Is it possible to apply load on nodes?

I am using PDE toolbox for Dynamic Analysis. I can only apply Boundary loads on Faces, Edges,... . I was wondering, if it is possible to apply load on nodes after generating mesh

[Ravi Kumar]

Hello Mohammadmahdi,

Please provide some detail on your use case. What is the geometry and why do you want to apply loads on nodes?

It is currently not possible to apply boundary loads on nodes. But knowing your specific use case I might be able to suggest you a workaround.

Regards,

Ravi

[Mohammadmahdi Malakizandi]

Thanks for the comment. Here is my code. I want to simulate a pedestrian bridge. In order to simulate the walking, I want to apply four rows of forces, 20 forces each, presenting four pedestrians. I have already developed functions for each row in a way that when one force ends, the next one starts. But I need to to be able to apply forces on 20*4 positions of the bridge

model = createpde('structural','transient-solid');

gm=multicuboid(10,4,0.3);

model.Geometry = gm;

E = 210E9; nu = 0.3; rho = 8000; structuralProperties(model,'YoungsModulus',E, ... 'PoissonsRatio',nu, ... 'MassDensity',rho);

structuralBC(model,'Face',[1 3],'XDisplacement',0,'YDisplacement',0,'ZDisplacement',0);

generateMesh(model);

 structuralBoundaryLoad(model,'Face',3,'Pressure',10^5,'RiseTime',0.5,'FallTime',0.5,'EndTime',3);
d0=[0,0,0];
v0=[0,0,0];
structuralIC(model,'Displacement',d0,'Velocity',v0);

tlist=0:t_max; structuralResults=solve(model,tlist);

stress = evaluateStress(structuralResults);

figure pdeplot3D(model,'ColorMapData',stress.sxx(:,end)) title('x-Direction Normal Stress in the Beam of the Last Time-Step')

Answer 1

[Ravi Kumar]

Hello Mohammadmahdi,

Sorry for the delay. I have shown below an example that should guide you to model your problem. This is a classical moving load problem. Instead of applying loads on nodes, I have used a function that applies pressure at different location on the bridge as people/load travel with time. The load can be much complicated distribution, here I am assuming it is a uniformly distributed over a short span that represents typical stride of walking.

The loading function is movingPulseFcn. Put the code below in a MATLAB file and execute. Note that I have plotted displacement using a for loop which has a pause, it will wait for you to look at the result, press any key to continue to next time step.

model = createpde('structural','transient-solid');
gm=multicuboid(10,4,0.3);
model.Geometry = gm;

E = 210E9; nu = 0.3; rho = 8000; 
structuralProperties(model,'YoungsModulus',E, ... 
    'PoissonsRatio',nu, ... 
    'MassDensity',rho);

structuralBC(model,'Face',[5 3],'XDisplacement',0,'YDisplacement',0,'ZDisplacement',0);
generateMesh(model);
structuralBoundaryLoad(model,'Face',2,'Pressure',@movingPulseFcn);
d0=[0,0,0];
v0=[0,0,0];
structuralIC(model,'Displacement',d0,'Velocity',v0);
t_max = 20;
tlist=0:0.1:t_max; 
structuralResults=solve(model,tlist);

for i = 1:numel(structuralResults.SolutionTimes)
    pdeplot3D(model,'ColorMapData',structuralResults.Displacement.uz(:,i))
    title(['Deflection of bridge at Time = ' num2str(structuralResults.SolutionTimes(i))]);
    pause
end

function P = movingPulseFcn(region,state)
x = region.x+5; % Make the left end x = 0
dx = 0.4; % Approximate half stride. Stride is 2*dx = 0.8 (m)
%Distribute the load over an area:
A = 0.8*4;
P = zeros(1,numel(x));

loadVelocity = 1.5; %m/sec
if isnan(state.time)
    P = nan(1,numel(x));
end

if state.time < 7 % Load would cross the bridge in about 7 sec
    loadLocation = loadVelocity*state.time;
    x1 = loadLocation-dx;
    x2 = loadLocation+dx;

      idx = x>x1 & x<x2;
      % Weight of four people
      F = 2000;

      P(idx) = 2000/A;
  end

end