I want to get 2*V^2 from the operation below
syms A V
rem(2*V^2+3A,A)
but it seems like rem() function does not work with symbolic variables. Is there a way to achieve this in another way?I want to get 2*V^2 from the operation below
syms A V
rem(2*V^2+3A,A)
but it seems like rem() function does not work with symbolic variables. Is there a way to achieve this in another way? I want to get 2*V^2 from the operation below
syms A V
rem(2*V^2+3A,A)
but it seems like rem() function does not work with symbolic variables. Is there a way to achieve this in another way? symbolic MATLAB Answers — New Questions

​

Hello and sorry for this long query. I am not very good at this , I have to admit it.
I am encountering an issue when trying to apply custom boundary conditions in a PDE model using MATLAB. Specifically, I have a custom boundary condition function mybc1 that works correctly in another code when using structuralBC to apply displacement conditions to vertices. However, in my current code, when I try to use applyBoundaryCondition to set mixed boundary conditions on specific faces, it seems that the solver does not enter the custom boundary condition function mybc1.
Here’s a brief description of what I am trying to do:
Model Definition: I have defined a PDE model with certain geometry and mesh.
Boundary Condition Application: I attempt to apply mixed boundary conditions on specific faces using applyBoundaryCondition with the u parameter set to a custom function handle @(location, state)mybc1(location, state, dis, ts, in).
Issue: It appears that the solver does not call the mybc1 function during the solution process. I verified this by setting breakpoints inside mybc1, which are never hit.
The mybc1 function interpolates the acceleration data (dis) at the times specified by the solver (state.time) and returns the corresponding values. This function has been tested and works correctly in another program with structuralBC.

code as follows:

%____________Define dimensions of the plate________________________________
len = 1.22; % length in x direction
width = 1.22; % Width in y direction
sq_side = 0.10; % Side length of the squares in corners
% Create the geometry description matrix___________________________________
% —–Define the outer boundary——————————————-
outer_boundary = [3, 4, 0, len, len, 0, 0, 0, width, width]’;
%——Define squares in the corners—————————————
square_1 = [3, 4, 0, sq_side, sq_side, 0, 0, 0, sq_side, sq_side]’;
square_2 = [3, 4, len – sq_side, len, len, len – sq_side, 0, 0, sq_side, sq_side]’;
square_3 = [3, 4, len – sq_side, len, len, len – sq_side, width – sq_side, width – sq_side, width, width]’;
square_4 = [3, 4, 0, sq_side, sq_side, 0, width – sq_side, width – sq_side, width, width]’;
%——Combine all the geometries——————————————
gdm = [outer_boundary, square_1, square_2, square_3, square_4];
%——Define the names for each region————————————
ns = (char(‘R1′,’R2′,’R3′,’R4′,’R5′))’;
sf = ‘R1+R2+R3+R4+R5’;
%——-Create the geometry————————————————
model = createpde(2);
geometryFromEdges(model, decsg(gdm, sf, ns));
%——-Generate the mesh and plot the geometry—————————-
msh = generateMesh(model, ‘Hmax’, 0.1); % Use ‘Hmax’ to control mesh density
figure
pdemesh(model)
%_____________Create the different regions of the model___________________
% Obtain nodes and elements of the mesh
[p,e,t] = meshToPet(model.Mesh);
% ———-Plot with Faces labels—————————————-
figure;
pdegplot(model, ‘FaceLabels’, ‘on’, ‘FaceAlpha’, 0.5);
figure
pdemesh(model, ‘NodeLabels’, ‘on’);
% Definition of the constants
E = 4E9;
h_thick = 0.05;
nu = 0.3;
mass = 100;
D = E*h_thick^3/(12*(1-nu)^2);
% Now we create the PDE systems as symbolic equations_____________________
syms pres
syms u1(x,y,t) u2(x,y,t)
pdeeq = [-laplacian(u1,[x y])+u2; D*laplacian(u2,[x y])+ mass*diff(u1,t,t)-pres];
symcoeffs = pdeCoefficients(pdeeq,[u1,u2],’Symbolic’,true);
c2=symcoeffs.c;
m2=symcoeffs.m;
%——Display the symbolic coefficients———————————–
structfun(@disp,symcoeffs);
symcoeffs=subs(symcoeffs,pres,1);
coeffs=pdeCoefficientsToDouble(symcoeffs);
%——pass these coefficients to the pde model—————————-
specifyCoefficients(model,’m’,coeffs.m,’d’,coeffs.d,’c’,…
coeffs.c,’a’,coeffs.a,’f’,coeffs.f);
% INITIAL CONDITIONS ——————————————————
setInitialConditions(model,[0;0],[0;0]);
%USE THE DATA FROM ASHMOLEAN AS BOUNDARY CONDITIONS————————
%load the vector containing the acceleration values
load(totaldata.mat’, ‘DATA’,…
‘TIME’,’fs’);
ac=DATA;
% ——-Create vector time, not starting in 0
num_samples = size(DATA, 1);
dt = 1 / fs; % interval between measurements
t = (1:num_samples) * dt; % vector of times
% TRANSFORM ACCELERATIONS INTO DISPLACEMENTS_______________________________
acvedi=AccVelDis(962.54,1005.11,992.35,ac,fs,t);
dis=acvedi{3};
t=[0,t]; % I start the time at 0
% Boundary conditions in the faces using the displacement vectors
in=0; %counter variable
Faces=[1,2,3,5]; %Vector with faces numbers
for jk = 1:numel(Faces)
in=in+1;%add 1 in every loop to access the different measurmentes contained in the matrix acceleration
face= Faces(jk);
dis1=dis(:,in);

