A question regarding your paper

  1. saeid Khadem Moshir

    Dear Prof. Yu,

    I have studied your paper entitled “Variational asymptotic beam sectional analysis – An updated version” published in 2012.

    The theory which you used for determining the stiffness of the cross-section of a beam is very interesting.

    I have difficulty with the Eq. 85) of that paper. I cannot find out how the kernel matrix capital Psi is obtained. It is mentioned in the paper that the Psi is the null space of the matrix E and Psi are nodal values of psi. I have not realized how we can use the Eq. 85) to find the V0hat).

    I was wondering if you let me know how I can obtain V0hat)?

    Is it possible to use the Eq. 82) for obtaining V0hat)?  yes, the matrix E is not invertible and it is a singular matrix. Is there any way to calculate its inverse? Can we use pseudo method to invert the matrix E and using Eq. (82)?

    Thank you so much

    Sincerely Yours 
    Saeed Khadem Moshir
  2. Wenbin Yu

    E is four times singular. You can use E\phi=0 to find out the kernel. If the right hand side is corrected by the kernel, then you can find a unique solution for the system. You can find more detailed explanation of this in my PhD dissertation which is also available on cdmHUB. ---- Emailed forum response from