MECH 4604 Finite Element Methods (FEM)

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1 MECH 4604 Finite Element Methods (FEM) FEM or FEA (finite element analysis) is a numerical method, which is widely used in various fields of engineering in stress/strain, heat transfer, and fluid flow analyses, etc. Prerequisite: Basic operation skills of Pro/ENGINEER software. Instructor: Professor R. Liu Room 6207 Canal Building, Telephone: 8397, rliu@mae.carleton.ca Course Outline This course is designed to introduce the fundamental concepts of finite element modeling and enable the students to use a general-purpose finite element analysis software, Pro/ENGINEER/MECHANICA, to solve engineering problems mainly in Structure (some in Thermal) effectively. Part I (FEM theory) Chapter 1 Introduction to FEM Introduction to finite element method (FEM) concepts; basic steps in FEM for solid mechanics problems, heat transfer problems and fluid flow problems. Chapter 2 Formulations of FEM Direct formulation; minimum total potential energy formulation and weighted residual formulation (collocation method, subdomain method, Galerkin method and least-squares method). Chapter 3 Trusses FEM formulation of truss problems. Chapter 4 Axial Members, Beams and Frames FEM formulation of axial members, beams and frames. 1

2 Chapter 5 One-Dimensional Elements Foundation for analysis of one-dimensional problems by introducing one-dimensional linear, quadratic, and cubic elements; concepts of one-dimensional elements and shape functions and their properties; global, local and natural coordinates; one-dimensional integrals: Gauss-Legendre Quadrature. Chapter 6 Two-Dimensional Elements Introduction to two-dimensional linear and higher order elements; rectangular element, quadratic quadrilateral element, linear triangular element, quadratic triangular element, axisymmetric element and isoparametric element; two-dimensional integrals: Gauss-Legendre Quadrature. Part II (FEM software Pro/ENGINEER/MECHANICA) Chapter 1 Introduction to FEM Fundamentals of FEM; introduction to Pro/ENGINEER/MECHANICA. Chapter 2 FEM with MECHANICA Features of Pro/ENGINEER/MECHANICA. Chapter 3 Solid Models Part 1 Simple statics analysis of a solid part; exploring the FEA mesh and AutoGEM. Chapter 4 Solid Models Part 2 Standard design studies; sensitivity design studies; optimization design studies. Chapter 5 Plane Stress and Plane Strain Models Plane stress models; exploring symmetry; plane strain models. Chapter 6 Axisymmetric Solids and Shells Axisymmetric solids; axisymmetric shells.. Chapter 7 Shell Models Automatic shell creation; manual shell creation; mixed solids and shells. 2

3 Chapter 8 Beams and Frames Beam coordinate systems; basic concepts; distributed loads and beam releases; 2D frame; 3D frame. Chapter 9 Miscellaneous Topics (Skipped) Chapter 10 Thermal Models 3D solid steady state models; 2D plate steady state models; transient analysis; thermally induced stresses. Course Materials (1) Course notes Soft copy is available on both WebCT and CULearn. (2) Reference book FINITE ELEMENT ANALYSIS, Theory and Application with ANSYS, Third Edition, Saeed Moaveni, Prentice-Hall Inc., 2008, ISBN This book is reserved in Carleton Library for this course. (3) Pro/ENGINEER/MECHANICA Tutorial MECHANICA Tutorial (Structure/Thermal), Pro/ENGINEER (WILDFIRE 5.0), Integrated Mode, Roger Toogood, Schroff Development Corporation, 2009, ISBN This book is available in the Bookstore of Carleton University. Assessment Pro/ENGINEER/MECHANICA Assignments: 20% Pro/ENGINEER/MECHANICA Examination: 20% (Three hours, open book, any types of calculator allowed) Final Examination (FEM theory): 60% (Three hours, one-sheet notes on both sides allowed, any types of calculator allowed) 3

