A semi-analytical approach for linear and non-linear analysis of unstiffened laminated composite cylinders and cones under axial, torsion and pressure loads

Castro, Saullo G.P.; Mittelstedt, Christian; Monteiro, Francisco Alex Correia; Arbelo, Mariano A.; Degenhardt, Richard; Ziegmann, Gerhard

doi:10.1016/j.tws.2015.01.002

Cited by 27 publications

(6 citation statements)

References 26 publications

(42 reference statements)

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“…is the geometric stiffness matrix calculated using the pre-buckling in-plane stresses. Their detailed derivation can be found in Castro et al [9,11,12,13], and the implementation is publicly available in a Python package [8]. Both and are integrated numerically, given that the constitutive stiffness represented by the the ABD matrix spatially changes due to fibre steering.…”

Section: Semi-analytical Approachmentioning

confidence: 99%

Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

Vertonghen¹,

Castro²

2020

Preprint

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Previous research has hinted on further improvements of the buckling behaviour of variable-stiffness laminates by incorporating overlaps, resulting in a variable thickness profile that is non-linearly coupled to the steering angles. The present study compares two modelling strategies to consider the variable thickness distribution: 1) as manufactured with discrete thicknesses; and 2) smoothed with a continuous thickness distribution. The as-manufactured discrete thickness created by overlapping tows is obtained by means of virtually manufactured laminates. The smeared approximation is much simpler to implement, whereby the local thickness is a non-linear function of the local steering angle. Linear buckling analyses are performed by means of fast semi-analytical models based on the Ritz method using hierarchical polynomials and classical plate formulation. By assuming a smooth manufacturing mould on one side, a one-sided thickness variation is produced, resulting in non-symmetric laminates for which the mid-plane surface is varied accordingly. Modelling guidelines are provided regarding the use of the smeared model in a study covering a wide range of geometries, loading and boundary conditions. With these guidelines, one can apply the smeared thickness technique in semi-analytical models to reach a correlation within ±5% compared to a costly discrete-thickness finite element model.

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Section: Semi-analytical Approachmentioning

confidence: 99%

Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

Vertonghen¹,

Castro²

2020

Preprint

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“…Semi-analytical methods are extremely recommended when the structural matrices can be analytically integrated, because these methods are able to approximate the continuum with less degrees-of-freedom when compared to other lower-order interpolation methods such as finite elements. However, when numerical integration is needed, the nonlocal support of the degrees-of-freedom involved in semianalytical modelling requires integrands of the size of the entire structural matrices to be evaluated per integration point, making the integration process slower [16,17]. Even tough the integration becomes slower, the reduced number of degrees-of-freedom to discretize the continuum might compensate [10].…”

Section: Fast Buckling Evaluation Of Variable Stiffness Platesmentioning

confidence: 99%

Overlap-Stiffened Panels for Optimized Buckling Performance Under Minimum Steering Radius Constraints

Ummels¹,

Castro²

2020

Preprint

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Recent research on variable stiffness laminates have shown both numerically and experimentally that further improvement on the buckling behaviour is possible by incorporating overlaps that result in variable thickness profiles, with the thickness non-linearly coupled with the local steering angle. We present the concept of overlap-stiffened panels, developing a design method that allows for incorporating higher-stiffness regions into individual plies of a variable-angle tow (VAT) laminate, taking advantage of the non-linear coupling between the tow steering angles and the local thickness. The proposed method naturally copes with minimum steering radius constraints of different manufacturing processes, and the present study considers two tow steering processes: automated fiber placement (AFP) and continuous tow shearing (CTS). The minimum radius constraint is satisfied by connecting two transition regions of thickness specified on each ply by means of circular fiber tow arcs, of which the radius of curvature always exceed the minimum manufacturing constraint. Each individual ply exploring the overlap-stiffened design is described using 5 design variables. Laminates made up of these overlap-stiffened plies are optimized for a maximum volume-normalized buckling performance under bi-axial compression, measured through FEM, by a genetic algorithm and benchmarked against a straight fiber panel optimized for the same load case. The conclusion can be drawn that both AFP and CTS overlap-stiffened VAT panels can at least achieve the double of the volume-normalized buckling performance of an optimized straight fiber panel, demonstrating the potential of the proposed design method.

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“…Gaussian quadrature integration is perhaps the most popular solution, already implemented in a freely available Matlab low-loss EELS simulation package 9 . Inspired on this solution, we have implemented a faster, multidimensional version using the freely available cubature Python wrapper [28][29][30] . Simpson-rule method is based on the well-known numerical integration formula, generalized for irregularly-spaced data meshes.…”

Section: A Optimization Of the Relativistic Ddcs Integrationmentioning

confidence: 99%

Design and application of a relativistic Kramers–Kronig analysis algorithm

Eljarrat

Koch

2019

Ultramicroscopy

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Low-loss electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM) probes the valence electron density and relevant optoelectronic properties such as band gap energies and other band structure transitions. The measured spectra can be formulated in a dielectric theory framework, comparable to optical spectroscopies and ab-initio simulations. Moreover, Kramers-Kronig analysis (KKA), an inverse algorithm based on the homonym relations, can be employed for the retrieval of the complex dielectric function (CDF). However, spurious contributions traditionally not considered in this framework typically impact low-loss EELS modifying the spectral shapes and precluding the correct measurement and retrieval of the dielectric information. A relativistic KKA algorithm is able to account for the bulk and surface radiative-loss contributions to low-loss EELS, revealing the correct dielectric properties. Using a synthetic low-loss EELS model, we propose some modifications on the naive implementation of this algorithm that broadens its range of application. The robustness of the algorithm is improved by regularization, appliying previous knowledge about the shape and smoothness of the correction term. Additionally, our efficient numerical integration methodology allows processing hyperspectral datasets in a reasonable amount of time. Harnessing these abilities, we show how simultaneous relativistic KKA processing of several spectra can share information to produce an improved result. arXiv:1811.07575v1 [cond-mat.mtrl-sci]

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A semi-analytical approach for linear and non-linear analysis of unstiffened laminated composite cylinders and cones under axial, torsion and pressure loads

Cited by 27 publications

References 26 publications

Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

Overlap-Stiffened Panels for Optimized Buckling Performance Under Minimum Steering Radius Constraints

Design and application of a relativistic Kramers–Kronig analysis algorithm

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