Isogeometric Analysis for Nonlinear Dynamics of Timoshenko Beams
The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and \(p\)-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko’s theory for bending and geometrical type of nonlinearity.
As a result, a nonlinear system of second order ordinary differential equations is obtained. Periodic responses are of interest and the harmonic balance method is applied. The nonlinear algebraic system is solved by an arc-length continuation method in frequency domain.
It is shown that IGA gives better approximations of the nonlinear frequency-response functions than the \(p\)-FEM when models with the same number of degrees of freedom are used.
Keywords\(p\)-FEM Bifurcation diagrams Isogeometric analysis B-Splines Continuation method Nonlinear frequency-response function
This work was supported by the project AComIn “Advanced Computing for Innovation”, grant 316087, funded by the FP7 Capacity Programme and through the Bulgarian NSF Grant DCVP 02/1.
- 5.Hughes, T.J.R., Reali, A., Sangalli, G.: Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of \(p\)-method finite elements with \(k\)-method NURBS. Comput. Methods Appl. Mech. Eng. 197(49–50), 4104–4124 (2008)CrossRefzbMATHMathSciNetGoogle Scholar