Syllabus
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.
Objectives and Outcomes
Course Objectives
- Inculcate the knowledge to develop finite element programs to solve 1D and Multi-D problems using different FE procedures.
- 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.
- Utilize commercial finite element packages to model, solve, and analyze real-world industrial
Course Outcomes
CO
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CO Description
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CO1
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Develop different finite element procedures to solve simple 1D and 2D static problems like bars,
beams, trusses, frames, etc
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CO2
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Formulate basic and higher order elements with applicability to 1D and Multi-D coordinate systems
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CO3
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Formulate and solve static and dynamic/transient problems in Solid Mechanics and Heat Transfer using
the Method of Weighted Residuals
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CO4
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Estimate finite element assembly procedure by constructing ID, IEN, LM arrays
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CO5
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Develop finite element models to solve and analyse, static and dynamic, linear and non-linear multi-
physics problems using a finite element package
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CO-PO Mapping
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PO1
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PO2
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PO3
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PO4
|
PO5
|
CO1
|
3
|
3
|
1
|
1
|
1
|
CO2
|
3
|
3
|
1
|
1
|
1
|
CO3
|
3
|
3
|
1
|
1
|
1
|
CO4
|
3
|
3
|
1
|
1
|
1
|
CO5
|
3
|
3
|
1
|
3
|
3
|
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.