applyBoundaryCondition(model,"mixed","Face",[face,face],"u",@(location,state)mybc1(location,state,dis1,t),"EquationIndex",1,"q",[0 0],"g",0);
%applyBoundaryCondition(model,"dirichlet","Face",face,"h",[0 0 ; 0 1],"r",bcfunc)
end
in=0;
tim=[t(2) t(3)]; %tim represents the time of interest to solve the pde
res=solvepde(model, tim);
% Access the solution at the nodal locations
sol=res.NodalSolution;

And this is the function that works in another code:

function bcMatrix = mybc1(location,state,acs,ti)
%This function is use to extrapolate the values of acceleration for the
%time instances chosen by the system to do the integration of the system.
%as imput it requires the measurements matrix and the corresponding time
%measurements. As output, it provices the extrapoleted values for the state
%time

T=state.time;
% Check if T is NaN and assign the previous value if true
if isnan(T)
vq = NaN(size(location.x)); %this is what documentation says????
else
ac = acs; %gets the value of the corresponding acceleration
vq = interp1(ti, ac, T); %interpolates it
end
bcMatrix = vq;
end

I would really appreciate any help/guidanceHello and sorry for this long query. I am not very good at this , I have to admit it.
I am encountering an issue when trying to apply custom boundary conditions in a PDE model using MATLAB. Specifically, I have a custom boundary condition function mybc1 that works correctly in another code when using structuralBC to apply displacement conditions to vertices. However, in my current code, when I try to use applyBoundaryCondition to set mixed boundary conditions on specific faces, it seems that the solver does not enter the custom boundary condition function mybc1.
Here’s a brief description of what I am trying to do:
Model Definition: I have defined a PDE model with certain geometry and mesh.
Boundary Condition Application: I attempt to apply mixed boundary conditions on specific faces using applyBoundaryCondition with the u parameter set to a custom function handle @(location, state)mybc1(location, state, dis, ts, in).
Issue: It appears that the solver does not call the mybc1 function during the solution process. I verified this by setting breakpoints inside mybc1, which are never hit.
The mybc1 function interpolates the acceleration data (dis) at the times specified by the solver (state.time) and returns the corresponding values. This function has been tested and works correctly in another program with structuralBC.

