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## Drawing Shape Function of Quadratic element (1D) or Beam element

version 1.0.0.0 (1.43 KB) by Mohamed Sajeer Ibn Azad Modavan

### Mohamed Sajeer Ibn Azad Modavan (view profile)

This code may help you to draw the shape function in Finite Element Analysis

Updated 01 Dec 2015

% This code can use for ploting shape function of
% Quadratic Element (One Dimensional Problem)
% Beam element
clc; clear all; close all
x_e = 0;
h_e = 1;
Phi_0 = zeros(10,1);
Phi_1 = zeros(10,1);
Phi_2 = zeros(10,1);
Phi_3 = zeros(10,1);
Phi_4 = zeros(10,1);

Case = input('Type 1 for Quadratic Element (1D), Type 2 for Beam Element ');
n = 0;
if Case == 1
for x = 0:.1:1
n = n+1;

phi_1 = (1-(x)/h_e)*(1-(2*x)/h_e);
phi_2 = 4*(x)/h_e*(1-(x)/h_e);
phi_3 = -(x)/h_e*(1-(2*x)/h_e);

Phi_0(:,n) = 0; % This Draws axis line
Phi_1(:,n) = phi_1;
Phi_2(:,n) = phi_2;
Phi_3(:,n) = phi_3;
end

plot (0:.1:1,Phi_1','c')
hold on
plot (0:.1:1,Phi_2','g')
plot (0:.1:1,Phi_3','r')
plot (0:.1:1,Phi_0','k')

else
% Beam element
for x = 0:.1:1
n = n+1;

phi_1 = 1-3*((x-x_e)/h_e).^2+2*((x-x_e)/h_e).^3;
phi_2 = -(x-x_e)*(1-((x-x_e)/h_e)).^2;
phi_3 = 3*((x-x_e)/h_e).^2-2*((x-x_e)/h_e).^3;
phi_4 = -(x-x_e)*(((x-x_e)/h_e).^2-((x-x_e)/h_e));

Phi_0(:,n) = 0; % This Draws axis line
Phi_1(:,n) = phi_1;
Phi_2(:,n) = phi_2;
Phi_3(:,n) = phi_3;
Phi_4(:,n) = phi_4;
end

plot (0:.1:1,Phi_1','c')
hold on
plot (0:.1:1,Phi_2','g')
plot (0:.1:1,Phi_3','r')
plot (0:.1:1,Phi_4','b')
plot (0:.1:1,Phi_0','k') % This Draws axis line
end

### Cite As

Mohamed Sajeer Ibn Azad Modavan (2020). Drawing Shape Function of Quadratic element (1D) or Beam element (https://www.mathworks.com/matlabcentral/fileexchange/54253-drawing-shape-function-of-quadratic-element-1d-or-beam-element), MATLAB Central File Exchange. Retrieved .