ME5130 : Finite Element Analysis

Dr. Viswanath R Chinthapenta

Course Objective

ME5130 is a graduate level course on the theory and implementation of finiteelement methods for solving boundary value problems in solid mechanics. Thiscourse introduces the computational methods to solve problems in solids andstructures. These concepts can be extended to any multi-physics problem, butthe focus of the present course will be more on solid mechanics. This courseis to train the students not only to use commercially software’s but also equipwith the theory and implementations of finite element methods. On successfulcompletion of this course one should be able to solve a BVP of a reasonablycomplex geometry computationally.

Course Plan

This course can be sub divided into 4 parts (1) Mathematical foundations (2)Guide to use a software (software is a black box). (3) Actual usage of one suchcommercially available software (4) How to develop your own code.

Part (1) and (4) will help students to develop their own algorithms and codeto solve a BVP. While, part (1) and (2) are essential to understand the problemso that they can be solved using part (3).

Course Outline

See Table 1

Instructor

Dr. Viswanath R Chinthapenta,117, IIT-Hyd, Ph: 7098,viswanath@iith.ac.in

Lectures

Slot Q, Monday 4.00-5.30PM and Thursday 2.30-4.00PM

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Lecture Hall

LH2

Office hours

Tuesday 10-1PM

Teaching Assistance

CH SIVANAND, ME12M1008@iith.ac.in, @ Mechtronics Lab, Mon and Wed2.30-4.30 ANWAR SADATH K T, ME12M1003@iith.ac.in, @ MTech Lab, Tueand Thr 2.30-4.30

Prerequisites

Continuum Mechanics, Linear Elasticity and Mechanics of Solids and Struc-tures.

Basics

Prerequisites wavier : Through class participations

Mid term

Closed notes

Final Exam

In class

Website

me.iith.ac.in/~viswanath/FEM

Notifications

Check emails regularly for notifications.

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Textbooks(Required):

1) RD Cook, DS Malkus and , Concepts and Applications of Finite ElementAnalysis, Wiley 1995, ISBN2) JN Reddy, An Introduction to the Finite Element Method, McGraw-Hill Ed-ucation, 2005, ISBN 0-07-124473-5.3) AF Bower, Applied Mechanics of Solids, Taylor & Francis Group, 2010, ISBN978-1-4398-0247-2.4) IH Shames, Energy and Finite Element Methods in Structural Mechanics,CRC Press, 1985, ISBN-978-0891165057

Suggested Reading

5) K-J Bathe, Finite Element Procedures, Prentice-Hall, 1996 ISBN 978-0133014587.6) OC Zienkiewicz and RL Taylor and JZ Zhu,The Finite Element Method:Its Basis and Fundamentals, Elsevier Butterwoth-Heinemann, 2005, ISBN 978-0750663205 7) OC Zienkiewicz and RL Taylor,The Finite Element Method forSolid and Structural Mechanics, Elsevier Butterwoth-Heinemann, 2005, ISBN978-0750663212 8) OC Zienkiewicz and RL Taylor and P Nithiarasu,The FiniteElement Method for Fluid Dynamics, Elsevier Butterwoth-Heinemann, 2005,ISBN 978-0750663229.9) K Atkinson,An Introduction to Numerical Analysis, Jhon Willey & Sons,1989, ISBN 0-471-62489-6.

Assessment:

1) Homeworks- 10 sets each carries 40 points.Late homeworks are not accepted.Collaborations are encouraged only within the pre-assigned group.Each individual should submit his/her own original work hand written to getcredits and any collaboration/help must be honored by declaring the source.2) One Mid Term and One Final Exam each carries 100 points.3) Final Project 150, project presentation 50 points.Strictly no collaborations allowed for final exams.Any online/textbook source should be appropriately cited.4)Except for medical and family emergencies, and research basedtravel no other reasons for skipping assignments and exams are enter-tained. To avail this proper proof has to be submitted appropriately.5) Full attendance carries 100 points, and nil attendance carries zeropoints and rest proportionally varies.6) Active class participation carries 100 points. (Participation in classroom discussions and Q&A).

