Sumários
P2 - Unidimensional problem of second order (Bar under tension)
25 setembro 2017, 09:30 • Miguel Matos Neves
Solution of the Linear elastic bar,under distributed force p, fixed at x=0 and with a punctual load at x=L. Analytical solution u(x) and N(x). Numerical solution by FEM [Example from the 2nd page of the slides (Chapter I, Uni-dimensional problems of 2nd order)] only up to the obtaining of the system Ku=F with introduced boundary conditions.
T3 - Discrete and continuous models. Unidimensional problems of second order.
25 setembro 2017, 08:00 • Miguel Matos Neves
Discrete models for Viscous Flow in Pipes and Electrostatic circuits. Continuous models and strong formulation for elastic cables, bars under axial loads; shafts under torsional loads; and thermal conduction in bars including convection. Unified differential equation for these problems. Physical interpretations. Unidimensional problems of second order: Discretization; Deduction of the elementar equations(1. weak formulation,2. Galerkin approximations,3. Choice of the functions, 4. Obtaining Ke and Fe); Assembling equations (incidence matrix); Imposing displacement (Dirichelet) boundary conditions and force (Neumann) boundary conditions.
T2 - Deduction of differential equations of 1D mechanical phenomena
20 setembro 2017, 09:30 • Miguel Matos Neves
Equilibrium or balance in static conditions. Constitutive laws (Hooke law for normal stresses, Hooke law for shear stresses; Moment-curvature relation, Newton's cooling law, Fourier conduction law). Deduction of differential equations of unidimensional models: 1. Linear Elastic Bar under axial loads; 2. Linear Elastic shaft under torsional loads; 3. Linear Elastic Beam under transverse loads and moments; and 4. Linear thermal conduction in bars including convection. (Materials of this week in chapters 1, 3 up to pp 112 and 4 up pp 180 of the course textbook).
P1L - Direct stiffness method and technique of weighted residuals
18 setembro 2017, 10:30 • Miguel Matos Neves
Prob.s 1.1 + 1.3 + 1.24m (solution for hipostatic case)
P1 - Direct stiffness method and technique of weighted residuals
18 setembro 2017, 09:30 • Miguel Matos Neves
Prob.s 1.1 + 1.3 + 1.24m (solution for hipostatic case). All from the course collection of problems available at course webpage in PDFs section (File: Problemas_MecComp_Enunciados_2017-18-MEAer.pdf )