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projectreport.lyx
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#LyX 2.2 created this file. For more info see http://www.lyx.org/
\lyxformat 508
\begin_document
\begin_header
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\textclass article
\begin_preamble
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{ME 477 FEA, Fall 2015}
\chead{C. Ça\u{g}r\i{} Özkan}
\rhead{FEM Project}
\rfoot{Yeditepe University}
\cfoot{\thepage}
\lfoot{Mechanical Engineering}
\usepackage{tikz}
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% recommended as of Pgfplots 1.3:
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\begin_body
\begin_layout Title
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FE Analysis of 2D Bridge Structure
\begin_inset Newline newline
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\family typewriter
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me 477 fea project, fall 2015
\end_layout
\begin_layout Author
C.
Çağrı Özkan
\end_layout
\begin_layout Date
05-I-2016
\end_layout
\begin_layout Standard
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status open
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\backslash
pagebreak
\end_layout
\end_inset
\end_layout
\begin_layout Section
Problem and Overview
\end_layout
\begin_layout Standard
I choose the similar problem to example problem which can be found at ME
477 section at unilica[dot]com.
The problem to deal with is how some arched bridge structure behaves under
load which is applied at its peak point by finite element method.
FEAP is used for its FE Analysis.
In finite element truss method will be used.
\end_layout
\begin_layout Standard
The example geometry can be seen in Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:3D-Model"
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.
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3D Model
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LatexCommand label
name "fig:3D-Model"
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\end_inset
\end_layout
\begin_layout Plain Layout
\end_layout
\end_inset
\end_layout
\begin_layout Standard
In these problem given parameters are
\begin_inset Formula $\alpha=72^{o}$
\end_inset
,
\begin_inset Formula $\hat{EOC=}\nicefrac{\alpha}{3}$
\end_inset
and
\begin_inset Formula $R=14m$
\end_inset
.
By knowing those properties the locations of points can be determined easily.
And in case of interest the element lengths can be found from Law of Cosine(Eq.
\begin_inset CommandInset ref
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)
\end_layout
\begin_layout Standard
\begin_inset Formula
\begin{equation}
a^{2}=b^{2}+c^{2}-2\:b\:c\:cos(\alpha)\label{eq:cos}
\end{equation}
\end_inset
\end_layout
\begin_layout Standard
Location points in Cartesian Coordinates are found using Octave.
Finding A and E point locations and |AE| length are demonstrated.
\end_layout
\begin_layout Standard
\begin_inset listings
lstparams "basicstyle={\normalsize\ttfamily},breaklines=true"
inline false
status open
\begin_layout Plain Layout
octave:1> A=[-14*cosd((180-72)/2);14*sind((180-72)/2)]
\end_layout
\begin_layout Plain Layout
A =
\end_layout
\begin_layout Plain Layout
-8.2290
\end_layout
\begin_layout Plain Layout
11.3262
\end_layout
\begin_layout Plain Layout
octave:2> E=[-14*cosd((180-72)/2+24);14*sind((180-72)/2+24)]
\end_layout
\begin_layout Plain Layout
E =
\end_layout
\begin_layout Plain Layout
-2.9108
\end_layout
\begin_layout Plain Layout
13.6941
\end_layout
\begin_layout Plain Layout
octave:3> AE=sqrt((14^2+14^2-2*14*14*cosd(24)))
\end_layout
\begin_layout Plain Layout
AE = 5.8215
\end_layout
\begin_layout Plain Layout
\end_layout
\end_inset
\end_layout
\begin_layout Standard
Structure is simplified as follows due to use the advantages of 2-D analysis.
Figure
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reference "fig:Simplified-Model"
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shows the simplified 2D model.
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Simplified Model
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\begin_layout Standard
As it can be seen from the figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Simplified-Model"
\end_inset
, this design have 5 nodes and 4 elements.
\end_layout
\begin_layout Standard
As a material A36 steel is chosen.
Which has a Young's Modulus (E) 200 10
\begin_inset script superscript
\begin_layout Plain Layout
9
\end_layout
\end_inset
[Pa].
Cross sectional area is chosen to be 0.1 meter-squared and squared profile,
also applied force chosen to be 30kN to demonstrate heavy load on the bridge
\begin_inset Foot
status open
\begin_layout Plain Layout
Maximum truck load is restricted with 27 metric tones by the law in Republic
of Turkey.