code as follows:

%____________Define dimensions of the plate________________________________
len = 1.22; % length in x direction
width = 1.22; % Width in y direction
sq_side = 0.10; % Side length of the squares in corners
% Create the geometry description matrix___________________________________
% —–Define the outer boundary——————————————-
outer_boundary = [3, 4, 0, len, len, 0, 0, 0, width, width]’;
%——Define squares in the corners—————————————
square_1 = [3, 4, 0, sq_side, sq_side, 0, 0, 0, sq_side, sq_side]’;
square_2 = [3, 4, len – sq_side, len, len, len – sq_side, 0, 0, sq_side, sq_side]’;
square_3 = [3, 4, len – sq_side, len, len, len – sq_side, width – sq_side, width – sq_side, width, width]’;
square_4 = [3, 4, 0, sq_side, sq_side, 0, width – sq_side, width – sq_side, width, width]’;
%——Combine all the geometries——————————————
gdm = [outer_boundary, square_1, square_2, square_3, square_4];
%——Define the names for each region————————————
ns = (char(‘R1′,’R2′,’R3′,’R4′,’R5′))’;
sf = ‘R1+R2+R3+R4+R5’;
%——-Create the geometry————————————————
model = createpde(2);
geometryFromEdges(model, decsg(gdm, sf, ns));
%——-Generate the mesh and plot the geometry—————————-
msh = generateMesh(model, ‘Hmax’, 0.1); % Use ‘Hmax’ to control mesh density
figure
pdemesh(model)
%_____________Create the different regions of the model___________________
% Obtain nodes and elements of the mesh
[p,e,t] = meshToPet(model.Mesh);
% ———-Plot with Faces labels—————————————-
figure;
pdegplot(model, ‘FaceLabels’, ‘on’, ‘FaceAlpha’, 0.5);
figure
pdemesh(model, ‘NodeLabels’, ‘on’);
% Definition of the constants
E = 4E9;
h_thick = 0.05;
nu = 0.3;
mass = 100;
D = E*h_thick^3/(12*(1-nu)^2);
% Now we create the PDE systems as symbolic equations_____________________
syms pres
syms u1(x,y,t) u2(x,y,t)
pdeeq = [-laplacian(u1,[x y])+u2; D*laplacian(u2,[x y])+ mass*diff(u1,t,t)-pres];
symcoeffs = pdeCoefficients(pdeeq,[u1,u2],’Symbolic’,true);
c2=symcoeffs.c;
m2=symcoeffs.m;
%——Display the symbolic coefficients———————————–
structfun(@disp,symcoeffs);
symcoeffs=subs(symcoeffs,pres,1);
coeffs=pdeCoefficientsToDouble(symcoeffs);
%——pass these coefficients to the pde model—————————-
specifyCoefficients(model,’m’,coeffs.m,’d’,coeffs.d,’c’,…
coeffs.c,’a’,coeffs.a,’f’,coeffs.f);
% INITIAL CONDITIONS ——————————————————
setInitialConditions(model,[0;0],[0;0]);
%USE THE DATA FROM ASHMOLEAN AS BOUNDARY CONDITIONS————————
%load the vector containing the acceleration values
load(totaldata.mat’, ‘DATA’,…
‘TIME’,’fs’);
ac=DATA;
% ——-Create vector time, not starting in 0
num_samples = size(DATA, 1);
dt = 1 / fs; % interval between measurements
t = (1:num_samples) * dt; % vector of times
% TRANSFORM ACCELERATIONS INTO DISPLACEMENTS_______________________________
acvedi=AccVelDis(962.54,1005.11,992.35,ac,fs,t);
dis=acvedi{3};
t=[0,t]; % I start the time at 0
% Boundary conditions in the faces using the displacement vectors
in=0; %counter variable
Faces=[1,2,3,5]; %Vector with faces numbers
for jk = 1:numel(Faces)
in=in+1;%add 1 in every loop to access the different measurmentes contained in the matrix acceleration
face= Faces(jk);
dis1=dis(:,in);

