image thumbnail

FEM 2D Truss Problem

version 1.0.0.0 (1.74 KB) by Sajeer Modavan
This code may help you to find the displacement and reactions in each element.

543 Downloads

Updated 01 Dec 2015

View License

% MATLAB Code for 2D Truss to find displacement and reactions using FEM
% =====================================================================
clear;
clc;

% Example: 2
% ===========
ND = [1 2 3 4 5]; % Node Number
NE = [1 2 3 4 5 6 7]; % Element Number
NC = [1 2;2 3;3 4;4 5;1 4;2 5;2 4]; % Node Connectivity
EL = [1 1 sqrt(2) 1 sqrt(2) sqrt(2) 1]; % Member Length (m)
alf = [0 0 3*pi/4 pi pi/4 3*pi/4 pi/2]; % Member Angle
E = 2.1E11; % Youngs Modulus (N/m2)
A = pi*(12.5/1000)^2/4; % Crossectional Ares (m2)
BC = [1 2 4 9 10]; % Boundary Condition
F_val = [0 200 -100 0 -100]; % Applied Load (kN)

n_D = length(ND);
n_E = length(NE);
dof = n_D*2;
dof_n = [(2.*ND-1)' (2.*ND)'];
KG = zeros(dof,dof);

for ii = 1:n_E
n1 = NC(ii,1);
n2 = NC(ii,2);
loc = [dof_n(n1,:) dof_n(n2,:)];
nj = length(loc);
c = cos(alf(ii));
s = sin(alf(ii));
T = [c s 0 0;-s c 0 0;0 0 c s;0 0 -s c];
ke = (E*A/EL(ii)).*[1 0 -1 0;0 0 0 0;-1 0 1 0;0 0 0 0];
Ke = T'*ke*T;
for jj = 1:nj
l1 = loc(jj);
for kk = 1:nj
l2 = loc(kk);
KG(l1,l2) = KG(l1,l2)+Ke(jj,kk);
end
end
end

K_temp = KG;
for jj = 1:length(BC)
K_temp(:,BC(jj)) = 0;
K_temp(BC(jj),:) = 0;
end
K_temp(~any(K_temp,2),:) = [];
K_temp(:,~any(K_temp,1)) = [];
KR = K_temp;

FR = F_val';
UR = KR\(FR.*1000);
UR = UR.*1000;
UG = [0 0 UR(1) 0 UR(2) UR(3) UR(4) UR(5) 0 0]';
Rc = (KG*(UG/1000))/1000;
disp('Displacement in mm')
disp(UR)
disp('Reaction in kN')
disp(Rc)

Cite As

Sajeer Modavan (2022). FEM 2D Truss Problem (https://www.mathworks.com/matlabcentral/fileexchange/54258-fem-2d-truss-problem), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2007b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Tags Add Tags
Acknowledgements

Inspired: create simple GUI

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!