There is no doubt about the equivalence between the dynamic stiffness method and the finite element method. However, there are currently many extensions of this equivalence in Euler beam theory, and Taylor element expansion of the dynamic stiffness matrix can improve the accuracy of finite element analysis. Can the Taylor expansion of the dynamic stiffness matrix elements be achieved for Timoshenko beam theory? Do you currently have any relevant research work? Seeking recommendation and cooperation.
I have no knowledge of Timoshenko beam theory in the context of the dynamic stiffness method, but I recall that Timoshenko theory is described by partial differential equations, just as Euler theory is. Accordingly, you should be able to derive from the (theoretically exact) Timoshenko PDEs the associated element dynamic stiffness matrix. If you then expand that dynamic stiffness matrix in powers of frequency-squared, the first term of the expansion should be the conventional finite-element static stiffness matrix, and the second term should be negative of the conventional finite-element consistent mass matrix (assuming that Timoshenko theory follows the same pattern as Euler theory). In the early 1980s, I wrote a couple articles on the dynamic stiffness method for Euler beam theory.
- Thank you very much.
- Is the article you mentioned the following？W.L. Hallauer Jr.; R.Y.L. Liu (1982). Beam bending-torsion dynamic stiffness method for calculation of exact vibration modes. , 85(1), 105–113. doi:10.1016/0022-460x(82)90473-4.
As you said，expanding the dynamic stiffness matrix in powers of frequency-squared is curcial. Perhaps， the difference between Timoshenko and Eular lies in the ease of calculation.
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