# ME8692 – Finite Element Analysis – Regulation 2017 Syllabus

## ME8692 – SYLLABUS

### UNIT I INTRODUCTION

Historical Background — Mathematical Modeling of field problems in Engineering — Governing Equations — Discrete and continuous models — Boundary, Initial and Eigen Value problems– Weighted Residual Methods — Variational Formulation of Boundary Value Problems — Ritz Technique — Basic concepts of the Finite Element Method.

### UNIT II ONE-DIMENSIONAL PROBLEMS

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 from solid mechanics and heat transfer. Longitudinal vibration frequencies and mode shapes. Fourth Order Beam Equation –Transverse deflections and Natural frequencies of beams.

### UNIT III TWO DIMENSIONAL SCALAR VARIABLE PROBLEMS

Second Order 2D Equations involving Scalar Variable Functions — Variational formulation –Finite Element formulation — Triangular elements — Shape functions and element matrices and vectors. Application to Field Problems — Thermal problems — Torsion of Non circular shafts –Quadrilateral elements — Higher Order Elements.

### UNIT IV TWO DIMENSIONAL VECTOR VARIABLE PROBLEMS

Equations of elasticity — Plane stress, plane strain and axisymmetric problems — Body forces and temperature effects — Stress calculations — Plate and shell elements.

### UNIT V ISOPARAMETRIC FORMULATION

Natural co-ordinate systems — Isoparametric elements — Shape functions for iso parametric elements — One and two dimensions — Serendipity elements — Numerical integration and application to plane stress problems — Matrix solution techniques — Solutions Techniques to Dynamic problems — Introduction to Analysis Software. ME8692 Finite Element Analysis

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