Topic 1

Review & Introduction

Review the strength of the material, review linear algebra, modeling and discretization, finite element method, 

Topic 2

Direct stiffness method

Basic FEM steps, spring element and stiffness matrix, types of boundary conditions, truss, beam stiffness matrix, equivalent nodal forces, 

Topic 3

Other FEM procedures

Minimum potential energy method, weighted residual methods, and Galerkin’s method for bar and beam elements

Topic 4

2D and 3D FEM

Plane stress and plane strain, constant strain triangular element (CST), rectangular plane element, linear strain triangular element (LST), three-dimensional stress and strain, tetrahedral and hexahedral elements

1.      Represent a simple engineering problem (structural and heat transfer) by selecting an appropriate  differential equation (governing equation), apply boundary conditions, and solve the problem using the finite element method;

2.      Develop a finite element solution by selecting the appropriate element and choosing the correct FEM methodology;

3.      Explain the differences between elements (e.g. bar, beam, CST, LST, Q4, Hex), examine and justify the use of an appropriate approximation methodologies (e.g. direct stiffness, min potential energy, weighted residual) in solving a problem;

4.      Verify a FEM solution using common engineering sense, and validate the FEM solution by comparing it with an exact solution;

5.      Apply the concepts and methods of FEM in commercial software (ANSYS) at an introductory level (geometry generation, mesh generation, mesh refinement, applying boundary conditions, contact surfaces, the convergence of the solution, post-processing, and interpretation of the results);

6.      Demonstrate effective teamwork in diverse groups in solving an authentic design problem;

Textbook

A first course in the FEM by Daryl L. Logan, 6^th Edition (2019), Cengage

Other books

Introduction to the Finite Element Method by J.N. Reddy, 4^th Edition (2019), McGraw-Hill

The Finite Element Method for Engineers, Huebner, Dewhirst, Smith, Byrom, 4th Edition (2001), Wiley

Finite Element for Engineers with ANSYS Applications by M.S. Gadala (2020), Cambridge University Press

Lying by Approximation, The Truth About Finite Element Analysis, V.C. Prantil, C. Papadopoulos, P.D. Gessler, Synthesis Lectures of Engineering, (2013) Morgan & Claypool