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Students those who are studying JNTUK R20 Mechanical Branch, Can Download Unit wise R20 3-1 Finite Element Methods (FEM) Material/Notes PDFs below.

OBJECTIVES:

• To understand the basic principles of finite element methods.
• To understand discretization principles and apply to analyse the trusses.
• To apply the finite element method to analyze and solve beam problems.
• To gain knowledge about two dimensional stress analysis.
• To understand and apply steady state analysis and dynamic analysis.

UNIT-1

Finite Element Methods: Introduction to finite element method, stress and equilibrium, strain – displacement relations, stress–strain relations, plane stress and plane strain conditions, variational and weighted residual methods, concept of potential energy, one dimensional problems.

UNIT-2

Discretization: Bar element formulation, Discretization of domain, element shapes, discretization procedures, assembly of stiffness matrix, band width, node numbering, mesh generation, interpolation functions, local and global coordinates, convergence requirements, treatment of boundary conditions.

Analysis of Trusses: Finite element modeling, coordinates and shape functions, assembly of global stiffness matrix and load vector, finite element equations, treatment of boundary conditions, stress, strain and support reaction calculations

UNIT-3

Analysis of Beams: Element stiffness matrix for Hermite beam element, derivation of load vector for concentrated and UDL, simple problems on beams.

UNIT-4

Finite element modeling: Finite element modeling of two dimensional stress analysis with constant strain triangles and treatment of boundary conditions, formulation of axi-symmetric problems.

Higher order and iso-parametric elements: One dimensional, quadratic and cubic elements in natural coordinates, two dimensional four node iso-parametric elements and numerical integration.

UNIT-5

Steady state heat transfer analysis: One dimensional analysis of a fin.

Dynamic Analysis: Formulation of finite element model, element consistent and lumped mass matrices, evaluation of eigen values and eigen vectors, free vibration analysis.

TEXT BOOKS:

1. The Finite Element Methods in Engineering / SS Rao / Pergamon.

REFERENCE BOOKS:

1. Finite Element Method with applications in Engineering / YM Desai, Eldho & Shah /Pearson publishers
2. An introduction to Finite Element Method / JN Reddy / McGraw Hill
3. The Finite Element Method for Engineers – Kenneth H. Huebner, Donald L. Dewhirst, Douglas E. Smith and Ted G. Byrom / John Wiley & sons (ASIA) Pte Ltd.
4. Finite Element Analysis: Theory and Application with Ansys, Saeed Moaveniu, Pearson Education
5. Finite Element Methods / Chen
6. Finite Element Analysis: for students & Practicing Engineers / G.Lakshmi Narasaiah / BSP Books Pvt. Ltd.

OUTCOMES:

• Understand the concepts behind variational methods and weighted residual methods in FEM
• Identify the application and characteristics of FEA elements such as bars, beams, plane 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.