Lecture Introduction to the finite element method has contents: Introduction, finite element equations for heat transfer, fem for solid mechanics problems, finite elements, discretization, assembly and solution. | I NTRODUCTION TO THE F INITE E LEMENT M ETHOD G. P. Nikishkov 2004 Lecture Notes. University of Aizu, Aizu-Wakamatsu 965-8580, Japan niki@ 2 Updated 2004-01-19 Contents 1 5 What is the finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 How the FEM works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Formulation of finite element equations . . . . . . . . . . . . . . . . . . . . . . . . . 6 Galerkin method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Introduction Variational formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 11 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Finite element discretization of heat transfer equations . . . . . . . . . . . . . . . . . 12 3 Finite Element Equations for Heat Transfer Different Type Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 15 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Finite element equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4 FEM for Solid Mechanics Problems Assembly of the global equation system . . . . . . . . . . . . . . . . . . . . . . . . . 18 Finite Elements 21 Two-dimensional triangular element . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Two-dimensional isoparametric elements . . . . . . . . . . . . . . . . . . . . . . . . 22 Shape functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Strain-displacement matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Element properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Integration in quadrilateral elements . . . . . . . . . . . . . . . . . . . . . . . 25 Calculation of
