Finite element analysis teaching plan
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This course aims to impart knowledge of finite element methods (FEM) and their application to engineering problems. The course objectives are to introduce concepts of mathematical modeling, discretization, and the finite element approach. The course outcomes include being able to recognize and apply FEM to various engineering problems, formulate field problems and governing equations, interpret FEM steps like determining stiffness matrices, and analyze one-dimensional, two-dimensional, axisymmetric, and isoparametric elements and their applications. The course content is divided into five modules covering topics such as introduction to FEM, one-dimensional problems, two-dimensional continua, axisymmetric continua, and isoparametric elements.
Finite element analysis teaching plan
- 1. COURSE OBJECTIVE: To impart the knowledge to the students on the use of FEM to various Engineering Problems. To introduce the concepts of Mathematical Modeling of Engineering Problems To know the principles involved in discretization and finite element approach. COURSE OUTCOME: Ability to 1. recognize the use of FEM in various engineering problems and application 2. outline the different formulation of field problems and governing equations for different models and problems 3. Interpret the steps to find stiffness matrix and shape function for structural and thermal problems using suitable approaches. 4. Demonstrate and categorise the 2D continuum and their various applications. 5. Illustrate the axisymmetric continnum and find stress, temperature and velocity head based on the application. 6. Analyse the various isoparametric 2D continuum elements in 1-D, 2-D and 3-D.. COURSE CONTENT Module I - INTRODUCTION: (09 Hours) Historical background – Matrix approach – Application to the continuum –Discretisation – Matrix algebra –General field problems, Governing equations- Weighted Residual Method- Ritz method. Module II - ONE DIMENSIONAL PROBLEMS: (09 Hours) Finite Element Modeling- FEM analysis of one dimensional problems- Coordinates and Shape functions- Derivation of Shape functions- discretization of domain, element equations and assembly, derivation of stiffness matrices and load vectors- Solution of problems from solid mechanics and heat transfer. Module III - TWO DIMENSIONAL CONTINUUM: (09 Hours) Second order equation involving a scalar variable function – Triangular and quadrilateral elements- Shape functions and element matrices and force vectors- Application to Field Problems - Thermal problems. MODULE IV - AXI-SYMMETRIC CONTINUUM: (09 Hours) Equations of elasticity- Plane stress, plane strain and axisymmetric problems- Element stiffness matrix- body forces- Temperature effects- Stress calculation- head and fluid flow problems, time dependent problems- Application to Cylinder under internal and external pressure. Module V - ISOPARAMETRIC ELEMENTS FOR 2-D CONTINUUM: (09 Hours) Isoparametric formulation- Shape functions for isoparametric elements-, Lagrangean and serendipity elements- element stiffness matrix- formulation of element equations- Stress calculations- Numerical integration Text Books: 1. Rao, S.S., The Finite Element Method in Engineering”, 3rd Edition, Butterworth Heinemann, 2004 2. Logan, D.L., “A first course in Finite Element Method”, Thomson Asia Pvt. Ltd., 2002 Reference Books: 1. Seshu, P, “Text Book of Finite Element Analysis”, Prentice-Hall of India Pvt. Ltd., New Delhi, 2007. 