Dynamic response of thin-walled structures by variable kinematic one-dimensional models

Abstract

This paper investigates the accuracy capabilities of using variable kinematic modeling in compact and thin-walled beam-like structures with dynamic loadings. Carrera Unified Formulation (CUF) is employed to introduce refined one-dimensional (1D) models with a variable order of expansion for the displacement unknowns over the beam cross-section. Classical Euler–Bernoulli and Timoshenko beam theories are obtained as particular cases of these variable kinematic models while a higher order expansion permits the detection of in-plane cross-section deformation, since it leads to shell-like solutions. Finite element (FE) method is used to provide numerical results and the Newmark method is implemented as a time integration scheme. Some assessments with closed form solutions are discussed and comparisons with shell-type results obtained with commercial FE software are made. Further analyses address both compact and thin-walled cross-sections. In particular, the case of a deformable thin-walled cylinder loaded by time-dependent internal forces is discussed. The results clearly show that finite elements which are formulated in the CUF framework do not introduce additional numerical problems with respect to classical beam theories. Comparisons with elasticity solutions prove that the present 1D CUF model offers an accuracy in analyzing thin-walled structures which is typical of shell or three-dimensional models with a remarkable reduction in the computational cost required.