JNTUA B.Tech. R20 Regulations

########## JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR B.Tech (ME) - III-II Sem L T P C 3 0 0 3 (20A03602) FINITE ELEMENT METHODS Course Objectives:

- • Familiarize basic principles of finite element analysis procedure.
- • Explain theory and characteristics of finite elements that represent engineering structures.
- • Apply finite element solutions to structural, thermal, dynamic problem.
- • Learn to model complex geometry problems and solution techniques.

########## Course Outcomes:

Upon successful completion of this course you should be able to

- • Understand the concepts behind variational methods and weighted residual methods in FEM.
- • Identify the application and characteristics of FEA elements such as bars, beams, and isoparametric elements, and 3-D element.
- • Develop element characteristic equation procedure and generation of global stiffness equation will be applied.
- • Able to apply Suitable boundary conditions to a global structural equation, and reduce it to a solvable form.
- • Able to identify how the finite element method expands beyond the structural domain, for problems involving dynamics, heat transfer and fluid flow.

########## UNIT I Introduction to finite element methods

Introduction to finite element methods for solving field problems, applications, Stress and equilibrium, Boundary conditions, Strain-Displacement relations, Stress- strain relations for 2D and 3D Elastic problems. Potential energy and equilibrium, Rayleigh-Ritz method, Formulation of Finite Element Equations. Finite element modelling of ID bar elements coordinates and shape One dimensional Problems: dimensional Problems: functions. Requirements for Convergence and Interpolation functions, Pascal's Triangle, Assembly of global stiffness matrix and load vector. Finite element equations, Treatment of boundary conditions, Quadratic shape functions.

UNIT II 1 D Analysis of Trusses and Beams Stiffness Matrix for 1D truss element, Stress Calculations and Problems with Analysis of trusses: Stiffness Matrix for 1D truss element, Stress Calculations and Problems with Analysis of trusses: maximum of three elements. Element Stiffness Matrix and Load vector for 1 D beam element, Hermite shape Analysis of beams: of beams: functions and simple problems.

########## UNIT III 2D Analysis

Finite element modeling of two dimensional stress analysis with constant strain triangles and treatment of boundary conditions. Estimation of load Vector, Stresses. Finite element modeling of Axi-symmetric solids subjected to axi-symmetric loading with triangular elements.

UNIT IV Quadrilateral Elements &Thermal Analysis Isoparametric, Sub parametric and Super parametric elements, Modelling of Quadrilateral Elements: Isoparametric, Sub parametric and Super parametric elements, Modelling of Quadrilateral Elements: 4 noded and 8 noded quadrilateral elements and simple problems. Numerical Integration. Steady dimensional analysis of composite slab and fin. Steady dimensional analysis of composite slab and fin. state heat transfer analysis: UNITV Dynamic analysis One dimensional analysis of composite slab and fin. state heat transfer analysis:

Analysis of a 1D uniform shaft subjected to torsion - Simple problems Formulation of finite element model, element - mass matrices, evaluation of Eigen Dynamic analysis: analysis: values and Eigen vectors for a bar and shaft.

########## Textbooks:

- 1. T. Chandraputla, Ashok Belegundu, Introduction to Finite Element in Engineering, Pearson Publications, 4/e, 2011.
- 2. S.S.Rao, The Finite Element Methods in Engineering, Elsevier Butterworth -Heinemann, 2/e, 2011.
- 3. S.Md.Jalaludeen, Finite Element Analysis in Engineering, 2/e, Anuradha Publications, 2016.