Unexpected (wrong?) results of thermal deflection using PDE Toolbox

Question

Filippo90 2019-1-27

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https://ww2.mathworks.cn/matlabcentral/answers/441720-unexpected-wrong-results-of-thermal-deflection-using-pde-toolbox

评论： Ravi Kumar 2019-11-11

I'm trying to use the PDE Toolbox to analyze the thermal deflection of a beam subjected to a non-uniform temperature distribution.

The heat transfer analysis allows the temperature distribution to be calculated as shown below. I imposed a fixed temperature of 0 degC in the Face 5 and a fixed temperature of 25 degC in the Face 3.

Then I defined the structural mechanics problem giving to temperature distribution as a thermal load. The deflection that I have obtained is far from what I expected (8.9566e-04 m). The thermal deflection of the same beam subjected to a constant temperature (25 degC) is 3.0411e-04 m. How the deflection can be lower if the thermal energy introduced in the beam is higher???

See below the code:

% Create thermal model for PDE toolbox
thermalmodel = createpde('thermal','steadystate');
% Define geometry and import
gm = multicuboid(1,0.1,0.1);
thermalmodel.Geometry = gm;
% Mesh geometry
generateMesh(thermalmodel,'Hmax',0.030);
% Material properties
thermalProperties(thermalmodel,'ThermalConductivity',5e-3);
% Boundary conditions
thermalBC(thermalmodel,'Face',5,'Temperature',0);
thermalBC(thermalmodel,'Face',3,'Temperature',25);
% Solve heat transfer problem
thermalresults = solve(thermalmodel);
% Create structural model for PDE toolbox
structuralmodel = createpde('structural','static-solid');
% Define geometry and import
structuralmodel.Geometry = gm;
% Mesh geometry
generateMesh(structuralmodel,'Hmax',0.030);
% Material properties
structuralProperties(structuralmodel,'YoungsModulus',200E9,'PoissonsRatio',0.300,'CTE',12.0E-6);
% Boundary conditions and thermal load
structuralBC(structuralmodel,'Face',5,'Constraint','fixed');
structuralBodyLoad(structuralmodel,'Temperature',thermalresults);
structuralmodel.ReferenceTemperature = 0;
% Solve heat transfer problem
structuralresults = solve(structuralmodel);
% Create structural model for PDE toolbox using a constant temperature for
% all nodes
structuralmodel2=structuralmodel;
structuralBodyLoad(structuralmodel2,'Temperature',25);
structuralmodel2.ReferenceTemperature = 0;
structuralresults2 = solve(structuralmodel2);
max(structuralresults.Displacement.Magnitude)
max(structuralresults2.Displacement.Magnitude)

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Answer 1

Sander Struycken 2019-11-11

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Did you figure out what's happing here? I run into the same problem. Gradient temperature gives my unexpected thermal expansion. I expecte 0.5*length*dT*CTE but I get someting higher than heating up teh whole thing where the number matches length*dT*CTE.

An explanatin would be verty much appreciated!

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Ravi Kumar 2019-11-11

Hi Sander,

This is a bug in R2018b version. If you can upgrade to R2019a or R2019b then you should not encounter this issue associated with nonconstant temperature distribution. Sorry for the inconvenience.

Regards,

Ravi

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