Problem $3.($verso$)$

Objective. To determine displacements and stresses in a plate, loaded $($strained$)$ in its own plane, using constant strain triangle $($CST$)$ finite elements. To observe areas of high stress gradient and to determine stress concentration factors $($if applicable$).$

Notes. Take advantage of symmetry in the shape and loading $($if applicable$),$ which allows you to consider only a part of the member. Select a finite element mesh such that the number of nodes is not less than $50$ and not greater than $200.$ Locate larger elements in regions of relatively uniform stress and small elements in the regions of high stress gradient. Obtain a grid similar to a "spider web".

Warning. Elements should have good aspect ratios $($maximum $3$ or $4),$ as near equilateral as possible. Elements node numbers must be given anticlockwise. Use consistent units.

Tasks. $1.$ Draw the FE mesh on a graph paper $($or print it using a line printer$),$ together with node and element numbering.

$2.$ Tabulate the input data in a form suitable for direct input to the data file.

$3.$ Plot the stress values at the centroid of elements and draw smoothed curves for the spatial variation of ${}_x,{}_y$ and ${}_{xy}$ along the line $BC.$

$4.$ Determine the distribution of ${}_{\text{e}\text{q}\text{v}}$ along the boundary of the areas of high stress gradient.

$5.$ Determine the magnitude of the maximum equivalent stress and its location.

$6.$ Determine the stress concentration factor for the stress raiser.