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)?

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 wenbinyu@purdue.edu

saeid Khadem Moshir@ on — Edited @ @ onDear 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

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