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FEM
BIG
PICTURE
:
MATLAB
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MATRIKS
KEKAKUAN
DI
MATLAB• Menentukan koordinat tiap NODE
• Menuliskan persamaan di tiap elemen matriks stiffness
• Mengambil ELEMEN dari matriks
– Satu elemen
– Beberapa elemen
• Membuat FUNCTION planetrusselement.m
• PlaneTrussElement: fungsi matriks kekakuan untuk
beam element
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Example 1‐1
TrussElementEx.m
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Assembly
Matrix
• TrussElementEx: Hanya Satu elemen
• TrussAssemblyEx: Assembly elemen satu per satu
• FiveBarTrussAssembly: Assembly menggunakan
for
• Assembly menggunakan for untuk soal nomer 1.7
dan 1.8
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SOAL
LATIHAN
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NRP akhir GasalNRP akhir Genap
Susunlah Matriks Kekakuan per Elemen
menggunakan Program MATLAB
A
=
500
mm2
E = 210 GPa
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Soal
Nomer
1.7
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Soal
Nomer
1.8
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Menyelesaikan
matriks• Memasukkan boundary conditions
• Menyederhanakan matriks gabungan
• Membuat function nodalsoln.m
• Mendapatkan gaya reaksi
• Mendapatkan stress
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Boundary
Conditions
• Dalam kasus yang praktis, PDE memiliki
boundary conditions.
• Boundary conditions dibagi menjadi 2 macam:
Essential dan
Natural
• Secara umum, natural boundary conditions
susah untuk dipenuhi oleh metode numerik.
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Mengatur ulang persamaan
Boundary Conditions T1 = 5, T4 = ‐7, T5 = 0
The Global Stiffness Matrix in this stage is Singular Matrix
Det(K) = 0
Memasukkan boundary conditions supaya didapat matriks yang bisa
diselesaikan
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Mengatur ulang persamaan
Boundary Conditions T1 = 5, T4 = ‐7, T5 = 0
1. Hapus Persamaan 1, 4, dan 5
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Mengatur ulang persamaan
2.
Tambahkan
perkalian
stiffness
matrix
dengan
boundary
conditions ke sisi kanan
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3. Selesaikan dengan pembagian matriks
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Function nodalsoln.m
untuk merekayasa
boundary
conditions
function [d, rf] = NodalSoln(K, R, debc, ebcVals)
% [nd, rf] = NodalSoln(K, R, debc, ebcVals)
% Computes nodal solution and reactions
% K = global coefficient matrix
% R = global right hand side vector
% debc = list of degrees of freedom with specified values
% ebcVals
= specified
values
dof = length(R);
df = setdiff(1:dof, debc);
Kf = K(df, df);
Rf = R(df) ‐ K(df, debc)*ebcVals;
dfVals = Kf\Rf;
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REAKSI
DAN
STRESS
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Menghitung
Reaksi
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STRESS
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