Solve following differential equation $\frac{d^2y}{dx^2} - 10x^2 = 5 ; \hspace{0.6cm} 0 \leq x \leq 1$

BCs : y(0) = y(1) = 0. using Rayieigh-Ritz method, mapped over entire domain using one parameter method.

Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 12M

Year: Dec 2015

$y = C_0 + C-1x + C-2 x^2$

$y(0) = 0 \hspace{2cm} \therefore 0 = C_0 + 0 + 0\\ \hspace{2.5cm} \therefore C_0 = 0\\ \hspace{2cm} y = C_1x + C_2 x^2$

$y(1) = 0 \hspace{1.5cm} \therefore 0 = C_1 + C_2\\ \hspace{2.5cm} C_1 = - C_2\\ \hspace{1cm} \therefore y …