User:Eml4500.f08.jamama.justin/HW7b



$$\tilde{d}^{(e)}=\tilde{T}^{(e)}d^{(e)}$$

6x1 6x6 6x1 (known after solving finite element system)

Compute $$u(\tilde{x}),v(\tilde{x})$$



$$u(\tilde{x})=u(\tilde{x})\vec{\tilde{i}}+v(\tilde{x})\vec{\tilde{j}}$$

$$=U_{x}(\tilde{x})\vec{i}+U_{y}(\tilde{x})\vec{j}$$

Compute $$U(\tilde{x}), V(\tilde{x})$$ using eq.(1) and (2) from page 38-3.

*Compute $$U_{x}(\tilde{x}), V_{y}(\tilde{x})$$ from $$U(\tilde{x}), V(\tilde{x})$$

$$\begin{Bmatrix} U_{x}(\tilde{x})\\ U_{y}(\tilde{x}) \end{Bmatrix}=R^{T}\begin{Bmatrix} U(\tilde{x})\\ V(\tilde{x}) \end{Bmatrix}$$ Where R is from P 37-3 $$\begin{Bmatrix} U(\tilde{x})\\ V(\tilde{x}) \end{Bmatrix}=\begin{bmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   N_{1} & 0 & 0 & N_{4} & 0 & 0\\ 0& N_{2} & N_{3} & 0 & N_{5} & N_{6} \end{bmatrix}\begin{Bmatrix} \tilde{d}_{1}^{(e)}\\ .\\   .\\    .\\    .\\    \tilde{d}_{6}^{(e)} \end{Bmatrix}$$ $$N(\tilde{x})$$$$\tilde{d}^{(e)}$$ $$\begin{Bmatrix} U_{x}(\tilde{x})\\ U_{y}(\tilde{x}) \end{Bmatrix}=R^{T}N(\tilde{x})\tilde{T}^{(e)}d^{(e)}$$