(Szilard’s book “Theories and Applications of Plate Analysis”) is
presented below. Consider that the plate has the dimension of 1.5m
x 1.5m, the central hole size is 0.5mx0.5m, thickness of 2 mm and
is made of steel (E=210 GPa and v=0.29). Create a mesh formed of 8
linear quadrilateral elements. Apply a point downward load on the
edges of the hole of the plate having the magnitude of F=1N per
node. Assume that
a) All edges are simply supported
b) Right edge is clamped and all other edges are free
- Consider A Plate Whose Nonconformal Element Stiffness Matrix Szilard S Book Theories And Applications Of Plate Analy 1 (5.25 KiB) Viewed 35 times
displacements and
rotations by modifying the Matlab code given as attachment. Compare
your
results by the solutions of a commercial code (e.g., Abaqus, Ansys
etc.). Note
that the difference between your solution and the solution of the
commercial
code is due to the element type (Mindlin plate and conformal
element).
Question: What are the boundary conditions at the corners ? Are
they create
any problem ? Why or why not ?
Question: How could you calculate the strains ?
Hint: Use below given definitions of strain components Szilard p.29
and then
use Eq.(7.6.2.) on p. 407 and to find α coefficients use
Eqs.(7.6.8) to (7.6.11)
- Consider A Plate Whose Nonconformal Element Stiffness Matrix Szilard S Book Theories And Applications Of Plate Analy 2 (12.75 KiB) Viewed 35 times
generalized Hooke’s law)
There is a claim that the most accurate points for the strain and
stress are Gauss
integration points. There is a claim that the most accurate points
for the
displacements are nodes. If you compare your solutions with the
those of
commercial program, what can you say ?
- Consider A Plate Whose Nonconformal Element Stiffness Matrix Szilard S Book Theories And Applications Of Plate Analy 3 (102.63 KiB) Viewed 35 times
- Consider A Plate Whose Nonconformal Element Stiffness Matrix Szilard S Book Theories And Applications Of Plate Analy 4 (75.31 KiB) Viewed 35 times
- Consider A Plate Whose Nonconformal Element Stiffness Matrix Szilard S Book Theories And Applications Of Plate Analy 5 (27.44 KiB) Viewed 35 times
Simple Plate Elements 407 X 5 yi Zw N 6 10 12 y4 00 8 Figure 7.6.1 Rectangular element with four corner nodes. from the complete fourth-order polynomial to be able determine the 12 parameters a; in the shape function w(x, y) = a1 + a2x +azy + apr? +Q5xy +Q6y2 +Q7x + agr’y + agxy? +10y +Quixºy +Q12xy = w'a (7.6.2)
To determine the unknown parameters a; in Eq. (7.6.2), we substitute the nodal point coordinates x; and y; into Eqs. (7.6.2), (7.6.6) and (7.6.7). Thus, we can write WO 00 8,0 w 80 , 3) 0. 0, de a 02 03 04 095 06 07 ds 09 010 Q11 = =A (7.6.8) WO 0.0 0, 12
Since de = Aa and a=Ald (7.6.10) the shape function can be obtained from w(x, y) = w'a=w"A-'de = {N}'de. = (7.6.11)