# PDE toolbox: unexpected result of static structural model for stretchy sheet

조회 수: 1(최근 30일)
Myrtle42 2022년 5월 9일
I'm trying to model spatial deformation of a triangular stretchy sheet of material (think stretchy fabric or rubber). The top corner is fixed in place, while the bottom two corners at pulled with a specified force as shown below. Imagine holding one bottom vertex in each hand and pulling to make the sheet taut. I'd like to solve for the final shape of the sheet.
The results seems completely wrong, which means I am doing something completely wrong. I expect to see displacement of the x coordinate (result.Displacement.ux) change from negative to positive as x increases. Instead, x displacement mostly increases with y. If I decrease the mesh size the result changes apparently randomly. Any hint what I am doing wrong? Code below. Code:
%% Generate x,y coordinates of edges of a triangle
a.XY1 = [0 0; 1.5 0; .75 3]; % (m)
% Create geometry in pde toolbox form
gd = [2; size(a.XY1,1); a.XY1(:,1); a.XY1(:,2)];
sf = 'P1';
dl = decsg(gd,sf,double(sf(:)));
%% Create model and apply geometry
model = createpde('Structural','static-planestrain');
geometryFromEdges(model, dl);
structuralProperties(model,'YoungsModulus',1e9,'PoissonsRatio',.4); % (Pa) (unitless)
structuralBC(model, 'Vertex', 3,'Constraint','fixed');
f = 1e3; % (N)
generateMesh(model);
% Solve
result = solve(model)
fprintf('Max x: %.2g, max y: %.2g\n',max(result.Displacement.ux),max(result.Displacement.uy))
%% Plot stuff
figure;
subplot(221)
pdegplot(dl,'VertexLabels','on') % Plot PDE geometry
title('Geometry'); axis off
subplot(222);
pdeplot(model)
title('Mesh')
subplot(223)
pdeplot(model,'XYData',result.Displacement.ux)
title('x-displacement')
axis equal
subplot(224)
pdeplot(model,'XYData',result.Displacement.uy)
title('y-displacement')
colormap('jet')
axis equal

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