applyBoundaryCondition(model,"mixed","Face",[face,face],"u",@(location,state)mybc1(location,state,dis1,t),"EquationIndex",1,"q",[0 0],"g",0);
%applyBoundaryCondition(model,"dirichlet","Face",face,"h",[0 0 ; 0 1],"r",bcfunc)
end
in=0;
tim=[t(2) t(3)]; %tim represents the time of interest to solve the pde
res=solvepde(model, tim);
% Access the solution at the nodal locations
sol=res.NodalSolution;

And this is the function that works in another code:

function bcMatrix = mybc1(location,state,acs,ti)
%This function is use to extrapolate the values of acceleration for the
%time instances chosen by the system to do the integration of the system.
%as imput it requires the measurements matrix and the corresponding time
%measurements. As output, it provices the extrapoleted values for the state
%time

T=state.time;
% Check if T is NaN and assign the previous value if true
if isnan(T)
vq = NaN(size(location.x)); %this is what documentation says????
else
ac = acs; %gets the value of the corresponding acceleration
vq = interp1(ti, ac, T); %interpolates it
end
bcMatrix = vq;
end

I would really appreciate any help/guidance Hello and sorry for this long query. I am not very good at this , I have to admit it.
I am encountering an issue when trying to apply custom boundary conditions in a PDE model using MATLAB. Specifically, I have a custom boundary condition function mybc1 that works correctly in another code when using structuralBC to apply displacement conditions to vertices. However, in my current code, when I try to use applyBoundaryCondition to set mixed boundary conditions on specific faces, it seems that the solver does not enter the custom boundary condition function mybc1.
Here’s a brief description of what I am trying to do:
Model Definition: I have defined a PDE model with certain geometry and mesh.
Boundary Condition Application: I attempt to apply mixed boundary conditions on specific faces using applyBoundaryCondition with the u parameter set to a custom function handle @(location, state)mybc1(location, state, dis, ts, in).
Issue: It appears that the solver does not call the mybc1 function during the solution process. I verified this by setting breakpoints inside mybc1, which are never hit.
The mybc1 function interpolates the acceleration data (dis) at the times specified by the solver (state.time) and returns the corresponding values. This function has been tested and works correctly in another program with structuralBC.

code as follows:

