In this work we propose a numerical solution procedure for nonlinear instability problems geometrically exact beams (representing arbitrary large displacements and rotations) under either conservative or non-conservative load. Both static dynamics frameworks are developed, with the latter needed case. The proposed model can also successfully deliver analytic to linearized (with small pre-buckli...

This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system...

Abstract In this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory further development and extension space-fractional (non-local) Euler–Bernoulli model (s-FEBB) to Timoshenko (s-FTB) one by proper taking into account shear deformation. Furthermore, detailed parametric study on influence le...

We consider the problem of minimizing supplied energy infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit turnpike phenomenon towards certain subspaces induced by dissipation dynamics. The theoretical foundations are illustrated means numerical examples concerning a Timoshenko beam heat equation.