University of Mumbai Syllabus For Semester 6 (TE Third Year) Finite Element Analysis: Knowing the Syllabus is very important for the students of Semester 6 (TE Third Year). Shaalaa has also provided a list of topics that every student needs to understand.

The University of Mumbai Semester 6 (TE Third Year) Finite Element Analysis syllabus for the academic year 2021-2022 is based on the Board's guidelines. Students should read the Semester 6 (TE Third Year) Finite Element Analysis Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the University of Mumbai Semester 6 (TE Third Year) Finite Element Analysis Syllabus pdf 2021-2022. They will also receive a complete practical syllabus for Semester 6 (TE Third Year) Finite Element Analysis in addition to this.

## University of Mumbai Semester 6 (TE Third Year) Finite Element Analysis Revised Syllabus

University of Mumbai Semester 6 (TE Third Year) Finite Element Analysis and their Unit wise marks distribution

### University of Mumbai Semester 6 (TE Third Year) Finite Element Analysis Course Structure 2021-2022 With Marking Scheme

# | Unit/Topic | Marks |
---|---|---|

C | Module 1 | |

101 | Introduction | |

CC | Module 2 | |

201 | Fea Procedure | |

CCC | Module 3 | |

301 | One-dimensional Problems | |

CD | Module 4 | |

401 | Two Dimensional Finite Element Formulations | |

D | Module 5 | |

501 | Two Dimensional Vector Variable Problems | |

DC | Module 6 | |

601 | Finite Element Formulation of Dynamics and Numerical Techniques | |

Total | - |

## Syllabus

- Introductory Concepts: Introduction to FEM, Historical Background, General FEM procedure. Applications of FEM in various fields. Advantages and disadvantages of FEM.
- Mathematical Modeling of field problems in Engineering, Governing Equations, Differential Equations in different fields.
- Approximate solution of differential equations-- Weighted residual techniques, Least squares, Galerkin methods, Boundary Value problems.

- Discrete and continuous models, Weighted Residual Methods – Ritz Technique – Basic concepts of the Finite Element Method.
- Definitions of various terms used in FEM like element, order of the element, internal and external node/s, degree of freedom, primary and secondary variables, boundary conditions.
- Minimization of a functional. Principle of minimum total potential. Piecewise Rayleigh-Ritz method. Formulation of “stiffness matrix”; transformation and assembly concepts

- One Dimensional Second Order Equations – Discretization – Element types- Linear and Higher order Elements – Derivation of Shape functions and Stiffness matrices and force vectors.
- Assembly of Matrices - solution of problems in one dimensional structural analysis, heat transfer and fluid flow (Stepped and Taper Bars, Fluid Network, Spring-Cart systems) 3.3 Analysis of Plane Trusses, Analysis of Beams.
- Solution of one Dimensional structural and thermal problems using FE Software, Selection of suitable Element Type, Modeling, Meshing, Boundary Condition, Convergence of solution, Result analysis, Case studies.

- Introduction, Three nodded triangular element, four nodded rectangular element, four nodded quadrilateral element, eight nodded quadrilateral element.
- Natural coordinates and coordinates transformations: serendipity and Lagranges methods for deriving shape functions for triangular and quadrilateral element
- Sub parametric, Isoperimetric, super parametric elements. Compatibility, Patch Test, Convergence criterion, Sources of errors.

- Equations of elasticity – Plane stress, plane strain and axisymmetric problems.
- Jacobian matrix, stress analysis of CST and four node Quadratic element
- Solution of 2-D Problems using FE Software (structural and Thermal), selection of element type, meshing and convergence of solution. (Can be covered during practical hours).

- Applications to free vibration problems of rod and beam. Lumped and consistent mass matrices.
- Solutions Techniques to Dynamic problems, longitudinal vibration frequencies and mode shapes. Fourth Order Beam Equation, Transverse deflections and Natural frequencies of beams.
- Finding frequencies of beam using FE Software (Can be covered during practical hours).