R22 M.Tech. ENGG. DESIGN

#### JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD M. TECH. I Year II Sem. (ENGG. DESIGN)

#### ADVANCED FINITE ELEMENT AND BOUNDARYELEMENT METHODS (Professional Core - IV)

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##### Prerequisite: of Materials, Mathematics, Heat Transfer and Vibrations. Prerequisite: of Materials, Mathematics, Heat Transfer and Vibrations.

#### Course Course Objectives

- • To Introduce the basic concepts of the finite element method, the boundary element method
- • To discuss the advantages and limitations of each method
- • To Demonstrate the capabilities of each method on a variety of problems

##### Course After completing this course, the student should be able to Course After completing this course, the student should be able to outcomes

- • Understand the background of mathematical equations used for development of modeling software modules to develop the various structural related applications
- • Identify mathematical model for solution of common engineering problems.
- • Solve structural, thermal, fluid flow problems.
- • Use professional-level finite element software to solve engineering problems in Solid mechanics, fluid mechanics and heat transfer.

#### UNIT - I:

One Formulation of Stiffness Matrix for a Bar Element by the Principle of One Formulation of Stiffness Matrix for a Bar Element by the Principle of Dimensional Problems Minimum Potential Energy, Properties of Stiffness Matrix, Characteristics of Shape Functions, Quadratic shape functions.

##### Analysis of Stiffness Matrix for Trusses, Stress and strain Calculations, Analysis of Stiffness Matrix for Trusses, Stress and strain Calculations, of Trusses: Calculation of reaction forces and displacements.

Analysis of Stiffness matrix for two noded, two degrees of freedom per node Analysis of Stiffness matrix for two noded, two degrees of freedom per node of Beams: beam element, Load Vector, Deflection, Stresses, Shear force and Bending moment, Problems on uniform and stepped beams for different types of loads applied on beams.

#### UNIT - II:

Finite of Element stiffness matrix for two- Finite of Element stiffness matrix for two- element - formulation of 2D Problems: dimensional CST Element, Derivation of shape functions for CST Element, Elasticity Equations, constitutive matrix formulation, Formulation of Gradient matrix. Two dimensional Isoparametric Elements and Numerical integration.

#### Finite of Element stiffness matrix for Finite of Element stiffness matrix for element - formulation of 3D problems:

Tetrahedron Element, Properties of Shape functions for 3D Tetrahedral Element, Stress-Strain Analysis for 3D Element, Strain Displacement for Relationship Formulation.

#### UNIT - III:

Steady One Dimensional Finite Element analysis of fin and composite Steady One Dimensional Finite Element analysis of fin and composite state heat transfer analysis slabs. Derivation of Thermal Stiffness Two-dimensional steady state heat transfer problems: matrix for 2D heat transfer problems-CST, Derivation of thermal force vector for 2D heat transfer problems. : Formulation of mass matrices for uniform bar and beam Elements using lumped Dynamic Analysis and consistent mass methods, Evaluation of Eigen values and Eigen vectors for a stepped bar and beam Problems.