FrameLoad#

\[\boldsymbol{p}_{In} = - \int N_I(x) \boldsymbol{p}_{n}(x) \, d x\]

and

\[\boldsymbol{p}_{Im} = - \int N_I(x) \boldsymbol{p}_{m}(x) \, d x\]

where

\[\boldsymbol{p}_{n}(x) = \sum Q_i(x) \boldsymbol{n}_{i}\]

`Dirac`#

$P_i = \delta(x - x_i)$ so that $\boldsymbol{p}_I = N_I(x_i) \boldsymbol{p}_i$

Let $left{xi_i, w_iright}$ be your standard quadrature nodes and weights on $[0,1]$. You define the new variable $x$ by an affine transformation:

$$ x=r+(1-r) xi $$

which maps $xi=0$ to $x=r$ and $xi=1$ to $x=1$. The differential transforms as:

$$ d x=(1-r) d xi $$

so the weights must be scaled by $(1-r)$.