Abstract
This paper presents an application of refined one-dimensional (1D) models to the static and free vibration analysis of thin-walled layered structures. Carrera Unified Formulation (CUF) is employed to easily introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the beam cross-section. Classical Euler-Bernoulli beam theory is obtained as a particular case of these variable kinematic models while a higher-order expansion permits the detection of the in-plane cross-section deformation. Finite element (FE) method is used to provide numerical results. In particular, the case of a deformable clamped-clamped thin-walled layered cylinder loaded by a non-uniform internal pressure is discussed. The static analysis reveals the model capabilities in accurately describing the three-dimensional deformation of the cylinder. The free vibration analysis provides results not detectable by typical 1D models in excellent agreement with a solid (3D) FE solution. The present models do not introduce additional numerical problems with respect to classical beam theories. Moreover, the results clearly show that finite elements which are formulated in the CUF framework offer shell-type capabilities in analyzing thin-walled structures with a remarkable reduction in the computational cost required.
Highlights
In many areas such as aerospace, civil and biomechanical engineering different kinds of slender structures are involved nowadays
Many theoretical and computational approaches were taken to address issues such as warping effects and in-plane cross-secton deformation. Refined theories such as those based on the 1D Carrera Unified Formulation (CUF) [7, 8] and variational asymptotic methods (VABS) [32] as well as the Generalized Beam Theory (GBT) [25] have presented remarkable advances in static, buckling, and free vibration analysis
According to the framework of Carrera Unified Formulation (CUF) [8], the displacement field is assumed to be an expansion of a certain class of functions Fτ, which depend on the cross-section coordinates x and z: u (x, y, z, t) = Fτ (x, z) uτ (y, t)
Summary
In many areas such as aerospace, civil and biomechanical engineering different kinds of slender structures are involved nowadays. Many theoretical and computational approaches were taken to address issues such as warping effects and in-plane cross-secton deformation Refined theories such as those based on the 1D Carrera Unified Formulation (CUF) [7, 8] and variational asymptotic methods (VABS) [32] as well as the Generalized Beam Theory (GBT) [25] have presented remarkable advances in static, buckling, and free vibration analysis. Kant and Gupta [18] proposed a refined FE higher-order model with quadratic transverse shear strain that was applied to the free vibration analysis of angle-ply laminated, deep sandwich and composite beams [22, 23]. The influence of higher-order effects over the three-dimensional cross-section deformation, not detectable by classicalbeam theories, is enhanced on the evaluation of vibrational modes of layered structures. The use of variable kinematic 1D CUF models reveals their shell-type capabilities in accurately describing the dynamic behavior of thin-walled structures
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