A CST element has nodal coordinates (10,10) , (70, 35) for nodes 1,2 and 3 respectively. The element is 2 mm thick and is of material with properties E=70 GPA. Poisson's ratio os 0.3. After applying the load to the element the nodal deformation were found to be $u_1=0.01mm, \ \ v_1=-0.04mm \ \ u_2=0.03mm, v_2=0.02mm, \ \ u_3=-0.02m, \ \ u_1=-0.04mm$

Determine the strains $e_x,e_y,e_z$ and corresponding element stresses.

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

Marks: 10M

Year: Dac 2016

$\hspace{1cm} x_1= 10 mm\hspace{1cm} y_1= 10 mm\\ \hspace{1cm} x_2= 70 mm\hspace{1cm} y_2= 35 mm\\ \hspace{1cm} x_3= 75 mm\hspace{1cm} y_1= 25 mm$

$\beta_1=y_2-y_3 = 10\hspace{2.5cm} r_1= x_3-x_2=5\\ \beta_2=y_3-y_1 = 15\hspace{2.5cm} r_2= x_1-x_3=65\\ \beta_1=y_1-y_2 = 25\hspace{2.5cm} r_3= x_2-x_1=60$

$2A=\begin{vmatrix} \ 1 & 10 & 10 \\ \ 1 & 70 & 35 …