2. Reddy. J.N., “An Introduction to the Finite Element Method”, 3rd Edition, Tata McGraw-Hill, 2005 3. Tirupathi, R.Chandrupatla and Ashok, D. Belegundu., "Introduction to Finite Elements in Engineering", Prentice Hall of India Private Limited., New Delhi, 2004. MICRO LESSON PLAN 17ME2031 – FINITE ELEMENT ANALYSIS (Credits 3:0:0) Unit No Lect. No. Topics to be covered Book & Page Nos. Date Taught MODULEI 1 Introduction Reference Book 3 – Page Numbers from 1 to 21 2 Historical background 3 Matrix approach 4 Application to the continuum 5 Discretisation 6 Matrix algebra 7 General field problems 8 Governing equations- Weighted Residual Method 9 Rayleigh Ritz method MOD ULE II 10 One Dimensional Problems Text Book 1 – Page Numbers from 53 to 65 11 Finite Element Modeling 12 FEM analysis of one dimensional problems
- 2. 13 Coordinates and Shape functions 14 Derivation of Shape functions 15-16 discretization of domain, element equations and assembly, derivation of stiffness matrices and load vectors 17-18 Solution of problems from solid mechanics and heat transfer MODULEIII 19 Two Dimensional Continuum Text Book 1 – Page Numbers from 157 to 189 20-21 Second order equation involving a scalar variable function 22-23 Triangular and quadrilateral elements 24-25 Shape functions and element matrices and force vectors 26 Application to Field Problems 27 Thermal problems MODULEIV 28 Axi-Symmetric Continuum Text Book 2 – Page Numbers from 441 to 465 29 Equations of elasticity 30 Plane stress, plane strain and axisymmetric problems 31 Element stiffness matrix 32 body forces - Temperature effects 33 Stress calculation 34 head and fluid flow problems 35 time dependent problems 36 Application to Cylinder under internal and external pressure MODULEV 37 Isoparametric Elements For 2-D Continuum Text Book 2 – Page Numbers from 475 to 517 38 Isoparametric formulation- 39 Shape functions for isoparametric elements-, 40-41 Lagrangean and serendipity elements- 42 element stiffness matrix- 43 formulation of element equations- 44 Stress calculations- 45 Numerical integration *Mode of Teaching: Sketch Board (Gallery Hall), PPT, Video, Tutorials, Quiz Text Books: 1. Rao, S.S., The Finite Element Method in Engineering”, 3rd Edition, Butterworth Heinemann, 2004 2. Logan, D.L., “A first course in Finite Element Method”, Thomson Asia Pvt. Ltd., 2002 Reference Books: 1. Seshu, P, “Text Book of Finite Element Analysis”, Prentice-Hall of India Pvt. Ltd., New Delhi, 2007. 2. Reddy. J.N., “An Introduction to the Finite Element Method”, 3rd Edition, Tata McGraw-Hill, 2005 3. Tirupathi, R.Chandrupatla and Ashok, D. Belegundu., "Introduction to Finite Elements in Engineering", Prentice Hall of India Private Limited., New Delhi, 2004. ASSESSMENT PATTERN COURSE ARTICULATION MATRIX MAPPING OF PROGRAMME OUTCOMES WITH COURSE OUTCOMES Name of Assessment Marks Allotted Tentative Date Duration TEST 1 15 31st working day 03/02/2020 120 minutes TEST 2 15 57th working day 10/03/2020 120 minutes TEST 3 15 81st working day 16/04/2020 120 minutes QUIZ 5 81st working day 16/04/2020 10 minutes Quality Assessment 5 - - - Attendance 5 - - - End Semester 40 After 90th working day 04/05/2020 180 minutes
- 3. PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 CO1 3 3 3 3 2 2 1 1 1 2 2 2 CO2 3 3 2 2 3 3 2 1 1 2 1 2 CO3 3 3 3 2 2 2 2 1 1 2 2 2 CO4 3 2 3 3 1 2 2 1 2 2 1 1 CO5 3 3 3 3 1 2 1 1 2 2 2 2 CO6 3 3 2 3 3 3 2 2 2 2 2 1 NOTE: 3 – HIGH CORRELATION; 2 – MEDIUM CORRELATION; 1 – LOW CORRELATION; MAPPING OF PROGRAMME SPRCIFIC OUTCOMES WITH COURSE OUTCOMES PSO1 PSO2 PSO3 CO1 3 3 3 CO2 3 2 2 CO3 3 3 1 CO4 3 2 1 CO5 3 2 1 CO6 3 3 2 NOTE: 3 – HIGH CORRELATION; 2 – MEDIUM CORRELATION; 1 – LOW CORRELATION; Subject Teacher Head of the Department CO PO CO PSO