Exact solutions for the macro-, meso- and micro-scale analysis of composite laminates and sandwich structures

Abstract

The present work proposes a closed-form solution based on refined beam theories for the static analysis of fiber-reinforced composite and sandwich beams under simply supported boundary conditions. The higher-order beam models are developed by employing Carrera Unified Formulation, which uses Lagrange-polynomials expansions to approximate the kinematic field over the cross section. The proposed methodology allows to carry out analysis of composite structure analysis through a single formulation in global-local sense, i.e. homogenized laminates at a global scale and fiber-matrix constituents at a local scale, leading to component-wise analysis. Therefore, three-dimensional stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. The governing equations are derived in a strong-form and solved in a Navier-type sense. Three benchmark numerical assessments are carried out on a single-layer transversely isotropic beam, a cross-ply laminate false[0∘/90∘/0∘] beam and a sandwich beam. The results show that accurate displacement and stress values can be obtained in different parts of the structure with lower computational cost in comparison with traditional, enhanced as well as three-dimensional finite element methods. Besides, this study may serve as benchmarks for future assessments in this field.

Analytic solution of angle-ply laminated plates under extension, bending, and torsion

“…First, equation 16is used to obtain the eigenvalues (ð n Þ, n ¼ 1, N ), equations (25) to (30) are then used to find the particular and zero solutions, and finally equation 31is used to find the parameters (D n ). The displacement and stress fields are obtained using the combination of equations (24) to (28). The integration of equations (32) and (33) can be determined explicitly, so the above procedures only require the solutions of matrix and eigen equations.…”

“…Yan et al. 24 developed an exact solution based on refined beam theory which uses Lagrange-polynomials expansions for the multiscale analysis of composite laminates and sandwich beams, and the stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. Wackerfuß and Kroker 25 presented an efficient semi-analytical simulation framework that allows a highly systematic analysis of the mechanical behavior of laminated prismatic thin-walled beams, and this approach is suitable for extensive case studies.…”

“…23 presented an analytic solution based on the classical Vlasov's beam theory for torsion of thin-walled laminated composite beams of symmetrical open cross sections, and this analytical model can be efficiently used as a tool in the early design stages of thin-walled laminated composite beams. Yan et al 24 developed an exact solution based on refined beam theory which uses Lagrange-polynomials expansions for the multiscale analysis of composite laminates and sandwich beams, and the stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. Wackerfuß and Kroker 25 presented an efficient semi-analytical simulation framework that allows a highly systematic analysis of the mechanical behavior of laminated prismatic thin-walled beams, and this approach is suitable for extensive case studies.…”

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

“…Since the transverse variation of the material characteristics is very large in the core and the face sheet and the thickness of sandwich plates is often greater than that of laminated composite plates, the traditional global theories (equivalent single layer theories) such as the classical lamination theory (CLT), 1 the first-order shear deformation theory (FSDT), 2 and the higher order shear deformation theories (HSDT) 3–6 may not provide accurate results in the cases wherein the core is made up of very soft materials or the number of the layers is large. To overcome these drawbacks, layerwise theories 7–12 have been proposed to model the local distributions of the displacement components. Layerwise theories can produce accurate displacements and stresses, while huge computational efforts are required as the number of the displacement variables grows with the number of the layers.…”

Thermo-mechanical analysis of multilayered composite beams based on a new mixed global-local model

“…Nevertheless, such global higherorder models [7][8][9][10][11][12] have a drawback which is the continuity conditions of transverse shear stresses at interfaces that are not satisfied. To overcome this drawback, the layer-wise theories [13][14][15][16] were proposed. Layerwise models can produce very accurate displacements and stresses, but huge computational efforts are required as the number of displacement variables generally depends on the number of layers of the plate.…”