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Subject Syllabus

ME-504 (C) - Finite Element Method

ME · Semester 5

Course Modules

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Structural analysis, objectives, static Dynamic and kinematics analyses Skeletal and continuum structures Modeling of infinite d.o.f. system into finite d.o.f. system Basic steps in finite element problem formulation General applicability of the method.

Discretization of the domain Basic element shapes Aspect ratio Shape functions Generalized co-ordinates and nodal shape functions.ID spar and beam elements, 2D rectangular and triangular elements Axisymmetirc elements.

Concept of element assembly Global and local co-ordinate systems Band width and its effects Banded and skyline assembly Boundary conditions Solution of simultaneous equations Gaussian elimination and Choleksy decomposition methods Numerical integration One and 2D applications.

One dimensional quadratic and cubic elements Use of natural co-ordinate system Area co-ordinate system continuity and convergence requirements, 2D rectangular and triangular requirement.

Analysis of trusses and frames Analysis of machine subassemblies Use commercial software packages Advantages and limitations Hamilton's principle Derivation of equilibrium Consistent and lumped mass matrices Derivation of mass matrices for ID elements Determination of natural frequencies and mode shapes Use of commercial software packages.