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Timoshenko Stiffness Matrix of K66

  1. bei li

    VABS outputs the 6 × 6 stiffness matrix and compliance martrix for the Timoshenko beam model with respect to the beam coordinate system.

    In the (cs_1. sg. K) file, Timoshenko Stiffness Matrix (1-extension; 2,3-shear, 4-twist; 5,6-binding), then k66 should be Principal binding stiffness EI22, right? Why is the gap so large?

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    Replying to bei li

    1. Wenbin Yu

      If you create both models corrects, you should be able to get the same results. The best way is to do an easier example, those published by us or released with VABS and verify you get the same results.

      From: bei li @ cdmHUB - The Composites HUB <support@cdmhub.org>
      Sent: Wednesday, February 8, 2023 10:21 AM
      To: Yu, Wenbin <wenbinyu@purdue.edu>
      Subject: cdmHUB - The Composites HUB Forum: yugroup - Timoshenko Stiffness Matrix of K66

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      Replying to Wenbin Yu

    2. bei li

       

      This is the result of the same section calculated using ansys-vabs gui and ivabs respectively. The K66 obtained by ansys-vabs gui corresponds to the Principal binding stiffness EI22, but the result calculated by ivabs does not correspond. Why?

      K.zip

      3 KBClick to download

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      Replying to bei li

    3. Su Tian

      VABS directly output the principal bending stiffness EI22 and EI33 above the Timoshenko stiffness matrix. They are very close. The remaining difference could be due to the difference of cross-sectional modeling in the two tools. You may want to compare the two models carefully. For instance, the origin might be not at the same location.

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      Replying to Su Tian

      1. bei li

        Thank you for your answer. I may not be very clear. What does the K66 element of timoshenko stiffness matrix in the cs_1.sg.k file represent? Isn't it E22?

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    4. Wenbin Yu

      It is not. k66 is an element of the fully coupled 6x6 stiffness matrix with the coordinate system chosen by the user. EI22 is the inverse of 66 term of the compliance matrix when the coordinate system is located at the neutral axis and align with the principal bending axis. 

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      Replying to Wenbin Yu

      1. bei li

        Ok, thank Professor Yu for your answer! What is the way to set the coordinate system at the neutral axis and align it with the main bending crankshaft to get the same result as the ansys-vabs gui?

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      2. bei li

        Well, I understand what you mean, but I don't know where to start. Is it to modify the airfoil file? I want to get timoshenko stiffness matrix when the coordinate system is located at the central axis and align with the principal binding axis

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      3. bei li

        Thank you very much for your answer. My problem has been solved. Thank you！

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    5. Wenbin Yu

      run it the first time, VABS will tell you where the neutral axis  and principal bending axis. Then translate and rotate your coordinate system to create another model to get the results you want.

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      Replying to Wenbin Yu

      1. bei li

        Thanks！ Professor Yu, I understand what you mean. But I don't know the coordinate system defined in which file. Sorry to bother you again!

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      2. Su Tian

        Coordinate system is defined implicitly when you define/transform the geometry. There are two input options for translating and rotating the cross-section. See https://wenbinyugroup.github.io/ivabs/prevabs/contents/guide/pre_coordinate.html for more details.

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      3. bei li

        I tried to modify the sample file, and the result was correct, but when I modified my section, the following error occurred: Something wrong with the mesh The Jacobian of element 5971 is less than zero. Why? Sorry to bother you again

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      4. Su Tian

        It could mean that this element has the nodes ordered in the clockwise direction, which should be counterclockwise. You can plot the cross-section in the gmsh and search this element to see the issue.

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