notation and matrix notation. Stiffness matrices for the CST element using alfa, beta, gama.Load vector due to distributed heat source and due to the imposed flux at the boundary. Assembling of matrices and load vector. Introducing the boundary conditions of imposed temperature (exact method) and imposed flux (using the line integral).
Torsion of a generic shaft. Non-constrained wrapping and Saint-Venant assumptions. Displacement field and wrapping as function of distortion angle. Equilibrium (Cauchy law) and stress equations.

AP6L - 1D Problems + 2D Problems

21 outubro 2019, 10:30 • Miguel Matos Neves

Prob. 14 - A: Admissibility, sparsity, bandwidth, skyline, node numbering optimization.
Prob. 15 - Single Value 2D problem (Poisson Equation). Strong and weak formulation. Stiffness and load vector for the reference element.

AP6 - 1D Problems + 2D Problems

21 outubro 2019, 09:30 • Miguel Matos Neves

Prob. 14 - A: Admissibility, sparsity, bandwidth, skyline, node numbering optimization.
Prob. 15 - Single Value 2D problem (Poisson Equation). Strong and weak formulation. Stiffness and load vector for the reference element.