4 FEM Theory Exercises: No submission The electronic files of Exercises and Solutions are available on both WebCT and CULearn. Pro/ENGINEER/MECHANICA Assignments: (Given in Pro/ENGINEER/MECHANICA Tutorial) These assignments must be submitted on due dates. Requirements: Submit soft copies on WebCT or CULearn or through Prepare the submissions in MS Word but submit the files in pdf. Please do not submit the Pro/M models directly. In the submission files, please include the following images with required annotations: (1) FEM models with mesh, loads and constraints and (2) results of stress, strain, displacement, reaction, convergence and so on, depending on the questions for different problems. For example, for a loaded structure, it is required to report the maximum Von Mises stress. In the submission, an image of the Von Mises stress fringe should be provided in a MS Word file, with the value and location of the maximum Von Mises stress indicated. Assignment 1 (Due on Wednesday of Week 8) Chapter 3: The example of Simple Static Analysis of a Solid Part The example of Exploring the FEA Mesh and AutoGEM Exercises 1, 3 and 4 Chapter 4: The example of Standard Design Studies The example of Sensitivity Design Studies The example of Optimization Design Studies Chapter 5: The example of Plane Stress Models The example of Plane Strain Models Exercises 1 Chapter 6: The example of Axisymmetric Solids The example of Axisymmetric Shells 4

5 Assignment 2 (Due on Wednesday of Week 11) Chapter 7: The example of Automatic Shell Creation (Model #1) The example of Manual Shell Creation (Model #2) Exercises 1 Chapter 8: Example #1 Basic Concepts Example #2 Distributed Loads, Beam Releases Example #3 Frames (Model A 2D Frame) Exercises 2 (Note: The distance between the two supports is 6 m. Check Beam Tensile Stress in the result window to discuss buckling.) Chapter 10: The example of Steady State Models (3D Solid Model) The example of Steady State Models (2D Plate Model) The example of Transient Analysis The example of Thermally Induced Stresses Class Schedule and Classroom Lecture: 2:30 pm ~ 4:00 pm, Monday, Mackenzie Building 3328 (Both on Monday and Wednesday in Week 1 and Week 2; Monday only in the following weeks) Pro/ENGINEER/MECHANICA Lab: 5:30 ~ 7:00 pm on Wednesday (? This time will be discussed in class), Mackenzie Building 2256 Note: Please make sure that your computer account in Mackenzie Building 2256 works before the lab starts. If not, please contact Mr. Neil McFadyen in the department. Office Hours Prof. Liu is happy to help you whenever you need. Please come to her office (Room 6207, Canal Building) directly, or use or phone to make an appointment. Office hours: Room 6207, Canal Building, Thursday between 2:30 pm ~ 4:30 pm Materials on WebCT Course Outline Timetable Course Notes Exercises FEM Theory Solutions FEM Theory (Other materials will be posted gradually during the term, please keep checking the WebCT and CULearn.) 5

6 Academic Accommodations for Students with Disabilities The Paul Menton Centre for Students with Disabilities (PMC) provides services to students with Learning Disabilities (LD), psychiatric/mental health disabilities, Attention Deficit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders (ASD), chronic medical conditions, and impairments in mobility, hearing, and vision. If you have a disability requiring academic accommodations in this course, please contact PMC at or pmc@carleton.ca for a formal evaluation. If you are already registered with the PMC, contact your PMC coordinator to send me your Letter of Accommodation at the beginning of the term, and no later than two weeks before the first in-class scheduled test or exam requiring accommodation (if applicable). After requesting accommodation from PMC, meet with me to ensure accommodation arrangements are made. Please consult the PMC website for the deadline to request accommodations for the formally-scheduled exam (if applicable). This assignment is due on Wednesday of Week 8 (October 31st). The details of the assignment are given in the Course Outline and the Pro/MECHANICA Tutorial. The assignment can be submitted on-line or through to Prof. R. Liu (rliu@mae.carleton.ca). 6

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