The deflection of a lead strip with rectangular cross sec$-$

tion as a cantilever beam loaded with its self$-$weight is to

be analysed.

$1\mathrm{.}1)$ Determine the tip deflection of the beam assuming

Euler$-$Bernoulli theory. Show all calculations and explain

all symbols used.

An inexperienced analyst proposes to use the finite element

method using a mesh with only $3$ rectangular elements:

$2\mathrm{.}1)$ Using the numbering scheme in the figure above, write

down the IEN array for the mesh.

$2\mathrm{.}2)$ Write a Matlab $/$ Python script to compute the

following:

a$)$ The element stiffness matrix. Use Gauss integration

with $22=4$ integration points.

b$)$ The global stiffness matrix.

c$)$ The horizontal and vertical deflection at all nodes.

$2\mathrm{.}3)$ Compare your tip deflection obtained in Q$2\mathrm{.}2($c$)$ to the

analytical prediction in Q$1\mathrm{.}1.$ Can you propose a reason

why the answers differ?