Free-edge stress fields in cylindrically curved symmetric and unsymmetric cross-ply laminates under bending load

Schnabel, Jan Eike; Yousfi, Mejdi; Mittelstedt, Christian

doi:10.1016/j.compstruct.2017.08.002

Cited by 19 publications

(6 citation statements)

References 23 publications

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“…In this context, in order to investigate the underlying structural situation illustrated in Fig. 1, Kappel and Mittelstedt [5] developed a layerwise analysis method wherein the three-dimensional displacement field is assumed to be of higher order and where a space ratio in the thickness direction is employed in order to improve the accuracy and the efficiency of the semi-analytical approach originally developed by Schnabel et al [3]. This contribution enhances the presented higher-order analysis method in [5] by taking a solution procedure into account that enables a depiction of the free-edge effect on both load-free edges and therefore makes it possible to have a better representation of the underlying stress fields in cylindrically curved cross-ply laminated shells.…”

Section: Introductionmentioning

confidence: 99%

“…While for the free-edge effect in laminated plates there have been plenty of experimental, numerical and analytical investigations in the Fig. 1: Analytical discretisation schemes of the semi-analytical approach for a cylindrically curved cross-ply laminated shell subjected to bending load [5,6] last 50 years [1], the unfolding problem, which describes the free-edge effect in shells, has only been the topic of a comparatively small amount of scientific research [2][3][4][5]. In this context, in order to investigate the underlying structural situation illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Semi‐analytical assessment of free‐edge stress fields in cylindrically curved cross‐ply laminated shells

Kappel

Mittelstedt

2021

Proc Appl Math and Mech

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The present work deals with the semi-analytical assessment of the three-dimensional stress fields in cylindrically curved symmetrically and unsymmetrically cross-ply laminated shells subjected to bending load. The developed approach incorporates a layerwise plane-strain analysis in the innermost regions of the shell. The closed-form 'inner solution', further on, is upgraded by a displacement-based approach that enables an adequate depiction of the interlaminar stresses at the free edge. This so-called 'free-edge solution' employs a discretization scheme of each lamina into a number of numerical plies with respect to the thickness direction. Herein, the displacement field of each layer is specified via a priori unknown displacement-and Lagrangian interpolation functions. By applying the principle of minimum elastic potential, the governing equations can be derived in an exact manner and further on can be solved by employing the state space approach. The results of the higherorder analysis method are verified through comparison with highly detailed finite element simulations and it is found that the semi-analytical approach works with comparable accuracy, however, only at a fraction of the required computational effort.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semi‐analytical assessment of free‐edge stress fields in cylindrically curved cross‐ply laminated shells

Kappel

Mittelstedt

2021

Proc Appl Math and Mech

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“…Schnabel et al. 21 presented an analysis method for the determination of displacement, strain, and stress fields in cylindrically curved cross-ply laminates under bending load, and their method was compared to the results of finite element simulations in good agreement. Hajikazemi and Van Paepegem 22 developed a variational model to determine stress and displacement fields at free edges of symmetric composite laminate strips under thermomechanical loads, and the method is also applicable to thin-ply laminates.…”

Section: Introductionmentioning

confidence: 99%

“…Liang et al 20 developed a Hamiltonian state space approach for the analytic determination of deformation and stress fields in multilayered cross-ply laminates under extension and bending, while the laminates should be arranged symmetrically in 0 and 90 . Schnabel et al 21 presented an analysis method for the determination of displacement, strain, and stress fields in cylindrically curved cross-ply laminates under bending load, and their method was compared to the results of finite element simulations in good agreement. Hajikazemi and Van Paepegem 22 developed a variational model to determine stress and displacement fields at free edges of symmetric composite laminate strips under thermomechanical loads, and the method is also applicable to thin-ply laminates.…”

Section: Introductionmentioning

confidence: 99%

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

Hsu

et al. 2019

Journal of Composite Materials

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This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

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“…Sabit eğrilik ve kalınlıklı tabakalı eğrisel kirişlerde gerilme analizi için yüksek mertebe kiriş modeli geliştirilmiştir [34]. Dik-açılı tabakalı silindirik kirişlerin deplasman ve gerilmeleri yarı analitik bir analiz metodu kullanarak incelenmiştir [35].…”

Section: Introductionunclassified

Kompozi̇t Eğri̇sel Ki̇ri̇şlerde Kesi̇t Çarpilmasi Gözeti̇lerek Normal Ve Kayma Geri̇lmeleri̇ni̇n Karişik Sonlu Elemanlarla Anali̇zi̇

Aribas

2019

Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi

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Bu çalışmada, karşık sonlu eleman analizi ile kompozit eğrisel kirişlerin kesit çarpılması gözetilen normal ve kayma gerilmeleri incelenmiştir. İki düğüm noktalı eğrisel sonlu elemanlar yirmi dört adet bölge değişkenine sahiptir. Bünye bağıntıları, üç boyutlu elastisite kuramından ortotropik kompozit çubuklar için türetilmiş, kuple etkiler ve Poisson oranları gözetilmiştir. Karışık sonlu eleman formülasyonuna kesit çarpılması gözetilen burulma rijitliğinin yerdeğiştirme tabanlı sonlu eleman formülasyonu entegre edilmiştir. Normal gerilmelerin hesabında ilgili kesitin karışık sonlu eleman analizinden elde edilen eğrilikleri kullanılmıştır. Kayma gerilmeleri ise karışık sonlu eleman analizi sonucu eksenel dönme açısı ve çarpılma fonksiyonu kullanılarak yer değiştirme tabanlı sonlu elemanlarla elde edilmiştir. Kompozit bir kirişin boyutsuz normal ve kayma gerilmeleri literatür ile kıyaslanmıştır. Kompozit dairesel bir kirişin normal ve kayma gerilmeleri SOLID186 elemanların sonuçları ile karşılaştırılmıştır. Kompozit eğrisel kirişlerde malzeme sabitleri oranının, kesit geometrisi ve takviye kalınlığının en büyük normal ve kayma gerilmeleri ve tabakalar arası normal gerilmeler üzerindeki etkisi incelenerek literatüre kazandırılmıştır.

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Free-edge stress fields in cylindrically curved symmetric and unsymmetric cross-ply laminates under bending load

Cited by 19 publications

References 23 publications

Semi‐analytical assessment of free‐edge stress fields in cylindrically curved cross‐ply laminated shells

Semi‐analytical assessment of free‐edge stress fields in cylindrically curved cross‐ply laminated shells

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

Kompozi̇t Eğri̇sel Ki̇ri̇şlerde Kesi̇t Çarpilmasi Gözeti̇lerek Normal Ve Kayma Geri̇lmeleri̇ni̇n Karişik Sonlu Elemanlarla Anali̇zi̇

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