Assigned 11-21-06 Due 11-30-06

(a) Find the deflection and bending stress at the center of a 10 x 10 x 0.1 inch thick steel plate that is simply supported on all edges and subject to a uniform 3 psi pressure on its upper surface. Use 4 node plate (shell63 in ANSYS) elements to develop an appropriate model of one quadrant of the plate and use 1, 2, 4, ... elements along the quadrant edge to study the convergence characteristics when using the h-method.

In ANSYS first create an area that represents the middle surface of a quadrant of the plate. Use Size controls > Picked Lines to divide the edges into the desired number of elements.

If X & Y axes lie in the plane of the plate, restrain Theta Z for all nodes, ux & uy at the center of the plate and apply the symmetry boundary conditions discussed in class. See ANSYS Tutorial Lesson 6.

As an alternative you can model the whole plate. (Also note that the 8-node shell93 elements are more accurate, but you can see the convergence better if you use the shell63 option.)

Plot the deflection (w) and bending stress (Sx or Sy) at the center of the plate as a function of the number of elements used along a quadrant edge. Compare your deflection results with theoretical value for the displacement at the center of the plate given below.

w = (4.062e-3)*q*(L^4)/D

Where

D = E*(t^3)/(12*(1-nu^2))

q = 3 psi; L = 10 inches; E = 3.e7 psi; t = 0.1 inch; nu = 0.3

(b) Solve this problem again using a solid model. First create a 5 x 5 x 0.1 inch volume representing a quadrant of the plate. Extrude (sweep) a square along an axis. Then mesh with brick elements, apply bc and loads. Compare your results with those found in (a) and with the theoretical deflection value.

Solution times in 3D problems can be significantly decreased by using

Solution (Unabridged Menu) > Fast Sol'n Optn > Solve > Current LS

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