MEE521­ Finite Element Methods (Proposed Syllabus)   MEE 521 2 1 2 4 Version No. Objectives:

• To introduce the mathematical and physical principles underlying the Finite Element Method (FEM) as applied to solid mechanics. • To train the students in analysis software to perform various analysis like static, thermal, fatigue, Harmonic and transient analysis on components and structures. Expected Outcome: Upon completion of this course, the student will be able to:

• Derive finite element stiffness and mass matrices • Analyze linear solid mechanics or heat-transfer problems using commercial FEM codes. • Perform static analysis, Modal analysis, Harmonic analysis and transient analysis.• Perform nonlinear analysis, thermal analysis, and fluid flow analysis. • Perform structural optimization Unit I Fundamental Concepts Physical problems, Mathematical models, and Finite Element Solutions. FiniteElement Analysis as Integral part of Computer Aided Design;. Stresses and Equilibrium; Boundary Conditions; Strain-Displacement Relations; Stress –strain relations, Linear and nonlinear material laws; Temperature Effects; Definition of Tensors and indicial notations; Deformation gradients; Classification of different types of deformations: Deformations and stresses in bars, thin beams, thick beams, plane strain- plane stress hypothesis , thin plate, thick plate, axisymmetric bodies..; Approximate nature of most of these deformation hypotheses; General 3D deformation (linear small deformation), Large deformation (nonlinear). Unit II General Techniques and Tools of Displacement Based 

Finite Element Analysis Energy and Variational principles for boundary value problems; Strong, or classical,form of the problem and weak, or Variational, form of the problem; Integral Formulations; Galerkin’s and Weighted residual approaches; Shape and interpolation functions for 1D, 2D & 3D applications; Use of shape (interpolation) functions to represent general displacement functions and in establishment of coordinate and geometrical transformations; Hermite, Lagrange and other interpolation functions; Numerical integration of functions; Gauss and other integration schemes. Unit III One­Dimensional Problems: Trusses, Beams & Frames Introduction; Local and global coordinate systems; Transformation of vectors in twoand three dimensional spaces; Finite Element Modeling of a basic truss element in local coordinate system using energy approach; Assembly of the Global Stiffness Matrix and Load vector; The Finite Element Equations; Treatment of boundary Conditions; Euler Barnoulli (thin) beam element and Timoshenko (thick) beam element; Beam element arbitrarily oriented in space; Plane Trusses, Plane frames and Three-dimensional frames; Solution algorithms of linear systems.

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Unit IV Plane Stress and Plane Strain Problems  & 3D Problems Plane stress and plane strain problems; Isoparametric Elements; Constant StrainTriangles (CST); Bilinear Quadrilateral Q4; Modeling boundary conditions; Orthotropic materials; Numerical integration; Higher Order Elements; Four-node Quadrilateral for Axisymmetric Problems; Hexahedral solid elements; Tetrahedral solid elements; Numerical integration. Unit V Plate elements and Dynamical Analysis Basic assumptions and formulations of classical Kirchhoff thin plate bending elements and thick Mindlin plate elements including bending and transverse shear energies; Degenerated shell elements; Construction of stiffness matrices. Dynamical equations of motion; Consistent and lumped Mass Matrices; Damping matrices; Vibration Analysis; Eigen value problems and solution techniques; Transient dynamical and structural dynamical problems, Explicit and implicit schemes of integrations, Stability issues. Text book 1. Robert Cook, R.D. et al. Concepts and Applications of Finite Element Analysis, John Wiley & Sons, 2004. 2. Tirupathi R. Chandrapatla, Ashok D. Belegundu Introduction to Finite Element in Engineering Prentice- Hall of India Private limited, New Delhi – 110 001. References 1. Bathe, K.J, “Finite Element Procedures”, Prentice-Hall of India Pvt. Ltd., third Edition,1996. 2. Zienkiewicz O.C., “The Finite Element Method”, McGraw-Hill, 1989. 3. Reddy J.N., “The Finite Element Method”, McGraw-Hill, Third Edition, 1993. 4. C.S. Krishnamoorthy, Finite Element Analysis, Tata McGraw-Hill, 1994. MEE 521 L ­Lab Exercises 

 • 3D Part Modeling, Assembly and Analysis of Automobile components using Hypermesh, LSDYNA • Dynamic and normal Mode Dynamic Analysis using FEA Technique. • Finite Element Analysis of structural problems, heat Transfer problems, fatigue and fracture analysis using ANSYS • Analysis of Mechanisms using ADAMS

Mode of Evaluation: Assignments / Seminars / Written Examination.  

 

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