How can I fix "Error in sym/subsref (line 898) R_tilde = builtin('s​ubsref',L_​tilde,Idx)​; ?

Error is also stated as being in line 43;

Error in Assignment2CodeQuadratic2 (line 43)

KgQ(indiciesQ,indiciesQ) = KgQ(indiciesQ,indiciesQ) + subs(KeQ,[x1Q x2Q x3Q], [xQ(i*2-1)

xQ(i*2) xQ(i*2+1)]); % Ke into Kg contribution

% ENME302-22S2, 21 Sep 2022, linear finite elements demonstration

% Derives the element equations using linear shape functions.

clear;close all;clc;

% % Quadratic shape element:
syms xQ x1Q x2Q x3Q u1Q u2Q u3Q a b c
W = 0.01; % Width [m]
tau0 = 1; % Initial Stiffness [Pa]
tau = (1+0.9*sin((sqrt(2)*pi*xQ)/W))*tau0; % Stiffness Equation
f = 100; % Force Density (N/m^3)
uQ = a*xQ^2 + b*xQ + c; % interpolation function (quadratic here) from Equation 8.16
eqn1Q = subs(uQ,xQ,x1Q) == u1Q; % evaluating at left node, Equation 8.18a
eqn2Q = subs(uQ,xQ,x2Q) == u2Q; % evaluating at left node, Equation 8.18b
eqn3Q = subs(uQ,xQ,x3Q) == u3Q; % evaluating at left node, Equation 8.18c
consQ = solve([eqn1Q eqn2Q eqn3Q], [a b c]); % solve simultaneous equations for constants a, b and c, Equation 8.19
uQ = subs(uQ,[a b c],[consQ.a consQ.b consQ.c]); % substitute/plug into interpolation function, Equation 8.20a
[NQ,~] = coeffs(uQ, [u1Q u2Q u3Q]); % collect coefficients for defining shape functions, Equation 8.20b
N1Q=NQ(1); % N1 = 2*xi^2 - 3*xi + 1;
N2Q=NQ(2); % N2 = -4*xi^2 + 4*xi;
N3Q=NQ(3); % N3 = 2*xi^2 - xi;

% Element equations, Ke*Te=Fe (symbolic):
KeQ = sym(zeros(3)); % element stiffness matrix
FeQ = sym(zeros(3,1)); % element rhs forcing vector
for i = 1:3 % 3 dof for quadratic elements
    eleqQ = int(tau*diff(uQ,xQ)*diff(NQ(i),xQ),xQ,x1Q,x3Q) - int(f*NQ(i),xQ,x1Q,x3Q);
    [coefQ,~] = coeffs(eleqQ, [u1Q u2Q u3Q]); % collect coefficients
    KeQ(i,:) = coefQ(1:3); % coefficients of u1 and u2 and u3
    FeQ(i) = -coefQ(4); % remaining terms (not a coefficient of u1, u2 or u3 )
end

for kk = 2:4:22
    % Global equations, Kg*Tg=Fg (numeric):
    L = W; % length (mm)
    noe = kk; % number of elements
    dof = noe+1; % number of degrees of freedom
    x = linspace(0,L,dof); % x-coordinates of dof
    KgQ = sym(zeros(dof)); % global stiffness matrix
    FgQ = sym(zeros(dof,1)); % global rhs forcing vector
    
    for i=1:noe % assemble each set of element equations
        indiciesQ = i*2-1:i*2+1; 
        KgQ(indiciesQ,indiciesQ) = KgQ(indiciesQ,indiciesQ) + subs(KeQ,[x1Q x2Q x3Q], [xQ(i*2-1) xQ(i*2) xQ(i*2+1)]); % Ke into Kg contribution
        FgQ(indiciesQ) = FgQ(indiciesQ) + subs(FeQ,[x1Q x2Q x3Q], [xQ(i*2-1) xQ(i*2) xQ(i*2+1)]); % Fe into Fg contribution
    end
    
    % Final equations with boundary conditions, K*Tbc=F (numeric):
    Ta = 0; % Dirichlet boundary condition on lhs
    FgQ(1) = FgQ(1) - KgQ(1,1)*Ta;
    KgQ(1,1) = 1;
    FgQ(2) = FgQ(2) - KgQ(2,1)*Ta;
    KgQ(2,1) = 0;
    KgQ(3,1) = 0;
    Tb = 0; % Dirichlet boundary condition on rhs
    FgQ(dof) = FgQ(dof) - KgQ(dof,dof)*Tb;
    KgQ(dof,dof) = -1;
    FgQ(dof-1) = FgQ(dof-1) - KgQ(dof-1,dof)*Tb;
    KgQ(dof-1,dof) = 0;
    KgQ(dof-2,dof) = 0;
    
    KgQ = double(KgQ);
    FgQ = double(FgQ);
    
    % Solve and plot solution:
    TbcQ = KgQ\FgQ; % unknown variables, in this case, we have calculated dT/dx|x1 and -dT/dx|x5
    TgQ = [Ta;TbcQ(2:dof-1);Tb]; % global vector of displacement values, i.e. replaced for our Dirichlet b.c.s
    
    %Finding Displacement at Middle for each number of elements
    loc = find(x==0.005);
    displacement(kk) = Tg(loc)*10^3;
end

Index exceeds the number of array elements. Index must not exceed 1.

Error in indexing (line 1079)
R_tilde = builtin('subsref',L_tilde,Idx);

%Displacement Array
centreDisplacement = displacement(2:4:22) % Removes Zeros from Array

%Relative Error
relError(kk) = abs((centreDisplacement(end)-centreDisplacement(kk))/centreDisplacement(kk))*100; 


plot(x*10^3,Tg,'k.-'); xlabel('x (mm)'); ylabel('Deflection (m)');
title("Linear Shape Function Displacement")
legend("Linear");

Answer 1

[Torsten]

KgQ(indiciesQ,indiciesQ) = KgQ(indiciesQ,indiciesQ) + subs(KeQ,[x1Q x2Q x3Q], [xQ(i*2-1) xQ(i*2) xQ(i*2+1)]); % Ke into Kg contribution
FgQ(indiciesQ) = FgQ(indiciesQ) + subs(FeQ,[x1Q x2Q x3Q], [xQ(i*2-1) xQ(i*2) xQ(i*2+1)]); % Fe into Fg contribution
 

xQ is a symbolic scalar variable. But you address array elements of xQ (xQ(i*2-1) xQ(i*2) xQ(i*2+1)) which do not exist.

[Matt Boyles]

Sorry the line x = linspace(0,L,dof) is meant to be xQ = linspace(0,L,dof) which creates an array of (0 0.5 1), but then this error still occurs

[Torsten]

Then you assume that xQ has dimension at least 2*noe+1 because i runs from 1 to noe. But xQ = linspace(0,L,dof) generates an array with only noe+1 elements.

And if you define xQ = linspace(0,L,dof), you should rename xQ in the list of symbolic variables.

[Matt Boyles]

Right got it, cheers for that appreciate it!!

Answer 2

[Star Strider]

Perhaps —

syms xQ
xQ = sym('xQ',[1 3])

xQ = 

xQ2 = xQ(2)

xQ2 = 

See the documentation on sym for details.