Finite Element Methods
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Follow on Instagram for UpdatesFinite Element Methods Syllabus — Unit-wise Content
The official GTU curriculum for Finite Element Methods (subject code ME02000411) as prescribed for ME · Semester 2 divides the course into 6 units, covering 44 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (ME02000411)Unit 1 Mathematical models for structural problems
- Equilibrium of continuum-Differential formulation
- Energy Approach- Integral formulation
- Principle of Virtual work - Variational formulation
- Overview of approximate methods for the solution of the mathematical models: Rayleigh-Ritz methods
- Methods of Weighted Residuals (Galerkin
Unit 2 Bars, Trusses and Beams
- Relevance of finite element analysis in design
- Modelling and discretization
- Shape functions
- elements and Degrees-of-Freedom
- Strain – displacement relation
- Local and Global equations
- Applications of FEA
- Iso-Sub-Super parametric formulations. 1D Elements Structural Problems: Linear and Quadratic elements
- Elimination and Penalty Approach
- Properties of global stiffness matrix. 1D thermal conduction and fluid flow problems
- Formulation of Truss element
- Plane truss
- Beam: Element formulation
- plane frames
- various loading and boundary conditions
Unit 3 2D and 3D Elements
- Gauss Quadrature formula
- Gauss Quadrature in two and three dimensions
- Plate stress and plane strain matrices
- Triangular (CST
- LST) and Rectangular (Q4
- Q8) Elements: Shape function
- Jacobian matrix
- strain-displacement matrix
- stress-strain relationship matrix
- force vector
- Limitations of elements
- Types of 3D elements and their comparison
Unit 4 Plate and Shell Elements
- thin and thick plates: Kirchoff theory
- Mindlin plate element
- conforming and nonconforming elements
- degenerated shell elements
- reduced and selective integration
- shear locking and hour glass phenomenon
Unit 5 Dynamic Problems
- Formulation of dynamic problems
- consistent and lumped mass matrices Solution of eigenvalue problems: Transformation methods Jacobi method
- Vector Iteration methods
- subspace iteration method
Unit 6 Non-Linearity
- Introduction and types of non-linearity
- Formulation for geometrical and material non-linearity
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