Construct the element matrix numerically using the 2, Other Engineering

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1. The cantilever beam-like structure shown below is modeled using a 2 x 10 mesh of
rectangular four-node plane stress elements of equal size. Geometric boundary conditions
at x ? 0 are as follows: The horizontal displacement is zero while the vertical
displacement is zero only at y ? 0. Do the following and compare with the beam theory
solution.
(a) Construct the element matrix numerically using the 2x2 point rule.
(b) Construct the element load vectors and global load vectors.
(b) Plot vertical displacement along the y ? 0 line.
(c) Plot stress values at the element centroids.
p A lb in
L
? ? where A is a given constant value.
7 E ?10 psi, ? ? 0.3
L ?10 in, h ?1.0 in , Width (in the z direction) ? 0.4 in
2. The structure shown Problem 1 is subject to the temperature change given
as?T ? By where B is a given constant value. There is no applied surface load.
(a) Print out the global load vector due to the temperature change.
(b) Plot vertical displacement along the y ? 0 line.
(c) Plot stress values at the element centroids.
3. Repeat the problem 2 with an additional constraint given as follows:
Vertical displacement is zero at x ? L, y ? 0.

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