I$=$

A$.$ASSIGNMENT $2/$ WERKSOPDRAG $2$

Due: $06$ May $2024$ at $136(6)$

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

tion as a cautilever bera bouded with its self$-$weight is to

be analysed. 'The strip has the following properties: Die

$E,v,A,1,N$

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

Ealer$-$Bernoulli theory, Show all calculations and explain

all symbels used.

An inexperienced analyst propoeses to thst the finite element

method ueing a mesh with ouly $3$ rectangular elements:

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

down the IEN array for the mesh.

$2\mathrm{.}2)$ Write in Mathan $/$ Python script to compute the

following:

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

with $22=4$ integration points.

b$)$ The global stiffpews matrix

e$)$ The horizontal and vertical deflection at all nocies.

$2\mathrm{.}3)$ Compare your tip deffection 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?

deflekste van $\text{'}$in loodstrook met reghoekage deursnee an $\text{'}$I

vrylcraghalk wat met sy eie pewig gelaai word, moet outleed

word. Die strook het die volgende eimakappe

$1\mathrm{.}1)$ Bepoual die punt$-$defleksie van die balk deur Euler$-$

Bermoulli teorie nan te neem. Toon alle berelorninge en

verduidelik alle simbole wat yebruik werd.

$\text{'}$n Onervare anulis stel voot otn die eindlige$-$elementmetode

te gebruik deur $\text{'}$n mas met slems $3$ reghoelige elemente te:

sebrulk

Instrietians:

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Eurat will he acrepied.

Source onde anay unt be shared amang groupe.

Each group should haud in a ueatly typed oue$-$page teport to$-$

gether with a clear printout of their somrer code $($PDF$-$format$).$

Lnstrulales:

Stuilente most in hal aumerwyske groepe werh.

Alle berelarsinge moet in Meriail of frotion gobloen wurl.

sal aanvaar waxil nive.

Eller sroep moet $\text{'}$n bet jies getikte orin bluby verslay waum mut $"$n

uitdrak lenper van hul hronkode $($PDF$-$formast$)$ inhandig

Add to noteThe deflection of a lead strip with rectangular cross sec$-$

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

be analysed. The strip has the following properties: Die

$1\mathrm{.}1)$ 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?