49047 Finite Element Analysis
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Subject handbook information prior to 2024 is available in the Archives.
Credit points: 6 cp
Subject level:
Postgraduate
Result type: Grade and marksRequisite(s): 120 credit points of completed study in spk(s): C10061 Bachelor of Engineering Diploma Engineering Practice OR 120 credit points of completed study in spk(s): C10066 Bachelor of Engineering Science OR 120 credit points of completed study in spk(s): C10067 Bachelor of Engineering OR 120 credit points of completed study in spk(s): C09067 Bachelor of Engineering (Honours) Diploma Professional Engineering Practice OR 120 credit points of completed study in spk(s): C09066 Bachelor of Engineering (Honours)
These requisites may not apply to students in certain courses. See access conditions.
Description
It is essential for structural engineers to have a basic understanding of the finite elements method to be able to model realistic structural behaviour. The main objectives of this subject are to help students acquire a fundamental knowledge of the finite elements technology, understand how different types of elements are produced, and develop an awareness of the context where these elements are used.
This subject is intended primarily for engineering students who wish to develop skills in finite element methodology. The course introduces fundamental concepts as well as practical implementations, of the finite element method.
This subject provides the theoretical basis for computer simulation and analysis of a vast spectrum of engineering problems. The method is used primarily in the field of structural mechanics to solve stress problems. This subject is intended as a first subject in finite elements and extends understanding of the method and its application to problems in solid/structural mechanics. Topics include: matrix analysis methods; the derivation of element stiffness matrices of bar and beam elements as well as stiffness matrices of triangular and quadrilateral elements for plane elasticity, shell and solid elements; work equivalent forces; the concept of natural coordinates and isoparametric element formulation; numerical integration and gauss points; finite element modelling techniques; and limitations, errors and solution accuracy of the Finite Element Method (FEM). This subject is also oriented toward users of the FEM and includes a hands-on laboratory component that requires the use of finite element programs in assignments.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Apply the fundamental theory of the finite element method to design real world civil engineering structures involving various types of elements. (C.1) |
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| 2. | Design and conduct a 2D and 3D static analysis of a building structure and its components. (D.1) |
| 3. | Perform analysis of engineering structures using commercial finite element analysis packages. (D.1) |
| 4. | Present the FEA results (stress, displacement, moment and forces) in a succinct and concise form for structural engineering projects. (E.1) |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of the following Course Intended Learning Outcomes (CILOs):
- Design Oriented: FEIT graduates apply problem solving, design thinking and decision-making methodologies in new contexts or to novel problems, to explore, test, analyse and synthesise complex ideas, theories or concepts. (C.1)
- Technically Proficient: FEIT graduates apply theoretical, conceptual, software and physical tools and advanced discipline knowledge to research, evaluate and predict future performance of systems characterised by complexity. (D.1)
- Collaborative and Communicative: FEIT graduates work as an effective member or leader of diverse teams, communicating effectively and operating autonomously within cross-disciplinary and cross-cultural contexts in the workplace. (E.1)
Contribution to the development of graduate attributes
Engineers Australia Stage 1 Competencies
This subject contributes to the development of the following Engineers Australia Stage 1 Competencies:
- 1.3. In-depth understanding of specialist bodies of knowledge within the engineering discipline.
- 2.1. Application of established engineering methods to complex engineering problem solving.
- 2.2. Fluent application of engineering techniques, tools and resources.
- 2.3. Application of systematic engineering synthesis and design processes.
- 3.2. Effective oral and written communication in professional and lay domains.
Teaching and learning strategies
The subject will be delivered in a remote learning mode primarily based on Canvas platform. There are Lectures covering key concepts, plus Tutorials during which students will undertake worked-out examples to reinforce learning concepts. Students will be given opportunities to explore learning materials before the lectures, thus affording a basic understanding and reasoning which enables improved opportunities for discussion and engagement. In-class problem solving activities will be conducted during lectures. After individually attempting each question, the students will receive feedback from their peers as a group activity as well as from the lecturer during the class discussion sessions.
The types of assignments will include preparation of small written reports, completion of a self-learning module and problem solving assignments.
Research projects will be allocated to groups of students after meeting with them through Zoom with the aim of connecting the defined research projects to one or some of the sessions. Constructive feedback on the progress of the project will be given regularly. Students are encouraged to use various online communication tools available at UTS to facilitate the required collaborative group work for planning and presenting the major assignments.
The class sessions provide a collaborative learning experience. Past examination questions will be posted on Canvas in the form of tutorial examples, quizzes and assignments. Class sessions will consist of problem-solving and discussion and students are encouraged to attempt the specified questions before having solutions. At the completion of the class sessions, students will be expected to complete further questions and submit these as assignments and receive feedback. As part of learning experience, students are required to complete 3 assignments (2 individual + 1 group) to demonstrate that students have the required knowledge to succeed in the subject. These strategies aim to enable students achieve the subject learning objectives.
