# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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# Undergraduate Course: Finite Element Methods for Solids and Structures 4 (CIVE10022)

 School School of Engineering College College of Science and Engineering Credit level (Normal year taken) SCQF Level 10 (Year 4 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 Summary The finite element method (FEM) (also called finite element analysis or FEA) originated from the need to solve complex problems in solid mechanics. FEM is used to obtain approximate numerical solutions to a variety of equations of calculus. Today it is used in a wide range of disciplines. This course is an introduction to FEA as applied to elasticity problems in solid and structural mechanics. The mathematical equations are developed using the virtual work basis of FEM and this is used to develop equations for one, two and three dimensional elements. As FEA is a computational tool this course includes practical exercises using the commercial package ABAQUS. A number of tutorials involving hand calculations are provided to aid understanding of the technique. Course description L1 Introduction Course outline; areas of application of the finite element (FE) method; examples of some problems for which FE analysis has been used. L2 FE terminology and steps Introduction to FE terminology; steps of the analysis using an assumed displacement field approach for linear elastic analysis of structures. L3 Input to and Output from a FE program 1 Feeding a finite element program (ABAQUS) with geometric, physical and loading information. L4 Input to and Output from a FE program 2 Understanding and interpreting results from a FE program. L5 FE Modelling Introduction to plane stress, plane strain, axisymmetric, and plate bending problems; degrees of freedom; stress-strain and strain-displacement relations. L6 Virtual Work Basis of Finite Element Method: 1 Definition of generic displacements, body forces, nodal displacements, and nodal actions; displacement shape functions with simple examples; relating generic displacements, strains, and stresses to nodal displacements. L7 Virtual Work Basis of Finite Element Method: 2 Derivation of FE equilibrium equations using the virtual work principle; examples of derivation of stiffness and equivalent load vector for a two node truss element. L8 Quadrilateral Elements 1 Normalised coordinates; shape functions for the bi-linear and quadratic elements; Isoparametric concept; examples L9 Quadrilateral Elements 2 Evaluation of element matrices; the Jacobian matrix; examples of specific cases. L10 Quadrilateral Elements 3 Numerical integration; examples of numerical evaluation of element matrices L11 Quadrilateral Elements 4 Examples of numerical and closed form evaluation of stiffness and load matrix terms L12 Triangular elements 1 Natural coordinates; shape functions of constant and linear strain triangular elements; isoparametric mapping; examples L13 Triangular elements 2 Evaluation of element matrices; the Jacobian matrix; examples of specific cases. L14 Triangular elements 3 Numerical integration; examples of numerical evaluation of element matrices L15 Beam elements 1 FE basis of Euler Bernoulli beam elements; FE matrices and shape functions L16 Beam elements 2 Strain-displacement and stress-strain relations for Euler Bernoulli beams; evaluation FE matrices; limitations; examples L17 Beam elements 3 FE basis of thick (Timoshenko) beam elements; shape functions L18 Beam elements 4 Generalised strain-displacement and generalised stress-strain relations; evaluation of FE matrices; reduced integration L19 Revision
 Pre-requisites Students MUST have passed: Computer Methods in Structural Engineering 3 (CIVE09027) OR Solid Mechanics 3 (MECE09009) Co-requisites Prohibited Combinations Students MUST NOT also be taking Computer Methods in Structural Engineering 3 (CIVE10018) Other requirements None
 Pre-requisites Structural Analysis/Mechanics High Demand Course? Yes
 Academic year 2016/17, Available to all students (SV1) Quota:  120 Course Start Semester 1 Course Start Date 19/09/2016 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 20, Seminar/Tutorial Hours 11, Supervised Practical/Workshop/Studio Hours 10, Formative Assessment Hours 1, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 54 ) Assessment (Further Info) Written Exam 60 %, Coursework 40 %, Practical Exam 0 % Additional Information (Assessment) Coursework: 40% Exam: 60% Feedback Through short formative assessments and the project. Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) CIVE10022 Finite Element Methods for Solids and Structures 4 2:00
 By the end of the course, the student should be able to: - describe the analytical methods and procedures which the finite element programs use to analyse elastic solid structures; - be able to use the computer based finite element methods to solve simple problems by hand calculations - identify and understand all the various matrix operations involved in the process; - use computer programs to analyse elastic structures, present results in appropriate graphical formats, carry out checks to assess the correctness of the output, and interpret results properly.
 Recommended texts: 1. Cook, RD; Malkus, DS; Plesha, ME; Witt, RJ. Concepts and Applications of Finite Element Analysis, Wiley, 2002. 2. Zienkiewicz, OC; Taylor, RL. The Finite Element Method for Solid and Structural Mechanics, Butterworth-Heinemann, 2005. 3. Bathe, KJ. Finite Element Procedures, Prentice Hall, 1996. 4. Smith, IM; Griffiths, DV. Programming the Finite Element Method, Wiley, 2004.
 Graduate Attributes and Skills Not entered Special Arrangements none Keywords Numerical Methods,solid mechanics,elasticity
 Course organiser Dr Pankaj Tel: (0131 6)50 5800 Email: Pankaj@ed.ac.uk Course secretary Mr Craig Hovell Tel: (0131 6)51 7080 Email: c.hovell@ed.ac.uk
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