21ME53 Finite Element Analysis syllabus for ME

Introduction to Finite Element Method:

General steps of the finite element method. Engineering applications of finite element method. Advantages of the Finite Element Method. Potential energy method, Displacement method of finite element formulation. Convergence criteria, Discretization process, Rayleigh Ritz method, Galerkin’s method (for study purpose only)

Types of elements:

1D, 2D and 3D, Node numbering, Location of nodes. Strain- displacement relations, Stress-strain relations, Plain stress and Plain strain conditions, temperature effects.

Interpolation models:

Simplex, complex and multiplex elements, linear interpolation polynomials in terms of global coordinates 1D, 2D, 3D Simplex Elements.

Introduction to the stiffness (Displacement) method:

Introduction, One-Dimensional Elements-Analysis of Bars and Trusses, Linear interpolation polynomials in terms of local coordinate’s for1D, 2D elements. Higher order interpolation functions for 1D quadratic and cubic elements in natural coordinates, Constant strain triangle, Four-Noded Tetrahedral Element (TET 4), Eight-Noded Hexahedral Element (HEXA 3 8), 2D iso-parametric element,

Numerical Problems:

Solution for displacement, stress and strain in 1D straight bars, stepped bars and tapered bars using elimination approach and penalty approach

Beams and Shafts:

Boundary conditions, Load vector, Hermite shape functions , Beam stiffness matrix based on EulerBernoulli beam theory, Numerical problems on simply supported, fixed straight and cantilever beams, propped cantilever beams with concentrated and uniformly distributed load.

Torsion of Shafts:

Finite element formulation of shafts, determination of stress and twists in circular shafts.

Heat Transfer:

Basic equations of heat transfer: Energy balance equation, Rate equation: conduction, convection, radiation, 1D finite element formulation using variational method, Problems with temperature gradient and heat fluxes, heat transfer in composite sections, straight fins.

Fluid Flow:

Flow through a porous medium, Flow through pipes of uniform and stepped sections, Flow through hydraulic networks.

Axi-symmetric Solid Elements:

Derivation of stiffness matrix of axisymmetric bodies with triangular elements, Numerical solution of axisymmetric triangular element(s) subjected to surface forces, point loads, angular velocity, pressure vessels.

Dynamic Considerations:

Formulation for point mass and distributed masses, Consistent element mass matrix of one dimensional bar element, truss element, triangular element, beam element. Lumped mass matrix of bar element, truss element, Evaluation of eigen values and eigen vectors, Applications to bars, stepped bars, and beams.

PRACTICAL COMPONENT

Experiments

1 Introduction to FEA software , Pre-processing tools, Solver tools and Post-processing tools.

2 Analysis of Bars of constant cross section area, tapered cross section area and stepped bar subjected to Point forces, Surface forces and Body forces(Minimum 2 exercises of different types)

3 Analysis of trusses (Minimum 2 exercises of different types)

4 Analysis of Beams – Simply supported, cantilever, Propped cantilever beams with point load , UDL, beams with 5 varying load etc.

6 Stress analysis of a rectangular plate with a circular hole.

7 Thermal Analysis – 1D & 2D problem with conduction and convection boundary conditions (Minimum 2

8 exercises of different types )

9 Dynamic Analysis to find: Natural frequency of beam with fixed – fixed end condition, Response of beam with fixed – fixed end conditions subjected to forcing function

10 Dynamic Analysis to find: Natural frequency of bar, Response of Bar subjected to forcing functions

11 Demonstrate the use of graphics standards (IGES, STEP etc) to import the model from modeler to solver.

12 Demonstrate one example of contact analysis to learn the procedure to carry out contact analysis.

13 Demonstrate at least two different types of example to model and analyze bars or plates made from composite material.

Course outcomes (Course Skill Set):

At the end of the course the student will be able to:

• Identify the application and characteristics of FEA elements such as bars, beams, plane and isoparametric elements.
• Develop element characteristic equation and generation of global equation.
• Formulate and solve Axi-symmetric and heat transfer problems.
• Apply suitable boundary conditions to a global equation for bars, trusses, beams, circular shafts, heat transfer, fluid flow, axi-symmetric and dynamic problems.

Assessment Details (both CIE and SEE)

• The weightage of Continuous Internal Evaluation (CIE) is 50% and for Semester End Exam (SEE) is 50%.
• The minimum passing mark for the CIE is 40% of the maximum marks (20 marks).
• A student shall be deemed to have satisfied the academic requirements and earned the credits allotted to each subject/ course if the student secures not less than 35% (18 Marks out of 50) in the semester-end examination(SEE), and a minimum of 40% (40 marks out of 100) in the sum total of the CIE (Continuous Internal Evaluation) and SEE (Semester End Examination) taken together

CIE for the theory component of IPCC

Two Tests each of 20 Marks (duration 01 hour)

• First test at the end of 5th week of the semester
• Second test at the end of the 10th week of the semester

Two assignments each of 10 Marks

• First assignment at the end of 4th week of the semester
• Second assignment at the end of 9th week of the semester

Scaled-down marks of two tests and two assignments added will be CIE marks for the theory component of IPCC for 30 marks.

CIE for the practical component

• On completion of every experiment/program in the laboratory, the students shall be evaluated and marks shall be awarded on the same day. The 15 marks are for conducting the experiment and preparation of the laboratory record, the other 05 marks shall be for the test conducted at the end of the semester.
• The CIE marks awarded in the case of the Practical component shall be based on the continuous evaluation of the laboratory report. Each experiment report can be evaluated for 10 marks. Marks of all experiments’ writeups are added and scaled down to 15 marks.
• The laboratory test (duration 03 hours) at the end of the 15th week of the semester /after completion of all the experiments (whichever is early) shall be conducted for 50 marks and scaled down to 05 marks.

Scaled-down marks of write-up evaluations and tests added will be CIE marks for the laboratory component of IPCC for 20 marks. .

SEE for Theory

SEE will be conducted by University as per the scheduled timetable, with common question papers for the course (duration 03 hours)

• The question paper will have ten questions. Each question is set for 20 marks.Marks scored shall be reduced proportionally to 50 marks
• There will be 2 questions from each module. Each of the two questions under a module (with a maximum of 3 sub-questions), should have a mix of topics under that module.
• The students have to answer 5 full questions, selecting one full question from each module.

The theory portion of the IPCC shall be for both CIE and SEE, whereas the practical portion will have a CIE component only. Questions mentioned in the SEE paper shall include questions from the practical component).

• The minimum marks to be secured in CIE to appear for SEE shall be the 12 (40% of maximum marks-30) in the theory component and 08 (40% of maximum marks -20) in the practical component. The laboratory component of the IPCC shall be for CIE only. However, in SEE, the questions from the laboratory component shall be included. The maximum of 04/05 questions to be set from the practical component of IPCC, the total marks of all questions should not be more than the 20 marks.
• SEE will be conducted for 100 marks and students shall secure 35% of the maximum marks to qualify in the SEE. Marks secured will be scaled down to 50.

Suggested Learning Resources:

Textbooks

1. A first course in the Finite Element Method, Logan, D. L, Cengage Learning, 6th Edition 2016.

2. Finite Element Method in Engineering, Rao, S. S, Pergaman Int. Library of Science 5th Edition 2010.

3. Finite Elements in Engineering Chandrupatla T. R PHI 2nd Edition 2013

Reference books

1. Finite Element Method, J.N.Reddy, McGraw -Hill International Edition.

2. Finite Elements Procedures Bathe K. J PHI