Funkcje kształtu

\begin{aligned} & {\left[\begin{array}{lll} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{array}\right]=\left[\begin{array}{lll} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{array}\right]^{-1}} \\ & N_1(x, y)=a_1 \cdot x+b_1 \cdot y+c_1 \\ & N_2(x, y)=a_2 \cdot x+b_2 \cdot y+c_2 \\ & N_3(x, y)=a_3 \cdot x+b_3 \cdot y+c_3 \end{aligned}

Macierz sztywności

\begin{aligned} & B=\left[\begin{array}{l} \frac{\mathrm{d}}{\mathrm{d} x} N_1(x, y) \frac{\mathrm{d}}{\mathrm{d} x} N_2(x, y) \frac{\mathrm{d}}{\mathrm{d} x} N_3(x, y) \\ \frac{\mathrm{d}}{\mathrm{d} y} N_1(x, y) \frac{\mathrm{d}}{\mathrm{d} y} N_2(x, y) \frac{\mathrm{d}}{\mathrm{d} y} N_3(x, y) \end{array}\right] \\ & K=B^{\mathrm{T}} \cdot B \cdot A \end{aligned}