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

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);

Answer 1

[Steve Miller]

Hi Makoto,

There are some options:

1. You can define the initial positions and speeds of the joints that connect the flexible beams.
2. 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

[Makoto Yoshioka]

Thank you for your response!

Sorry for my lack of understanding, but I think your 1st option is the same as using the joint target to specify an initial position of the beam.

You mean, there is any other option to specify the initial position?

Also, if using the option, can I start the analysis with the initial shape deformed to match any initial position?

Sorry to bother you again, but I would appreciate it if you could answer.

[Steve Miller]

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]

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

Thank you so much!