Course

Elective Streams General Electives

Lab Content 45 hours

Static linear and non-linear analysis of thermo-mechanical and other coupled-physics problems, Problems involving discontinuous interactions, Modal analysis to capture natural frequencies and mode shapes, Steady-state dynamic analysis of problems involving harmonic loading and predict conditions for resonance, Transient dynamic analysis of mechanical and industrial processes like machining, rolling, extrusion-forming, punching, etc., Utilize non-default controls available in FE packages for specific applications, Develop & Run script files for simple problems without using GUI, Develop user-defined codes and plug-ins for specific applications.

Unit 1

Fundamentals of governing equations: Governing equations in Solid Mechanics and Heat Transfer. Basic finite element procedures: Direct Stiffness Method, Principle of Minimum Potential Energy, Strong form, Weak form, Variational formulation, Weighted Residual Method – Galerkin formulation.

Unit 2

Formulation of the finite element equations – Element types – Basic and higher order elements –1D, 2D, 3D coordinate systems. Finite elements in Solid Mechanics: Analysis of trusses, beams and frames, Plane stress, Plane strain and Axisymmetric elements, Isoparametric formulation and elements. Finite elements in Heat Transfer: Formulation and solution procedures in 1D and 2D problems – Steady State and Transient problems.

Unit 3

Structural Dynamics: Formulation – Element mass matrices – Evaluation of Eigen values and Eigen vectors – Natural frequencies and mode shapes – Numerical time integration. Computer implementation of the Finite element method: Pre-processing, Element calculation, Equation assembly – Assembly Flowchart, ID, IEN, LM arrays, Solving – Numerical Integration – Gaussian Quadrature, Post processing – Primary and Secondary variables.

Course Objectives

1. Inculcate the knowledge to develop finite element programs to solve 1D and Multi-D problems using different FE procedures.
2. Inculcate the knowledge to formulate Strong, Weak, Galerkins, and Matrix forms to formulate and solve linear and non-linear multi-physics problems using the method of weighted residuals.
3. Utilize commercial finite element packages to model, solve, and analyze real-world industrial

Course Outcomes

CO-PO Mapping

Skills Acquired

Develop analytical and numerical models using the methodology of finite elements to solve and analyze linear and nonlinear problems involving single and multi-physics, and to effectively utilize commercial finite element packages for part and process modeling with applicability to real-world industrial problems.

Text Books / References

1. Thomas J. R. Hughes, “The Finite Element Method – Linear Static and Dynamic Finite Element Analysis”, 2^nd, Dover Publications Inc, 2012.
2. Rao S., “The Finite Element Method in Engineering”, Fifth Ed., Elsevier, 2022.
3. Daryl Logan, “A First Course in the Finite Element Method”, Sixth Ed., Cengage Learning, 2016.
4. David Hutton, “Fundamentals of Finite Element Analysis”, McGraw Hill, 2005.
5. Reddy N., “An Introduction to the Mathematical Theory of Finite Elements”, Dover Publications, 2011.
6. Jacob Fish and Ted Belytschko, “A First Course in Finite Elements”, Wiley Inter Science,
7. DS Simulia, “Abaqus Documentation”, Abaqus version 16.