UNIT - I Introduction to Finite Element Methods : Basic Equations in Elasticity Stress – Strain equation – Concept of plane stress - plane strain – Advantages and disadvantages of FEM. Element shapes – nodes – nodal degree of freedom displacement function – Natural coordinates – Strain displacement relations. (Chapter - 1) UNIT - II Lagrangian – Serendipity elements – Hermite polynomials – regular, irregular 2 D & 3D – Element – shape functions upto quadratic formulation. Finite Element Analysis (FEA) of – one dimensional problems – Bar element – Shape functions stiffness matrix – stress-strain relation. (Chapter - 2) UNIT - III FEA Beam Elements : Stiffness matrix - Shape function– Analysis of continuous beams. (Chapter - 3) UNIT - IV FEA Two Dimessional Problem : CST – LST element – shape function – stress – strain. Isoparametric formulation – Concepts of isoparametric elements for 2D analysis - formulation of CST element. (Chapter - 4) UNIT - V Solution Techniques : Numerical integration, Static condensation, assembly of elements and solution techniques for static loads. (Chapter - 5)
