Getting error while solving PDE

I am trying to solve this equation for thermal stress analysis.

The greens functions are as follows:

I have written the following code. But I am getting a error. How to resolve the issue? If the approacj is wrong, how to go about solving it?

function u = thermal_stress(T)


% Initialize the variables
a = 
1e-5;   % thermal expansion coefficient
E = 
200e9;   % Young's modulus
v = 
0.3;     % Poisson's ratio
p = 
1;        % load


% Discretize the domain
x = 
linspace(0, 1, 100);
z = 
linspace(0, 1, 100);
[X, Z] = 
meshgrid(x, z);


% Create the mesh
mesh = pde.Mesh(X, Z);


% Define the boundary conditions
bc = pde.DirichletBC(mesh, 
0, 'x');
bc = [bc; pde.DirichletBC(mesh, 
0, 'z')];


% Define the Green's function
G(x, z) = Zp / (
2(1 - v')^2) * (1 / (x + 2) + 1 / (z + 2));


% Define the temperature equation
T = (
0.1/sqrt(x^2+z^2))*(exp(-0.1*((sqrt(x^2 + z^2)+x)/2*3.75*10^(-6)))


% Define the PDE
eqn = a*E*(
1-2*v)*T*pde.Laplacian(u) - a*E*(1-2*v)*T;


% Solve the equation
u = pde.solve(eqn, bc, mesh);

end

Answer 1

[Karan Singh]

Hey AD, I had a look through your code and found that the functions that you have been using currently has no MATLAB documentation and would have previously belonged to R2022b, not to the one I am using R2023a. However here a demo code I can provide to get you started on PDE.

% Define the PDE problem

% Step 1: Define the PDE coefficients, boundary conditions, and initial conditions
% Create a PDE model
model = createpde();

% Step 2: Specify the geometry
% Use either geometryFromEdges or geometryFromMesh to define the geometry

% Step 3: Specify the boundary conditions
% Use applyBoundaryCondition to specify the boundary conditions

% Step 4: Specify the PDE coefficients and source term
% Use specifyCoefficients to specify the PDE coefficients and source term

% Step 5: Solve the PDE
result = solvepde(model);

% Step 6: Extract and analyze the solution
% Extract the solution using the result.Mesh and result.NodalSolution properties
% Analyze the solution as needed (e.g., plot, compute derived quantities)
% Example: Plot the solution
pdeplot(model, 'XYData', result.NodalSolution);

You may need to refer to the PDE Toolbox documentation and examples for more detailed information and specific usage of functions mentioned above.