Topology optimization. minimizing compliance for specified volume fraction

mohajerb@uwindsor.ca
mohajerb@uwindsor.ca Altair Community Member
edited October 2020 in Community Q&A

In topology optimization when minimizing compliance for specified volume fraction, the maximum deflection of optimized structure is less than the maximum deflection of original structure?

based on this formula 

<?xml version="1.0" encoding="UTF-8"?>post-31785-0-86003400-1427898981_thumb.p

For constant F when compliance is minimized U( deflection) should be minimized and vice versa. but in this formula volume fraction is not considered. 

I don't understand the concept of minimum compliance. The compliance of the optimized structure which is lighter than the original structure (since some material is removed from it) is even less than the original structure??!!

 

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Answers

  • Altair Forum User
    Altair Forum User
    Altair Employee
    edited April 2015

    Hi,

     

    the equation can be re-written as C= F[K]-1F where for a constant force only Stiffness can be changed. in which case, Volume fraction is an other entity of response.

     

    Again, A final optimization can then fine tune the design at the boundaries and hence allow local stiffening for reducing stresses.

  • mesun_20785
    mesun_20785 Altair Community Member
    edited March 2016

    Hi can anyone tell me what is the term exist in combined compliance index just before lamda (eigen value) after w_i

     

    i mean S=Sum w_i C_i+NORM sum (w_i (?) lamda_i)/ sum w_i

     

    thanks

  • Altair Forum User
    Altair Forum User
    Altair Employee
    edited March 2016

    Hi,

     

    Could you please let me know to which equation you are refering to?

     

    Weighted compliance (combined compliance) equation from OptiStruct help is shown in image below:

    <?xml version="1.0" encoding="UTF-8"?>Capture.JPG

  • mesun_20785
    mesun_20785 Altair Community Member
    edited March 2016

    Hi First thank you for you reply..

     

    I mentioned compliance index formulation..there is l like term which i couldnt understand.. 

  • Rahul Rajan_21763
    Rahul Rajan_21763 New Altair Community Member
    edited March 2016

    Hi,

    The way the norm is calculated automatically is ;

     

     

     

     

     

    Weighted_compliance*Sum_(weight/Eigenvalue)/Sum_weights

     

     

     

     

     

    Regards

    Rahul R

    <?xml version="1.0" encoding="UTF-8"?>Combined compliance index.JPG

  • Altair Forum User
    Altair Forum User
    Altair Employee
    edited September 2016

    what is the variable, T, in the equation?

  • Altair Forum User
    Altair Forum User
    Altair Employee
    edited September 2016
    Altair Forum User said:

    what is the variable, T, in the equation?

     

    Hi,

     

    T is not a variable, it is the Transpose of matrix U.

  • AJM
    AJM Altair Community Member
    edited November 2018

    Hello , 

     

    Is that possible to have many constrains with respect to many load case for topology  optimization targeting for weight reduction ? 

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