Is it possible to analyze the flexible multibody with hard initial position?

Question

Makoto Yoshioka 2021-11-4

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评论： Makoto Yoshioka 2021-11-8

I defined the 3 beams (all dimensions and materials are the same) with "Reduced Order Flexible Solid" , and connect them with revolute joints like Fig.1.

For one of the 3 revolute joints, I set the initial angle as follows.

Z revolute primitive

-> state targets

-> specify position target ✓

-> priority: high (desired), value=135[deg]

However, the definition of the coodinate system is set so that value = 0[deg] when the 2 connected beams are aligned in a straight line.

Fig.1 truss structure with flexible beams

Fig.2 time history of the rotation angle (vertical: rotation angle [rad], horizontal: time [s])

Finally, just in case, I've shown the code for defining the flexible beam.

% flexible multibody dynamics
close all;
%% step.1 import STL file
stlFile = 'beam.STL';
figure
trisurf(stlread(stlFile));
axis equal
%% step.2 set interface coordinates
origins = [5  5  100
           5  5  0];
%origins = origins / 1000; % 単位系: m
%% step.3 make meshes
% set parameters
% reference: https://kayo-corp.co.jp/common/pdf/pla_propertylist01.pdf
E = 3626*10e3;
nu = 0.3;
rho = 1.380*0.001;
feModel = createpde('structural', 'modal-solid');
importGeometry(feModel, stlFile);
structuralProperties(feModel, ...
    'YoungsModulus',E, ...
    'PoissonsRatio',nu, ...
    'MassDensity',rho);
generateMesh(feModel, 'GeometricOrder','quadratic');
%% step.4 set mutlipoint constraints for interface coordinate systems
figure
pdegplot(feModel,'FaceLabels','on','FaceAlpha',0.5)
faceIDs = [5, 6];
numFrames = 2;
% emphasize the selected faces (faceIDs)
figure
pdemesh(feModel,'FaceAlpha',0.5)
hold on
colors = ['rgb' repmat('k',1,numFrames-3)];
assert(numel(faceIDs) == numFrames);
for k = 1:numFrames
    nodeIdxs = findNodes(feModel.Mesh,'region','Face',faceIDs(k));
    scatter3( ...
        feModel.Mesh.Nodes(1,nodeIdxs), ...
        feModel.Mesh.Nodes(2,nodeIdxs), ...
        feModel.Mesh.Nodes(3,nodeIdxs), ...
        'ok','MarkerFaceColor',colors(k))
    scatter3( ...
        origins(k,1), ...
        origins(k,2), ...
        origins(k,3), ...
        80,colors(k),'filled','s')
end
hold off
for k = 1:numFrames
    structuralBC(feModel, ...
        'Face',faceIDs(k), ...
        'Constraint','multipoint', ...
        'Reference',origins(k,:));
end
%% step.5 make reduced order model
rom = reduce(feModel, 'FrequencyRange', [0 1e3]);
beam.P = rom.ReferenceLocations';  % Interface frame locations (n x 3 matrix)
beam.K = rom.K;                    % Reduced stiffness matrix
beam.M = rom.M;                    % Reduced mass matrix
dampingRatio = 0.05;
beam.C = computeModalDampingMatrix(dampingRatio,rom.K,rom.M);
frmPerm = zeros(numFrames,1);      % Frame permutation vector
dofPerm = 1:size(beam.K,1);       % DOF permutation vector
assert(size(beam.P,1) == numFrames);
for i = 1:numFrames
    for j = 1:numFrames
        if isequal(beam.P(j,:),origins(i,:))
            frmPerm(i) = j;
            dofPerm(6*(i-1)+(1:6)) = 6*(j-1)+(1:6);
            continue;
        end
    end
end
assert(numel(frmPerm) == numFrames);
assert(numel(dofPerm) == size(beam.K,1));
beam.P = beam.P(frmPerm,:);
beam.K = beam.K(dofPerm,:);
beam.K = beam.K(:,dofPerm);
beam.M = beam.M(dofPerm,:);
beam.M = beam.M(:,dofPerm);
beam.C = beam.C(dofPerm,:);
beam.C = beam.C(:,dofPerm);

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Answer 1

Steve Miller 2021-11-6

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Hi Makoto,

There are some options:

You can define the initial positions and speeds of the joints that connect the flexible beams.
You can save the final state of a previous simulation and start a new simulation from that final state.

One thing you cannot do is use joint targets to specify an initial position of the beam in a deflected position.

Looking at your model, I suspect you have connected the ends of beam 1 and beam 3 to World blocks. This is the exact same x-y-z location, so you will end up with the triangle as shown in the visualization.

--Steve

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Steve Miller 2021-11-8

Joint targets cannot be used to start the beam in a deformed position. If you simulate the system until it reaches the deformed position, save that state, and then start the simulation from that state you can start with a deformed position. The Configuration Panel has options for save final state and specify initial state which can be used for this purpose.

--Steve

Makoto Yoshioka 2021-11-8

Thanks to your advice, I was able to achive this analysis.

Thank you so much!

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