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SYLLABUS

UNIT-I

INTRODUCTION Concepts of FEM – Steps involved – Merits and demerits – Energy principles – Discretization – Rayleigh – Ritz method of functional approximation. PRINCIPLES OF ELASTICITY Equilibrium equations – Strain displacement relationships in matrix form – Constitutive relationships for plane stress, Plane strain and Axi-symmetric bodies of revolution with axi-symmetric loading.

UNIT-II

ONE DIMENSIONAL AND TWO DIMENSIONAL ELEMENTS Stiffness matrix for bar element – Shape functions for one dimensional elements – One dimensional problems – Two dimensional elements – Different types of elements for plane stress and plane strain analysis – Displacement models – Generalized coordinates – Shape functions – Convergent and compatibility requirements – Geometric invariance – Natural coordinate system – Area and volume coordinates.

UNIT-III

GENERATION OF ELEMENT Generation of element stiffness and nodal load matrices for 3-node triangular element and four noded rectangular elements.

UNIT-IV

ISOPARAMETRIC FORMULATION Concepts of, isoparametric elements for 2D analysis – Formulation of CST element, 4-noded and 8-noded iso-parametric quadrilateral elements – Lagrangian and serendipity elements. AXI-SYMMETRIC ANALYSIS Basic principles – Formulation of 4-noded iso-parametric axi-symmetric element.

UNIT-V

SOLUTION TECHNIQUES Numerical integration, Static condensation, Assembly of elements and solution techniques for static loads.