ME7227

(Nonlinear Finite Element Analysis of Solid Continua)

Programs

1. assign1_prob1_x-sinx.ipynb $$F(x)=\frac{x}{\sin x}$$
2. assign1_prob2_polynomial.ipynb $$f\ =\ \frac{1}{15}\sum_{k=0}^{n}\left(-1\right)^{k}\left(\frac{\left(2n+1\right)!}{\left(2n-2k\right)!\left(2k+1\right)!}\right)\left(1-x^{2}\right)^{\left(n-k\right)}\cdot x^{2k},\quad n=9$$
3. assign1_sysofeqns_decoupled.ipynb $$F_1 =\frac{x_1}{\sin x_1} - f_1 = 0 ,\quad F_2 =\frac{x_2}{\sin x_2} - f_2 = 0$$
4. assign1_sysofeqns_coupled.ipynb $$x_1^{2}+2x_1x_2+x_2+4=\ 0$$ $$x_2^{2}+6x_1x_2+x_1^{2}+6\ =\ 0$$