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7) Each misconduct of any nature carries a penalty of 50 points in ad-dition to the punishments from the department. (Misconduct is decidedbased on violation of code of conduct of IIT-Hyderabad)

Grading:

Absolute grading policy in evaluating the assignments and exams adopted. Rel-ative grading is used while evaluating the projects since this is intermediate gradlevel course. The grades are accordingly set as listed belowA :901-1000 pointsA-:801-900 pointsB :701-800 pointsB-:601-700 pointsC :501-600 pointsC-:401-500 pointsD :301-400 points

My office hours:

1) Designated hours : Tuesday 10-11AM, Rm 1172) Email (for appointments and special needs) : viswanath@iith.ac.in

Teaching Assistance (to be decided)

1) Email:2) Hours:

1 Notifications:

Look for course notification in www.iith.ac.in/~viswanath/FEM

2 Project:

The actual project will be finalized by Mid term. Each individual has to comeup with his project definition by Mid term (carries 25 points). Instructor willonly guide you to choose but its student responsibility to define his project. Tochoose there are four basic categories for this course project.

1. Development of element (coding/software).

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2. Development of material (coding/software).

3. Implementation of new solution schemes (coding).

4. Solve a BVP problem completely using commercial software.

One has to execute their project and solve a BVP. The solution obtainedshould be compared with either a benchmark problem, experiments or analyt-ical results. A 7 section report comprised of Abstract, Introduction, Method,Results, Discussions, Conclusion and Bibliography is due by last day of course(carries 125 points). A Project presentation is due by the course conference day(carries 50 points).

Rules

1. IITH code of conduct will be strictly enforced.

2. Please do not copy the assignment. If found you will loose all points forthat entire Assignment

3. Assignments are due in 7days

4. Please work on assignments much before the deadline.

5. Make full use of office hours and TA hours.

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Part # Topic # Topic Week

1 Mathematical foundation for computational 1-3methods in solids and structures

1.1 Review of Calculus of Variation1.2 Review of Interpolation Theory1.3 Review of Numerical Integration1.4 Review of Linear Algebra

2. Review of Energy Theorems 3-52.1 Principle of virtual work2.2 Principle of Minimum Potential Energy2.3 Principle of Minimum Complementary Energy2.4 Integral or weak form of Governing Equation of Linear Elasticity

3 A User Guide to use any software (ABAQUS/ANSYS) 5-83.1 FEA software’s : A Black Box3.2 Spatial Modelling3.3 Geometric discritization (Nodes and Elements)3.4 Element Library3.5 Material Modelling3.6 Loading and Boundary Conditions3.7 Constraints3.8 Surface/Interfaces Interaction Modelling3.9 Step and Job Handling3.10 Post-processing3.11 BVP solving using ABAQUS

4. FEA : Theory and Implementation of 1D case (MATLAB) 9-114.1 FE Mesh and Element Connectivity4.2 Element displacement vector4.3 Element interpolation function4.4 Element strains, stress, and strain energy density4.5 Element stiffness matrix4.6 Global stiffness matrix4.7 Global Residue force vector4.8 Equilibrium : Minimizing the potential energy4.9 Effective stiffness matrix reduction4.10 Solution and Post-processing

5. FEA : 2D and 3D Elastic (FORTRAN) 12-14

5.1 Static Linear Elasticity5.2 Dynamic Linear Elasticity(5.3) Hypo Elastic (incompressible materials)(5.4) Hyper Elastic (Finite Deformation theory)

6. Commercial Software’s 15-17

6.1 ABAQUS6.2 ANSYS

(7.) Special topics 17-18

(7.1) FEA : 2D and 3D Plasticity (FORTRAN)(7.1.1) Visco Plasticity(7.1.2) Crystal Plasticity(7.2) FEA : Heat Transfer(7.2.1) Unsteady Heat Conduction

Table 1: Course Outline

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