\end_layout
\end_inset
.
\end_layout
\begin_layout Standard
Also fixed points which are the beginning and the end of the bridge, will
be used for boundary conditions of the problem.
\end_layout
\begin_layout Standard
But with these force magnitude and material values, displacement values
came out to be enormous.
In this point I crossed with lowering the force or changing the design
dilemma, and I went with changing the design under same material and force
properties to get practical results.
\end_layout
\begin_layout Standard
As a modification 3 nodes and 9 elements are added.
The coordinates of the nodes and the structure can be seen on Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Design-v2"
\end_inset
.
The modified design's nodes, elements and degree of freedoms are shown
in Figure
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reference "fig:nedof"
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.
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Design v2
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\begin_layout Section
Pre-Process
\end_layout
\begin_layout Standard
To solve the problem input file is created in favorite text editor.
Even though odd look of it, it just contains the info about its nodes coordinat
es, elements that are created between these nodes and material properties
of those elements, applied force magnitude and its whereabouts, boundary
conditions and lastly what we hope to get from analysis.
The input file can be seen below.
\end_layout
\begin_layout Standard
\begin_inset listings
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FEAP * * 2-D Bridge Structure
\end_layout
\begin_layout Plain Layout
0 0 0 2 2 2
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
MATErial,1
\end_layout
\begin_layout Plain Layout
TRUSS
\end_layout
\begin_layout Plain Layout
ELAStic ISOTropic 200e9
\end_layout
\begin_layout Plain Layout
CROSs SECTion 0.1
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
COORdinates
\end_layout
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1 0 -8.2 11.3
\end_layout
\begin_layout Plain Layout
2 0 -2.9 13.7
\end_layout
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3 0 0.0 14.0
\end_layout
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4 0 2.9 13.7
\end_layout
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5 0 8.2 11.3
\end_layout
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6 0 -4.1 11.3
\end_layout
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7 0 0.0 11.3
\end_layout
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8 0 4.1 11.3
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
ELEMents
\end_layout
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1 0 1 1 2
\end_layout
\begin_layout Plain Layout
2 0 1 2 3
\end_layout
\begin_layout Plain Layout
3 0 1 3 4
\end_layout
\begin_layout Plain Layout
4 0 1 4 5
\end_layout
\begin_layout Plain Layout
5 0 1 1 6
\end_layout
\begin_layout Plain Layout
6 0 1 6 7
\end_layout
\begin_layout Plain Layout
7 0 1 7 8
\end_layout
\begin_layout Plain Layout
8 0 1 8 5
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9 0 1 6 2
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10 0 1 2 7
\end_layout
\begin_layout Plain Layout
11 0 1 7 3
\end_layout
\begin_layout Plain Layout
12 0 1 3 8
\end_layout
\begin_layout Plain Layout
13 0 1 8 4
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
BOUNdary restraints
\end_layout
\begin_layout Plain Layout
1 0 1 1
\end_layout
\begin_layout Plain Layout
5 0 1 1
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
FORCe
\end_layout
\begin_layout Plain Layout
3 0 0.0 -30000.0
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
END
\end_layout
\begin_layout Plain Layout
TIE
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
BATCH
\end_layout
\begin_layout Plain Layout
TANG,,1
\end_layout
\begin_layout Plain Layout
DISPlacement ALL
\end_layout
\begin_layout Plain Layout
STRESs ALL
\end_layout
\begin_layout Plain Layout
REACtion ALL
\end_layout
\begin_layout Plain Layout
PLOT MESH
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\begin_layout Plain Layout
PLOT LOAD 1,-1
\end_layout
\begin_layout Plain Layout
PLOT CONT 1
\end_layout
\begin_layout Plain Layout
END
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
INTEractive
\end_layout
\begin_layout Plain Layout
STOP
\end_layout
\begin_layout Plain Layout
\end_layout
\end_inset
\end_layout
\begin_layout Standard
According to these input file mesh created by FEAP can be seen on Figure
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.
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pagebreak
\end_layout
\end_inset
\end_layout
\begin_layout Section
\noindent
Post-process & Conclusion
\end_layout
\begin_layout Standard
After the solution is run, output file file and colorized picture for displaceme
nts are created [Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Colorized-Displacement"
\end_inset
].
\begin_inset Separator latexpar
\end_inset