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why interpolate density with theta (the projected design variable)?
Posted 29.02.2024, 21:32 GMT-5 Geometry, Structural Mechanics Version 6.1 1 Reply
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In this example: https://www.comsol.com/model/topology-optimization-of-an-mbb-beam-7428
It adopted 2 times of interpolation with different design variables theta and theta_p.
Interpolate the density using theta (the design variable after projection):
Interpolate the material property (Young's modulus) using theta_p:
As shown follows
Density rho root.comp1.dtopo1.theta*(7850[kg/m^3]) kg/m³ Basic
Young's modulus E root.comp1.dtopo1.theta_p*(E(T)) Pa Young's modulus and Poisson's ratio
Why do we interpolate the density using theta?
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If you are only looking at statics, you interpolate Young's modulus to control the stiffness, such that a low Y emulates removing the material. However, when looking at dynamics, you also have inertia, and so you also interpolate density to emulate removing the mass. (F=kx+ma).
-------------------René Christensen, PhD
Acculution ApS
www.acculution.com
info@acculution.com