B.E. (Automobile Engineering) Finite Element Analysis Syllabus - Mumbai University 2026

The University has moved this degree onto NEP 2020 one year at a time. The first and second years are NEP 2020 syllabi; the third and fourth years are still examined on the REV-2019 'C' Scheme, which is what the University sets for them this year.

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Syllabus for Finite Element Analysis

Semester 4 · Second Year AE · 3 credits

Module 0: Prerequisite

Differential Equations, Matrix Algebra, Basics of strength of materials and heat transfer.

Module I: Introduction :

Brief History of FEM, Finite Element Terminology (nodes, elements, domain, continuum, Degrees of freedom, loads & constraints). Application, Advantages, Steps of FEM, Stress and Equilibrium, Boundary conditions, Strain Displacement Relations, Stress-strain Relations, Von mises stress, Temperature effect, Potential Energy & Equilibrium, Gelerkin’s Method, stiffness (Displacement) Method. Home Exercise 1:Introduction to Ansys Tools( Pre Processing, Processing and Post-Processing)

Module II: Matrix Algebra &Gaussian Elimination:

Matrix Multiplication, Transposition, Diagonal Matrix, Symmetric Matrix, Upper Triangular Matrix, Determinant of Matrix, Matrix Inversion Eigen values & Eigen vectors, Gaussian elimination. Home Exercise 2: Finite Element Analysis (element selection, assigning properties, meshing, assigning loads, and boundary conditions, analysis and result interpretation).

Module III: 1D ELEMENT:

Types of 1D element: Displacement function, Global and local coordinate systems, Order of element, primary and secondary variables, shape functions and its properties. Formulation of elemental stiffness matrix and load vector for spring, bar, beam, truss and Plane frame. Transformation matrix for truss and plane frame, Assembly of global stiffness matrix and load vector, Properties of stiffness matrix, half bandwidth, Boundary conditions elimination method and penalty approach, Symmetric boundary conditions, Stress calculations. Home Exercise 3:Any two problems using bar element

Module IV: 1D Steady State Heat Transfer Problems :

Introduction, Governing differential equation, steady-state heat transfer formulation of 1D element for conduction and convection problem, boundary conditions and solving for temperature distribution. Home Exercise 4:Any one problem on steady state heat conduction

Module V: Dynamic Analysis:

Types of dynamic analysis, General dynamic equation of motion, point and distributed mass, lumped and Consistent mass, Mass matrices formulation of bar and beam element. Undamped free vibration- Eigen value problem, Evaluation of eigen values and eigenvectors (natural frequencies and mode shapes). Home Exercise 5:Any one problem of free vibration analysis using bar element

Module VI: 2D ELEMENTS:

Second Order 2D Equations involving Scalar Variable Functions — Variation formulation –Finite Element formulation — Triangular elements Shape functions and element matrices and vectors. Application to Field Problems —Torsion of Non circular shafts –Quadrilateral elements. Stress analysis of CST. Home Exercise 6:Any two problems using CST element

Text Books

1 Introduction to Finite Element Engineering – T.R.Chandrupatla, Belegunda; PHI
2 A First course in Finite Element Method- Darya Logon, Thompson Learning (TL Publisher)
3 Concepts and Applications of Finite Element Analysis, R. D. Cook, et al. Wiley, India
1 Seshu P., ―Text book of Finite Element Analysis‖, PHI Learning Private Ltd. New Delhi, 2010.
2 Bathe K. J., ―Finite Element Procedures‖, Prentice-Hall of India (P) Ltd., New Delhi.
3 Fagan M. J., ―Finite Element Analysis, Theory and Practice‖, Pearson Education Limited.
4 Kwon Y. W., Bang H., ―Finite Element Method using MATLAB‖, CRC Press, 1997
5 S. Moaveni, ―Finite element analysis, theory and application with Ansys‖,
6 Fundamental of Finite Element Analysis, David V. Hutton, Tata McGraw-Hill
7 The Finite Element Method in Engineering- S.S.Rao, Elsveir Pub.
8 An Introduction to Finite Element Method-J.N.Reddy, Tata Mc-grawHil Page | 56

Reproduced from the University of Mumbai syllabus for B.E. (Automobile Engineering) under NEP 2020, in force from the academic year 2025-26. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF 7.39 (R-A) B.E. (Automobile Engineering) Sem I & II (Revised, NEP 2020) NEP 2020 syllabus Read full PDF Read

PDF 6.46 (N) B.E. (Automobile Engineering) Sem III & IV (NEP 2020) NEP 2020 syllabus Read full PDF Read

PDF 6.10 B.E. (Automobile Engineering) Third Year, Sem V & VI (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read

PDF 6.46 (R) B.E. (Automobile Engineering) Fourth Year, Sem VII & VIII (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read

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