Content (topics)
Lecture 1 - An overview of the finite element method where the concepts of degree-of-freedom, discretization and error are introduced. For illustrative purposes stiffness coefficients of beams are obtained using the force method and incorporated for the analysis using the slope deflection method. This method is revised here because of the similarity of some aspects to finite element analysis. The intention is to introduce some concepts from the physical intuitive point of view. Matrix algebra is also revised.
Lecture 2 - The essential mathematical tool of Variational Calculus is introduced. Ritz method as a direct variational method forms the foundation of the finite element derivations. Some parts can be abstract for an engineer; however, these ideas later will be fixed with examples and applications.
Lecture 3 - Finite element method is introduced as a special form of the Ritz method. Nodal interpolation is introduced and continuity requirements are shown to be satisfied using interpolation. Elements that provide exact nodal solutions are shown for bar and beam problems.
Lecture 4 - Beam finite element formulations are derived. Alternative beam theories are discussed from the elasticity point of view and their limitations are illustrated. We show that a-priori imposed kinematic assumptions of the beam theories significantly simplify the problem; however some conditions of elasticity are violated which can be problematic in connections, elements with holes, machine parts etc. due to local stress distribution.
Lecture 5 - Elasticity solutions to some specific problems are introduced. The elasticity solution is presented directly without emphasis on the method of solution. It is shown that 2D elasticity problems can be conveniently solved numerically using membrane finite elements. Accuracies of some triangular and rectangular elements are illustrated through examples.
Lecture 6 - 3D elasticity equations are introduced. Plate kinematic assumptions and the Kirchhoff and Mindlin plate theories (analogous to Euler Bernoulli and Timoshenko beams) are introduced. Governing differential equations are obtained using variational principle. Solutions for simply supported rectangular plate problems are displayed. Finite element formulations for plates are derived. Advantageous and disadvantageous aspects of Kirchhoff and Mindlin plate theories in developing finite element formulations are discussed.
Lecture 7 - Several Brick elements are derived. A shell element is developed as a connection of membrane and plate elements and relevant coordinate transformations in space are discussed.
Lecture 8 - Isoparametric elements and Gauss quadrature as numerical integration are introduced
Lecture 9 - Locking phenomenon is introduced as an important problem in finite element analysis, which shows that FEA may not always work as expected. Methods to remedy locking issues are discussed.
There will be additional 2 lectures on modelling with a general purpose commercial FEA software.
Assessment
Assessment task 1: Assignment 1
| Intent: | To provide students with practice in problem solving and applying concepts of discrete systems and applying the Ritz method for a beam analysis. |
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| Objective(s): | This assessment task addresses the following subject learning objectives (SLOs): 1 and 2 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): C.1 and D.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 35% |
| Criteria: | Marking criteria is based on: (i) identify the questions and the use of appropriate method to solve the problem and deliver correct answers; (ii) present the results of the project in a succinct and concise form with suitable illustration where appropriate. |
Assessment task 2: Assignment 2
| Intent: | To provide students with practice in problem solving and applying concepts of FEM for truss analysis Euler-Bernoulli beam and Timoshenko beam. |
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| Objective(s): | This assessment task addresses the following subject learning objectives (SLOs): 1 and 2 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): C.1 and D.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 35% |
| Criteria: | Marking criteria is based on: (i) identify the questions and the use of appropriate method to solve the problem and deliver correct answers; (ii) present the results of the project in a succinct and concise form with suitable illustration where appropriate. |
Assessment task 3: Group project
| Intent: | To provide students with practice in problem solving and applying concepts of FEM for forming element stiffness matrix, solving for membrane, brick and shell elements. Students are also required to demonstrate their ability to use of a commercial FEM software to design for typical civil structural elements subjected to static loadings. |
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| Objective(s): | This assessment task addresses the following subject learning objectives (SLOs): 1, 2, 3 and 4 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): C.1, D.1 and E.1 |
| Type: | Project |
| Groupwork: | Group, group assessed |
| Weight: | 30% |
| Criteria: | Marking criteria is based on: (i) identify the questions and the use of appropriate method to solve the problem and deliver correct answers; (ii) present the results of the project in a succinct and concise form with suitable illustration where appropriate and (iii) Does the team demonstrate teamwork efforts (meeting minutes are required). |
Minimum requirements
In order to pass the subject, a student must achieve an overall mark of 50% or more.
Required texts
- Learning notes, slides, supplemetary reading materials.
- Recommended textbooks in the References
References
- Saeed Moaveni (2015). Finite Element Analysis: Theory and Application with ANSYS, Global Edition, 4th Edition, Pearson Education Limited
- Nam H. Kim, Bhavani V. Sankar, Ashok V. Kumar. (2018). Introduction to Finite Element Analysis and Design, 2nd Edition, Willey.
- Pepper and Heinrich. (2017). The Finite Element Method: Basic Concepts and Applications with MATLAB, MAPLE, and COMSOL, Third Edition, CRC Press.
- Khennane, A., 2013. Introduction to finite element analysis using MATLAB® and Abaqus. CRC Press.
- Cook, RD. (1995). Finite Element Modeling for Stress Analysis
Other resources
All important and updated annoucements will be posted on Canvas.