- #1

chowdhury

- 36

- 3

1.) I have the following equation

$$\nabla \cdot \left( \mathbf{A} : \nabla_{s}\mathbf{b} \right) - \frac{\partial^2\mathbf{c}}{\partial t^2} = - \nabla \cdot \left( \mathbf{D}^{Transpose} \cdot \nabla \phi \right )$$

Is my index notation correct?

$$(A_{ijkl} b_{k,l}),_{j} - c_{i,tt} = - (D_{ijk}^{Transpose} \phi_{,k}),j $$

This becomes

$$(A_{ijkl} b_{k,l}),_{j} - c_{i,tt} = - (D_{kij} \phi_{,k}),j $$

2.) New set of A, b, C, d below.

$$\nabla \cdot \left( \mathbf{A} \cdot \nabla \mathbf{b} \right) = \nabla \cdot \left( \mathbf{C} : \nabla_{s}\mathbf{d} \right) $$

Is my index notation correct?

$$(A_{ij} b_{,j}),i = (C_{ijk} d_{j,k})_{,i}$$

$$\nabla \cdot \left( \mathbf{A} : \nabla_{s}\mathbf{b} \right) - \frac{\partial^2\mathbf{c}}{\partial t^2} = - \nabla \cdot \left( \mathbf{D}^{Transpose} \cdot \nabla \phi \right )$$

Is my index notation correct?

$$(A_{ijkl} b_{k,l}),_{j} - c_{i,tt} = - (D_{ijk}^{Transpose} \phi_{,k}),j $$

This becomes

$$(A_{ijkl} b_{k,l}),_{j} - c_{i,tt} = - (D_{kij} \phi_{,k}),j $$

2.) New set of A, b, C, d below.

$$\nabla \cdot \left( \mathbf{A} \cdot \nabla \mathbf{b} \right) = \nabla \cdot \left( \mathbf{C} : \nabla_{s}\mathbf{d} \right) $$

Is my index notation correct?

$$(A_{ij} b_{,j}),i = (C_{ijk} d_{j,k})_{,i}$$

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