EM 319 - Structural Mechanics II (Mecānica das Estruturas II) Displacement method: Fundamentals. Energy methods. Virtual work principle. Flexibility and stiffness matrices. Stiffness matrix of a beam, in local and global axis. Stiffness matrix for a structure, as the assembly of element stiffness matrices. Element load vector. Load vector for the structure as the assembly of element load vectors. Boundary conditions. Reactions. Post processing. Element resultants. The finite element method: Fundamentals. Discrete and continuous problems. Linear-elastic bidimensional analysis, using the finite element method. Equilibrium of a 2D domain. Decomposition in 3 node triangular elements. Displacement field. Stress field. Nodal forces. Equilibrium of a finite element. Equilibrium of the whole domain. Interpolation using shape functions. Deformation matrix [B]. Elasticity matrix [D]. Stress matrix [K]. Load vector {F}. Higher order elements formulation. Standard and hierarquical shape functions. Lagrangean shape functions for 1D, 2D and 3D elements. Serendipity shape functions. Coordinate transformations. Parametric and non-parametric transformations. Isoparametric elements. Error analysis. Gauss numerical integration. Objectives Introduction to the finite element method (displacement formulation) applied to the linear elastic analysis of 1D, 2D and 3D structures. <<<<<<<<<<  BACK  <<<<<<<<<<