Finite element analysis
ME8692 FINITE ELEMENT ANALYSIS
UNIT I INTRODUCTION
Historical Background – Mathematical Modeling of field problems in
Engineering – Governing Equations – Discrete and continuous models – Boundary,
Initial and Eigen Value problems– Weighted Residual Methods – Variational
Formulation of Boundary Value Problems – Ritz Technique – Basic concepts of the
Finite Element Method.
UNIT II ONE-DIMENSIONAL PROBLEMS
One Dimensional Second Order Equations – Discretization – Element
types- Linear and Higher order Elements – Derivation of Shape functions and
Stiffness matrices and force vectors- Assembly of Matrices - Solution of
problems from solid mechanics and heat transfer. Longitudinal vibration
frequencies and mode shapes. Fourth Order Beam Equation –Transverse deflections
and Natural frequencies of beams.
UNIT III TWO DIMENSIONAL SCALAR VARIABLE PROBLEMS
Second Order 2D Equations involving Scalar Variable Functions –
Variational formulation –Finite Element formulation – Triangular elements –
Shape functions and element matrices and vectors. Application to Field Problems
- Thermal problems – Torsion of Non circular shafts –Quadrilateral elements –
Higher Order Elements.
UNIT IV TWO DIMENSIONAL VECTOR VARIABLE PROBLEMS
Equations of elasticity – Plane stress, plane strain and
axisymmetric problems – Body forces and temperature effects – Stress
calculations - Plate and shell elements.
UNIT V ISOPARAMETRIC FORMULATION
Natural co-ordinate systems – Isoparametric elements – Shape
functions for iso parametric elements – One and two dimensions – Serendipity
elements – Numerical integration and application to plane stress problems -
Matrix solution techniques – Solutions Techniques to Dynamic problems –
Introduction to Analysis Software.