How the Mass Matrix get in Subdyn

Wind & Water Structural Analysis
1

Dear All

I’m a novice in finite element analysis, and I’m currently trying to read the Subdyn theory manual. In the section on Element Formulation, I’m having trouble understanding the formulation for the elements in the mass matrix.

For example, in M(1,1), I understand that Az times Le represents the volume of the beam, but I’m unclear about how the coefficient 13/35 is derived. Also, what does +6/5 × Jy/Le represent?

I haven’t been able to find the answers in the references provided by Subdyn (Panzer et al. 2009).

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I’m very grateful for any assistance!

Best regards

Teng Long

2

Dear @Teng.Long,

You can find the derivation of this consistent mass matrix in classic finite element textbooks that cover 2-node Timoshenko beam FEs. E.g., see: https://people.duke.edu/~hpgavin/StructuralDynamics/StructuralElements.pdf.

Best regards,

3

Dear @Jason.Jonkman

Thank you very much for your share. The book you provided has greatly cleared up my confusion.

Best regards