Evaluation strategy: CWS 25 (quiz 15 + assignments 10) + MTE 25 + ETE 50

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Meeting hours: Lectures: 2:30 pm - 4 pm on Tues, and 4 pm - 5:30 pm on Weds, Tutorials: 10 am - 11 am on Weds

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​Reference books: 

• A few of the books that can serve as reference books (and not the textbook) are as the following:​

  1. A First Course in Finite Elements, J. Fish and T. Belytschko, John Wiley and Sons.

  2. An Introduction to the Finite Element Method, J.N. Reddy, Tata MacGraw Hill.

  3. Finite Element Procedures, Klaus-Jurgen Bathe, Prentice-Hall of India. 

  4. Concepts and Applications of Finite Element Analysis, R.D. Cook, John Wiley and Sons.

  5. Textbook of Finite Element Analysis, P. Seshu,  Prentice-Hall India

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​Summary of lectures:

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# 1: Introduction to the course and evaluation strategy 

# 2: Strong form of 1D elasticity: derivation of 1D elasticity equation for an axially deforming elastic rod, boundary conditions, exact solutions for distributed and end loads

# 3-4: Approximate solution, residue, collocation and least square residue method for finding approximate solutions, nature of approximate solutions, required polynomial order of the approximate solution ,weak form statement of 1D elasticity equation, its equivalence with virtual work statement and minimization of potential energy

# 5: Finding approximate solutions using weak from statement, trial solutions, test functions, example problem of 1D prismatic rod under linear distributed force, linear and quadratic solutions, comparison with analytical solution and solution obtained using weighted residual method employing strong form

# 6-8: Division of domain into two equal subdomains, piecewise linear displacement approximation, continuity condition at subdomain junction, trial solution and test functions, solution using weak form statement, nature of solution, nodes and elements, replacement of unknown constants using nodal displacements, local and global shape functions, trial solution and test functions

# 9: Use of weak form statement for generating global equations, elemental and global stiffness matrices, consistent force vectors and displacement vectors

#10 - #22 : Addressing the natural and essential boundary conditions, solution of finite element equations, deriving strain and stress distribution,  comparison with the analytical solution, nodal, elemental and global equilibrium of forces,

concept of gather matrix for assembling elemental matrices.

3 node quadratic element, Lagrange polynomials as shape functions, their properties, derivation of corresponding elemental matrices, advantages of higher order elements over refined mesh of lower order elements

Truss element, elemental and global node numbering, rank of stiffness matrix and number of constraints required, example problem.

Discussion of assignment and quiz problems, error estimation, discussion of bar with distributed springs problem.

Euler-Bernoulli Beam theory, derivation of strong form equations, conversion to weak form, approximation of transverse displacement and slope, finite element formulation of 2 node E-B beam element, sign conventions, example problem, handling boundary conditions with spring loaded ends, beam suspended on the elastic bed.

Derivation of 1D heat transfer equation, boundary conditions, comparison with the 1D elastic bar problem, conversion to weak form, finite element formulation of 2 node linear heat transfer element, example problem, discussion about the convective tip boundary conditions

Stiffness matrix and force vector evaluation using Gauss Quadrature numerical integration scheme. Demonstration of FE coding in matlab

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​​​Assignments:

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# 1

# 2

 

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​Quiz:

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# 1

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Exams:

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Announcements: 

 

Class timings for Wednesday, 22 Jan. will be 5 to 6:30 pm. 

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Submissions of all assignments will be through the google classroom. Students who are yet to join the google classroom of this course, get in contact with the TA latest by this weekend.

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Quiz 1 is scheduled to be held on Tuesday, Feb. 04 at 2:30 pm in SR # 1.

MTE of MIN324 will be held on 4th March at 10: 00 am, in room # 252 in MIED.

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One A4 sized hand written cheat sheet is allowed during the exam.

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BEST OF LUCK FOR THE EXAM!!!

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