The Rayleigh–Ritz Method and Simple Applications

Ilanko, Sinniah; Monterrubio, Luis E.; Mochida, Yusuke

doi:10.1002/9781118984444.ch3

Cited by 3 publications

(4 citation statements)

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“…46 The compression strength and compression after impact (CAI) strength of composite made from 2D woven fabrics is compromised by localised crimp in the fibres due to micro-buckling. 124 However, their residual compression strength is higher than that of unidirectional fabric composite due to the smaller damage areas during impact events.…”

Section: Methods Of Improving Damage Tolerancementioning

confidence: 99%

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Improving the impact resistance and damage tolerance of fibre reinforced composites: A review

Dalfi,

Jan,

Yousaf

et al. 2023

Journal of Composite Materials

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As the use of composite laminates are unceasingly increasing more and more in many applications, the in-depth understanding about the impact response of composite laminates in certain areas like sport, aerospace and automotive has gained more attention of the designers and scientists over the last two decades. The authors have focused to review the impact properties of fibre reinforced composites particularly impact damage tolerance. Impact resistance, damage tolerance, composite failure and methods of assessing damage tolerance are presented. Furthermore, the approaches for improving damage tolerance such as fibre architectures resin system, and hybridisation using either yarn hybridisation or hybrid layers are discussed. In the end, a survey of modelling the impact damage of laminated composites is made by considering the inter-laminar and intra-laminar failures as key point for evaluating the response of laminates under impact loading.

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Section: Methods Of Improving Damage Tolerancementioning

confidence: 99%

“…Lee et al 24 developed analytical model depending on Rayleigh–Ritz method 124 and theory of the wide plate deflection. This model assumes that the deformation modes under quasi-static loading and low-velocity impact are similar.…”

Section: Impact On the Composite Laminatesmentioning

confidence: 99%

Improving the impact resistance and damage tolerance of fibre reinforced composites: A review

Dalfi,

Jan,

Yousaf

et al. 2023

Journal of Composite Materials

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“…The Rayleigh-Ritz method has been applied to solve the given problem. 11 The first step of the method is to find a suitable approximative function, which satisfies the geometric boundary conditions. 12,13 Initial geometric imperfections of the rectangular plate associated with zero initial stress are denoted by normal displacement w 0 ; in-plane initial imperfections are neglected.…”

Section: Mechanical Modellingmentioning

confidence: 99%

Improving climate resilience: Reduced-order mechanical modelling of a temperature-adaptable sun protection facade system

Schneider

Hückler

et al. 2023

Composites and Advanced Materials

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Analytical models to describe the mechanical behaviour of an adaptive sun protection facade system (Adaptex) are presented. First, a one-dimensional (1D) rigid link model is developed. Stretching and bending deformation of textile bands are represented with the aid of extensional and rotational springs respectively. The model is described by two generalized coordinates only. The second analytical model employs a continuous description based on the Kirchhoff plate theory. The Rayleigh–Ritz method is applied to analyse the deformation behaviour of the textile bands. In comparison with the experimental results, it can be found that the continuous model simulates the real deformation of the facade system, thus its morphological behaviour, very effectively. The results of a parametric study indicate that the stiffness of the textile bands, the geometric dimensions and the position of load application have significant effects on the deformation behaviour.

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“…In numerical analyses, small-scale upscaling models have been used to simulate the damage pattern and damage extension of composites under low-speed impacts, which can lead to “softening” of the material. Robin Olsson et al [ 24 ] developed a computational model to analyze the damage generation and extension during the static response caused by a heavy punch, and analyzed the impact damage under different stacking sequences, geometries, and boundary conditions, while Lee et al [ 25 ] developed a computational model based on the Rayleigh-Ritz method [ 26 ] and the theory of wide-plate deflection. The model assumes that the deformation pattern under a low-velocity impact is consistent with quasi-static loading, and the model establishes a method for assessing the residual compressive strength after impact based on fracture energy according to the model’s prediction of the damage zone.…”

Section: Introductionmentioning

confidence: 99%

Study on the Low-Velocity Impact Response and Damage Mechanisms of Thermoplastic Composites

Han,

Qi,

Yang

et al. 2024

Polymers

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A comparative experimental and numerical study of the impact behaviour of carbon-fiber-reinforced thermoplastic (TP) and thermoset (TS) composites has been carried out. On the one hand, low velocity impact (LVI) tests were performed on TP and TS composites with different lay-up sequences at different energy levels, and the damage modes and microscopic damage mechanisms after impact were investigated using macroscale inspection, C-scan inspection, and X-ray-computed tomography. The comparative results show that the initial damage valve force under LVI depends not only on the material, but also on the layup sequence. The initial valve force of the P2 soft layer with lower stiffness is about 11% lower than that of the P1 quasi-isotropic layer under the same material, while the initial valve force of thermoplastic composites is about 28% lower than that of thermoset composites under the same stacking order. Under the same stacking order and impact energy level, the damage area and depth of TP composites are smaller than those of TS composites; while under the same material and impact energy level, the indentation depth of P2 plies is greater than that of P1 plies, and the damage area of P2 plies is smaller than that of P1 plies, but the change of thermoplastic composites is not as obvious as that of thermoset composites. This indicates that TP composites have a higher initial damage threshold energy and impact resistance at the same lay-up order, while increasing the lay-up ratio of the same material by 45° improves the impact resistance of the structure. In addition, a damage model based on continuum damage mechanics (CDM) was developed to predict different damage modes of thermoplastic composites during low velocity impact, and the analytical results were compared with the experimental results. At an impact energy of 4.45 J/mm, the error of the initial damage valve force is 5.26% and the error of the maximum impact force is 4.36%. The simulated impact energy and impact velocity curves agree with the experimental results, indicating that the finite element model has good reliability.

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The Rayleigh–Ritz Method and Simple Applications

Cited by 3 publications

References 0 publications

Improving the impact resistance and damage tolerance of fibre reinforced composites: A review

Improving the impact resistance and damage tolerance of fibre reinforced composites: A review

Improving climate resilience: Reduced-order mechanical modelling of a temperature-adaptable sun protection facade system

Study on the Low-Velocity Impact Response and Damage Mechanisms of Thermoplastic Composites

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