smmr89
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Hi
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?
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?