Free-edge stress fields in cylindrically curved cross-ply laminated shells

Kappel, Andreas; Mittelstedt, Christian

doi:10.1016/j.compositesb.2019.107693

Cited by 11 publications

(15 citation statements)

References 28 publications

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“…Considering the load case in Fig. 1, the three-dimensional displacement field of each numerical layer (k) can be expressed as follows [5,6]:…”

Section: Semi-analytical Approachmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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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“…Considering the load case in Fig. 1, the three-dimensional displacement field of each numerical layer (k) can be expressed as follows [5,6]:…”

Section: Semi-analytical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Current practice limits the understanding of composite behavior only to plane stress assumptions, and even if such approximations is true for thin laminates, reliability of numerical prediction of structural response is still quite poor (Kappel and Mittelstedt 2020).…”

Section: Three-dimensional Aspectsmentioning

confidence: 99%

“…Such stress distribution leads to Mode I openings, which is often critical as bonding properties of matrix are quite poor towards such failure mode, as showed in Figure 3 (Lorriot et al 2003). An analysis method for the computation of the threedimensional stress fields in cylindrically curved symmetric or unsymmetric cross-ply laminated shells under bending load is discussed by Kappel and Mittelstedt (2020).…”

Section: Three-dimensional Aspectsmentioning

confidence: 99%

Recent Industrial Developments of Marine Composites Limit States and Design Approaches on Strength

Barsotti

Gaiotti

Rizzo

2020

J. Marine. Sci. Appl.

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To further exploit the potential of marine composites applications in building ship hulls, offshore structures, and marine equipment and components, design approaches should be improved, facing the challenge of a more comprehensive and explicit assessment of appropriately defined limit states. The structure ultimate/limit conditions shall be verified in principle within the whole structural domain and throughout the ship service life. What above calls for extended and reliable materials characterization on the one hand and for accurate and wide-ranging procedures in structural analyses. This paper presents an overview of recent industrial developments of marine composites limit states assessments and design approaches, as available in open literature, focusing on pleasure crafts and yachts as well as navy ships and thus showing a starting point to fill the gap in this respect. After a general introduction about composites characterization techniques, current design practice and rule requirements are briefly summarized. Both inter-ply and intra-ply failure modes and corresponding limit states are then presented along with recently proposed assessment approaches. Three-dimensional aspects in failure modes and manufacturing methods have been identified as the main factors influencing marine composite robustness. Literature review highlighted also fire resistance and hybrid joining techniques as significant issues in the use of marine composites.

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Semi‐analytical assessment of free‐edge stress fields in circular cylindrical cross‐ply laminated shells subjected to transverse loads

Kappel

Mittelstedt

2021

Proc Appl Math & Mech

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The present work deals with the semi‐analytical assessment of the three‐dimensional stress fields in circular cylindrical symmetrically and unsymmetrically laminated cross‐ply shells undergoing different transverse loads. Starting from a closed‐form plane‐strain analysis in the innermost regions of the laminated shell, the elasticity solution is upgraded by a higher‐order displacement‐based approach which enables the developed method to capture the three‐dimensional stress state due to the free‐edge effect in thick, finite‐length composite laminated shells. In order to realize this, the shell panel is discretized into a number of numerical layers with respect to the thickness direction. By introducing a priori unknown displacement functions in the interfaces of those numerical plies and by making use of the principle of minimum elastic potential, a system of coupled ordinary differential equations is obtained, which, however, can be solved by utilizing the state‐space approach. The results of the developed analysis method are verified through comparison with existing analytical approaches in the literature and finite element simulations and it can be noted that the semi‐analytical approach works with comparable accuracy, however, only at a fraction of the computational effort coming with full‐scale three‐dimensional finite element computations.

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Free-edge stress fields in cylindrically curved cross-ply laminated shells

Cited by 11 publications

References 28 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

Recent Industrial Developments of Marine Composites Limit States and Design Approaches on Strength

Semi‐analytical assessment of free‐edge stress fields in circular cylindrical cross‐ply laminated shells subjected to transverse loads

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