Finite Element Methods

H S Rai

GNDEC, Ludhiana (India)

Math: Special Character

alpha \(\alpha\) psi \(\psi\) Psi \(\Psi\) Phi \(\Phi\) zeta \(\zeta\) rho \(\rho\) eta \(\eta\) omega \(\omega\) Omega \(\Omega\)

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Dynamic Analysis
Dynamic Analysis

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


  • A method to solve Engineering Problems
  • A approximate method

Solution to DE

  • Strong form
  • Weak form

Math stuff

  • We can have...
  • \(f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n\)

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.