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29/09/2015 1 FEM BIG PICTURE : MATLAB

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Page 1: FEM Matlab

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1

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

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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