Use or Pi and raising matrix to a Power

Hello

I have written the below scrip to investigate beam theory calculations for set dimensions of a beam. I keep the getting the follownig error message:

Error using ^ (line 51)

Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and

the power is a scalar. To perform elementwise matrix powers, use '.^'.

Error in Partial_UDL_Clarity_Version (line 26)

I1 = (pi)*r1^4/4; % [m^4] second moment of area

I am trying to add and upper and lower limit to the beam dimensions (length and radius) in order to then plot this variability as seperate lines. ideally i would then shade between these extremes with the mid point line going through the middle.

I have found this code for trying to shade between these two lines:

%This fills the area between the lower and upper bounds with one of the
%colours from the start. An example is shown below
 
%x'line1''line2' = [Delta'line1', fliplr(Delta'line2')];
%inBetween'line1''line2' = [F, fliplr(F)];
%'line1''line2' = fill(x'line1''line2', inBetween'line1''line2', Colour'x');
 
xef = [Deltae, fliplr(Deltaf)];
inBetweenef = [F, fliplr(F)];
ef = fill(xef, inBetweenef,Colour5);

Any help would be greatly appreciated.

Thanks in advance.

The Full script/Code is here:

%Created Friday 13th 2020 Robert Staruch Beam Deflection Partial UDL
%-------------------------------------------------------------------
 
 
%This code is to Calculate Deflection of a beam of Partial loading over a
%set length. 
%REMEMBER in this situation H1 is the greater height, and H2 is the lower
%height. 
%REMEMBER that the tip deflection value will be the difference between the
%TOTAL BEAM LENGTH, and the respective UDL heights. So for H1 that will be
%Total Length - H1, and for H2 that is Total Length - H2. In most of these
%cases we are using a 12mm beam, so it is 12-H1, 12-H2. V Important.
 
%The parameters are
 
r1 = 0.0007500: 0.0000025: 0.0007525                % [m]  radius of bar
P1 = 0.0001:0.0001:0.001;    % [N] load applied on the beam
l1 = 0.012: 0.00025: 0.01225                  % [m] length of beam
H1 = 0.010: 0.00025: 0.01025                  % Upper height of partial load
H2 = 0.00800;                  % Lower height of Partial Load
D1 = 0.00200;                  % Length of Partial load. Should be difference between H1&H2.
D2 = 0.00400;                  % Difference between L1 and H2.
E1 = 2.26e6;                 % [Pa] youngs modulas in Pa PDMS
E2 = 4.446e6;                % [Pa] youngs modulas in Pa Elastic
E3 = 10.5e6;                 % [Pa] youngs modulas in Pa Flexible         
I1 = pi*r1^4/4;               % [m^4] second moment of area
w1 = P1/D1;             % [N/m] uniformally distributed load (note w=0 for no loading);
 
%Now Calculate The Deflection at Height 1:
 
Delta_UDL_Height_PDMS_1 = [w1*H1^4/(8*E1*I1)]
 
Delta_UDL_Height_Elastic_1 = [w1*H1^4/(8*E2*I1)]
 
Delta_UDL_Height_Flexible_1 = [w1*H1^4/(8*E3*I1)]
 
%Now Calculate the Tip Deflection for Height 1:
 
Delta_tip_length_PDMS_1 = [w1*l1^3/(6*E1*I1)]*(D1)
 
Delta_tip_length_Elastic_1 = [w1*l1^3/(6*E2*I1)]*(D1)
 
Delta_tip_length_Flexible_1 = [w1*l1^3/(6*E3*I1)]*(D1)
 
%Add these values together:
 
Delta_Total_PDMS_H1 = Delta_UDL_Height_PDMS_1 + Delta_tip_length_PDMS_1;
 
Delta_Total_Elastic_H1 = Delta_UDL_Height_Elastic_1 + Delta_tip_length_Elastic_1;
 
Delta_Total_Flexible_H1 = Delta_UDL_Height_Flexible_1 + Delta_tip_length_Flexible_1;
 
%Now Calculate the Deflection at Height 2:
 
delta_UDL_Height_PDMS_2       = [w1*H2^4/(8*E1*I1)]
 
delta_UDL_Height_Elastic_2       = [w1*H2^4/(8*E2*I1)]
 
delta_UDL_Height_Flexible_2       = [w1*H2^4/(8*E3*I1)]
 
%Now Calculate the Tip Deflection for Height 2:
 
Delta_tip_length_PDMS_2 = [w1*l1^3/(6*E1*I1)]*(D2)
 
Delta_tip_length_Elastic_2 = [w1*l1^3/(6*E2*I1)]*(D2)
 
Delta_tip_length_Flexible_2 = [w1*l1^3/(6*E3*I1)]*(D2)
 
%Add these values tegether:
 
Delta_Total_H2_PDMS = delta_UDL_Height_PDMS_2+Delta_tip_length_PDMS_2
 
Delta_Total_H2_Elastic = delta_UDL_Height_Elastic_2+Delta_tip_length_Elastic_2
 
Delta_Total_H2_Flexible = delta_UDL_Height_Flexible_2+Delta_tip_length_Flexible_2
 
%Now Calculate the Total Deflection by Subtracting H2 from H1
 
Delta_Total_PDMS =  Delta_Total_PDMS_H1 - Delta_Total_H2_PDMS
 
Delta_Total_Elastic =  Delta_Total_Elastic_H1 - Delta_Total_H2_Elastic
 
Delta_Total_Flexible = Delta_Total_Flexible_H1 - Delta_Total_H2_Flexible
 
%Now Plot this data to a graph
 
%Finally I plot this data on a graph.
figure
hold on
plot(Delta_Total_PDMS)
plot(Delta_Total_Elastic)
plot(Delta_Total_Flexible)
legend('Flexible','Elastic','PDMS')
xlabel('Force in Newtons 0.00001<0.001')
ylabel('Deflection in metres')

[Rik]

This time I edited your question for you. Next time, please use the tools explained on this page to make your question more readable.

[Robert Staruch]

Thanks & Apologies. Extremely Novice user here - so thanks for highlighting that. WBW

Answer 1

[John D'Errico]

MATLAB tells you exactly what is wrong, and how to fix it. (This has nothing to do with your use of pi.)

Error using ^ (line 51)

Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and

the power is a scalar. To perform elementwise matrix powers, use '.^'.

Error in Partial_UDL_Clarity_Version (line 26)

I1 = (pi)*r1^4/4; % [m^4] second moment of area

The point is, MATLAB cannot perform element-wise squaring on a matrix using the ^ operator. For example, if you wish to square the elements of a vector then use .^ as the operator. See the difference here:

x = 1:3;
x.^2

ans = 1×3

1 4 9

●

x^2

Error using ^ (line 51)
Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers, use '.^'.