Finite Element Methods

Introduction, exact solution vs approximate solution, principle of FEM, application of FEM, general procedure for finite element analysis, pre‐processing, solution, post processing, Stresses and Equilibrium; Boundary Conditions.

Strain‐Displacement Relations, Stress–strain relations, Effect of temperature, various approximate methods: weighted residual method, variational or Rayleigh Ritz method, Galerkin’s method, principle of minimum potential energy.

Basic element shapes, generalized co‐ordinates, polynomials, natural co‐ordinates in one‐two‐and three‐ dimensions, Lagrange and Hermite polynomials, Application of Finite Element Methods to elasticity problems and heat conduction Problems.

One dimensional problem of finite element model, Coordinates and Shape function, Potential‐energy approach, Galerkine approach, Assembly of Global Stiffness Matrix and Load Vector. Plane trusses: Global and local coordinate system and stress calculation. Beams and Frames: finite element formulation and calculation of Shear Force and Bending Moment.

Two‐dimensional problem using Constant Strain Triangles and Four‐node Quadrilateral, Problem modelling and Boundary conditions. Practical consideration in finite element applications, problem solving on a general purpose FEM software package like ANSYS, ABAQUS, NISA etc.