Exact solutions for static analysis of laminated, box and sandwich beams by refined layer-wise theory

Abstract

In the present work, a close-form solution based on a unified one-dimensional model is proposed and then applied to static response analyses of cross-ply laminated and sandwich beams subjected to simply supported boundary conditions. The hierarchical beam model is derived within the framework of the Carrera Unified Formulation (CUF), which makes use of Lagrange polynomials to express the three-dimensional (3D) displacement field via arbitrary order approximation of pure displacement variables at each layer over the cross section, in a Layer-Wise (LW) sense. The governing equations are derived via the principle of virtual work and a Naviertype close-form solution is employed to solve the resulting boundary value problem. Four benchmark numerical examples are carried out to demonstrate the efficiency of this novel method, including compact multi-layered cross-ply laminated beams, a thin-walled composite box beam and a composite sandwich-box beam. The results show that accurate displacement and stress components can be obtained as the order of the expansion increases, accompanied by a significant reduction in computational costs in comparison with the 3D finite element solutions. Besides, numerical cases in this research may be taken as benchmarks for future assessments in this field.

Application of Pattern Recognition to the Identification of Cross-Section Deformation Modes of Thin-Walled Structures

“…With the singular value decomposition of χ (1) out , all of its ten singular values are obtained and exhibited in Table 1. The effective rank is determined as p = 3 through the analysis of contribution values (here the threshold is determined as 0.000001) employing (23). Thus, the first three columns of U (1)…”

“…Meanwhile, Carrera unified formulation has been developed by considering the displacement field through Taylor or Maclaurin expansions [21], [22]. Over the past decade, it has been extended for the analysis of thin-walled structures [23], which allows to improve the accuracy on representing higher order effects for arbitrary cross-sections [24], [25].…”

A Novel Approach to Perform the Identification of Cross-Section Deformation Modes for Thin-Walled Structures in the Framework of a Higher Order Beam Theory

“…Over the past decade, CUF has been developed for the higher order analysis of thin-walled structures. Some valuable developments were reported by Pagani et al [12] and Yan et al [13]. It should be noted that it allows special improvements on the accuracy of representing higher order effects [14].…”

Theoretical modeling and vibration control for pre-twisted composite blade based on LLI controller

“…The TWB theory incorporating fiber-reinforced and piezo-composite has been developed to investigate the vibration behavior, using the structural model accounting for transverse shear strain, primary and secondary warping, pre-twist and presetting angles (Wang et al, 2017). Static responses of cross-ply laminated and sandwich beams subjected to simply supported boundary conditions, have been analyzed by a close-form solution based on a unified one-dimensional model (Pagani et al, 2017). Vibration control of a rotating Euler-Bernoulli beam using optimal proportional integral derivative (PID) approach and linear quadratic theory has been investigated, with nonlinear coupling effects between the rotor rotation and the aerodynamic action demonstrated (Chang et al, 2018).…”