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why interpolate density with theta (the projected design variable)?

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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.

  1. Interpolate the density using theta (the design variable after projection):

  2. 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?


1 Reply Last Post 2024/03/01 1:34 GMT-5
Acculution ApS Certified Consultant

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Posted: 8 months ago 2024/03/01 1:34 GMT-5

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
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).

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