Finite Element Methods

H S Rai

GNDEC, Ludhiana (India)

Linear elliptical Differential equation

in one dimension

1D Elasticity at steady state 1D Mass diffusion at steady state 1D Heat conduction at steady state

Dynamic Analysis

The differential equation:

  • \(\dfrac{d\sigma}{dx} + f(x) = 0\) in \((0, L)\)

Dynamic Analysis

Introduction

  • A method to solve Engineering Problems
  • A approximate method

Solution to DE

  • Strong form
  • Weak form

Video 4

The differential equation:

\(\frac{d\sigma}{dx} + f(x) = 0 \quad in \quad (0, L)\)

  • Open interval: Domain between \(x=0 \quad \& \quad x=L\), excluding endpoints \(x=0 \quad \& \quad x=L\) themseleves.
  • Here boundary conditions either on \(u(x)\) or on \(u_{,x}\) at boundary points.