Finite Elements for Aeronautical and Aerospace Engineers

COURSE DESCRIPTION

1. i.Introductionto the course. Review of Linear Algebra. Review of discrete mechanical systems: basic principles, various forms of equilibrium equations and methods of solution.
2. Presentation of the finite element method for the case of one-dimensional continuous elastic solids(the case of rods). Presentation of the fundamental equations for the solution of the problem and of variational forms of equations of equilibrium. Introduction to the concepts of local approximation of field variables, shape functions, and finite element. Methods of controlling the accuracy of local approximation and convergence. Discritization of stiffness and applied loads. Synthesis of resultant discrete system of equilibrium equations, properties and physical meaning. Calculations of strains and stresses.

iii. Analysis of truss structures. Two-dimensional truss elements, rotation of parent elements, assembly of discrete system of equations. Properties of the stiffness matrix. Application of boundary conditions.

1. Analysis of two-dimensional continuum problems of elastic solids. Generalization of the FE method to plain strain problems. Variational forms of equations of equilibrium in two dimensions. Discretization in two dimensions. Common families of quadrilateral and triangular finite elements, and associated shape functions.
2. Isoparametric elements. Isoparametric transformation of parent elements to distorted finite element meshes in the physical domain. Application of numerical integration in the calculation of stiffness matrices and load vectors and its effect of the method accuracy and performance.
3. Applications of the FE method in field problems of other disciplines.Presentation of finite elements for the analysis of two-dimensional heat transfer problems.