Hi(adsbygoogle = window.adsbygoogle || []).push({});

I've been trying to get a simple solution to the 2D Navier-Lame equations using finite difference on a rectangular grid. I want to see the displacements, u and v, when a simple deformation is imposed - e.g. top boundary is displaced by 10%.

The equations are as follows:

\begin{eqnarray*}

(λ+2μ)\frac{∂^2u}{∂x^2} + (λ+μ)\frac{∂^2v}{∂x∂y} + μ\frac{∂^2u}{∂y^2} = 0

\\

\\μ\frac{∂^2v}{∂x^2} + (λ+μ)\frac{∂^2u}{∂x∂y} + (λ+2μ)\frac{∂^2v}{∂y^2} = 0

\end{eqnarray*}

I have tried using the Gauss-Siedel method but am not getting the expected results (which have been sovled using e.g. Mathematica/Abaqus)

Is there something else I have to consider since the two equations are coupled via the mixed partials?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Finite Difference solver for 2D Elasticity equations

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Finite Difference solver | Date |
---|---|

A Runge Kutta finite difference of differential equations | Yesterday at 6:31 PM |

A Convergence order of central finite difference scheme | Nov 8, 2017 |

A Finite Difference | Oct 30, 2017 |

A Better way to find Finite Difference | Oct 16, 2017 |

**Physics Forums - The Fusion of Science and Community**