# Finite Elements Method (Dept Elec - II) (2181911)

Syllabus

Sr. Topics Teaching Hours Module Weightage
1
Fundamentals of Continuum Mechanics:
Equilibrium of continuum-Differential formulation, Energy ApproachIntegral formulation. Overview of approximate methods for the solution of the mathematical models: Rayleigh-Ritz methods, Methods of Weighted Residuals (Galerkin, Least-squares & Collocation methods).
6
15 %
2
Numerical Integration:
Central Difference Method, Newmark’s Methods, Wilson’s method, Gauss quadrature.
4
5 %
3
Line Elements and Applications:
Concepts of Modelling and discretization, Shape functions, elements and Degrees-of-Freedom, Strain – displacement relation, Local and Global equations; Iso-Sub-Super parametric formulation.
4
5 %
4
Structural Problems:
Linear and Quadratic elements, Elimination and Penalty Approach, Properties of global stiffness matrix; Structural and Thermal strains; Treatment for various boundary conditions. Formulation of Truss element, Plane truss: Stiffness and Force matrix. Beam: Euler – Bernoulli Element formulation, plane frames, various loading and boundary conditions
10
25 %
5
Thermal and Fluid Problems:
Steady state heat transfer: Element formulations, treatment to boundary conditions with application to 1-D heat conduction, heat transfer through thin fins; Potential flow problems.
5
15 %
6
2D Elements:
Triangular (CST, LST): Shape function, Jacobian matrix, straindisplacement matrix, stress-strain relationship matrix, force vector. Quadrilateral Elements (Q4, Q8): Shape function, Jacobian matrix, straindisplacement matrix, stress-strain relationship matrix, force vector. Axisymmetric problems and applications.
8
20 %
7
Dynamic Problems:
Formulation of dynamic problems, consistent and lumped mass matrices for 1-D and 2-D element, Solution of eigenvalue 1-D problems: Transformation methods, Jacobi method, Vector Iteration methods, subspace iteration method.
7
15 %