Feasibility of MBD analysis with very thin flexible panels

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Makoto Yoshioka
Makoto Yoshioka 2021-11-9
回答： Ahmed Aboubakr 2022-4-12
Feasibility of MBD analysis with very thin flexible panels
I got the following error message and cannot proceed with the analysis of flexible MBD.
['flexible_square_panels/square_panel', 'flexible_square_panels/Solver Configuration']: Body 'flexible_square_panels/square_panel' caused a simulation error. This might be caused by extreme values in its geometry, material properties, cross-sectional properties, mass and stiffness properties, or deformation. For a flexible beam, this could also be caused by numerical ill- conditioning if the cross-sectional properties were calculated from geometry.
Is it possible to analyze a model that includes very thin flexible panels as shown below?
If possible, I would appreciate if you could tell me how to do so.
The following is model information.
100mm×100mm×0.25mm flat panel modeled in SolidWorks was imported as reduced order flexible solid.
The material is PET, and I set as follows.
Young's Modulus: 3500×10^6[g・mm/s^2/mm^2] ( = 3500[MPa])
Poisson's ratio: 0.3
density: 1.38×10^-3[g/mm^3] ( = 1.38[kg/m^3])
The unit system is mm, g, and s, because I was created in SolidWorks with mm as the length unit.
The code for setting the material is shown below.
% flexible multibody dynamics
close all;
%% step.1 import STL file
stlFile = 'square_plate.STL';
figure
trisurf(stlread(stlFile));
axis equal
%% step.2 set interface coordinates
origins = [0 0.125 50
50 0.125 100
100 0.125 50
50 0.125 0];
%% step.3 set material property and make mesh
% set parameters
% reference: https://kayo-corp.co.jp/common/pdf/pla_propertylist01.pdf
E = 3500*10e6; % g・mm/s^2/mm^2 = kg・m/s^2/m^2 = Pa
nu = 0.3;
rho = 1.380*10e-3; % g/mm^3
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 = [1, 2, 3, 4];
numFrames = 4;
% 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]);
panel.P = rom.ReferenceLocations'; % Interface frame locations (n x 3 matrix)
panel.K = rom.K; % Reduced stiffness matrix
panel.M = rom.M; % Reduced mass matrix
dampingRatio = 0.05;
panel.C = computeModalDampingMatrix(dampingRatio,rom.K,rom.M);
frmPerm = zeros(numFrames,1); % Frame permutation vector
dofPerm = 1:size(panel.K,1); % DOF permutation vector
assert(size(panel.P,1) == numFrames);
for i = 1:numFrames
for j = 1:numFrames
if isequal(panel.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(panel.K,1));
panel.P = panel.P(frmPerm,:);
panel.K = panel.K(dofPerm,:);
panel.K = panel.K(:,dofPerm);
panel.M = panel.M(dofPerm,:);
panel.M = panel.M(:,dofPerm);
panel.C = panel.C(dofPerm,:);
panel.C = panel.C(:,dofPerm);
Also, the reduced order flexible solid window and Simscape model are also shown in Fig.1, and 2, respectively.
Fig.1 setting window of reduced order flexible solid
Fig.2 Simscape model

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回答（1 个）

Ahmed Aboubakr
Ahmed Aboubakr 2022-4-12
Yes, it is possible to analyze a model that includes thin flexible panels. I would suggest you use the general flexible plate block for this model. You can find more information here Thin plate with elastic properties for deformation - MATLAB (mathworks.com)

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