%____________Define dimensions of the plate________________________________
len = 1.22; % length in x direction
width = 1.22; % Width in y direction
sq_side = 0.10; % Side length of the squares in corners
% Create the geometry description matrix___________________________________
% —–Define the outer boundary——————————————-
outer_boundary = [3, 4, 0, len, len, 0, 0, 0, width, width]’;
%——Define squares in the corners—————————————
square_1 = [3, 4, 0, sq_side, sq_side, 0, 0, 0, sq_side, sq_side]’;
square_2 = [3, 4, len – sq_side, len, len, len – sq_side, 0, 0, sq_side, sq_side]’;
square_3 = [3, 4, len – sq_side, len, len, len – sq_side, width – sq_side, width – sq_side, width, width]’;
square_4 = [3, 4, 0, sq_side, sq_side, 0, width – sq_side, width – sq_side, width, width]’;
%——Combine all the geometries——————————————
gdm = [outer_boundary, square_1, square_2, square_3, square_4];
%——Define the names for each region————————————
ns = (char(‘R1′,’R2′,’R3′,’R4′,’R5′))’;
sf = ‘R1+R2+R3+R4+R5’;
%——-Create the geometry————————————————
model = createpde(2);
geometryFromEdges(model, decsg(gdm, sf, ns));
%——-Generate the mesh and plot the geometry—————————-
msh = generateMesh(model, ‘Hmax’, 0.1); % Use ‘Hmax’ to control mesh density
figure
pdemesh(model)
%_____________Create the different regions of the model___________________
% Obtain nodes and elements of the mesh
[p,e,t] = meshToPet(model.Mesh);
% ———-Plot with Faces labels—————————————-
figure;
pdegplot(model, ‘FaceLabels’, ‘on’, ‘FaceAlpha’, 0.5);
figure
pdemesh(model, ‘NodeLabels’, ‘on’);
% Definition of the constants
E = 4E9;
h_thick = 0.05;
nu = 0.3;
mass = 100;
D = E*h_thick^3/(12*(1-nu)^2);
% Now we create the PDE systems as symbolic equations_____________________
syms pres
syms u1(x,y,t) u2(x,y,t)
pdeeq = [-laplacian(u1,[x y])+u2; D*laplacian(u2,[x y])+ mass*diff(u1,t,t)-pres];
symcoeffs = pdeCoefficients(pdeeq,[u1,u2],’Symbolic’,true);
c2=symcoeffs.c;
m2=symcoeffs.m;
%——Display the symbolic coefficients———————————–
structfun(@disp,symcoeffs);
symcoeffs=subs(symcoeffs,pres,1);
coeffs=pdeCoefficientsToDouble(symcoeffs);
%——pass these coefficients to the pde model—————————-
specifyCoefficients(model,’m’,coeffs.m,’d’,coeffs.d,’c’,…
coeffs.c,’a’,coeffs.a,’f’,coeffs.f);
% INITIAL CONDITIONS ——————————————————
setInitialConditions(model,[0;0],[0;0]);
%USE THE DATA FROM ASHMOLEAN AS BOUNDARY CONDITIONS————————
%load the vector containing the acceleration values
load(totaldata.mat’, ‘DATA’,…
‘TIME’,’fs’);
ac=DATA;
% ——-Create vector time, not starting in 0
num_samples = size(DATA, 1);
dt = 1 / fs; % interval between measurements
t = (1:num_samples) * dt; % vector of times
% TRANSFORM ACCELERATIONS INTO DISPLACEMENTS_______________________________
acvedi=AccVelDis(962.54,1005.11,992.35,ac,fs,t);
dis=acvedi{3};
t=[0,t]; % I start the time at 0
% Boundary conditions in the faces using the displacement vectors
in=0; %counter variable
Faces=[1,2,3,5]; %Vector with faces numbers
for jk = 1:numel(Faces)
in=in+1;%add 1 in every loop to access the different measurmentes contained in the matrix acceleration
face= Faces(jk);
dis1=dis(:,in);

applyBoundaryCondition(model,"mixed","Face",[face,face],"u",@(location,state)mybc1(location,state,dis1,t),"EquationIndex",1,"q",[0 0],"g",0);
%applyBoundaryCondition(model,"dirichlet","Face",face,"h",[0 0 ; 0 1],"r",bcfunc)
end
in=0;
tim=[t(2) t(3)]; %tim represents the time of interest to solve the pde
res=solvepde(model, tim);
% Access the solution at the nodal locations
sol=res.NodalSolution;

And this is the function that works in another code:

function bcMatrix = mybc1(location,state,acs,ti)
%This function is use to extrapolate the values of acceleration for the
%time instances chosen by the system to do the integration of the system.
%as imput it requires the measurements matrix and the corresponding time
%measurements. As output, it provices the extrapoleted values for the state
%time

T=state.time;
% Check if T is NaN and assign the previous value if true
if isnan(T)
vq = NaN(size(location.x)); %this is what documentation says????
else
ac = acs; %gets the value of the corresponding acceleration
vq = interp1(ti, ac, T); %interpolates it
end
bcMatrix = vq;
end

I would really appreciate any help/guidance handles, pde, applyboundaryconditions, function, differential equations MATLAB Answers — New Questions

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