Rotation-free Bernstein–Bézier elements for thin plates and shells — development and validation

Ludwig, Thomas; Hühne, Christian; Lorenzis, Laura De

doi:10.1016/j.cma.2019.01.039

Cited by 16 publications

(6 citation statements)

References 31 publications

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“…17right). The local snap-through buckling may already lead to premature collapse of a cylinder which was shown by Ludwig et al [76] by applying dynamic analysis, see Fig. 15 (left).…”

Section: Reduced Stiffness Analysismentioning

confidence: 80%

Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression

Wagner

Hühne

Elishakoff

2020

Thin-Walled Structures

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This article contains examples to demonstrate the use of different design concepts for cylindrical shells under axial compression. The examples are based on shells which were manufactured according to electroplating, machining, welding (isotropic cylinders) and prepreg hand layup on a mandrel (composite cylinders). Three of the four shell series are characterized by pure elastic buckling and one shell series buckled in the elastic-plastic region. All relevant data for the numerical analysis are described in the article and summarized in the Elsevier repository of this article (geometry, material, measured imperfection data and Python-ABAQUS scripts). The design concepts are based on the geometric imperfection signatures, probabilistic and deterministic lower-bound methods. The design concepts are representative for the development of design approaches for imperfection sensitive shells from the early 1980 to the late 2010 and are validated with experimental data. Recently developed design lower-bound curves for axially loaded cylinders are presented and compared with currently used design criteria like the Eurocode EN 1993-1-6 and the NASA SP-8007. The results of this article show that the design of imperfection sensitive cylinders has been significantly improved in the last 30 years.

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“…17right). The local snap-through buckling may already lead to premature collapse of a cylinder which was shown by Ludwig et al [76] by applying dynamic analysis, see Fig. 15 (left).…”

Section: Reduced Stiffness Analysismentioning

confidence: 80%

Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression

Wagner

Hühne

Elishakoff

2020

Thin-Walled Structures

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“…5 (middle right). For large-amplitude dimple imperfections, the snap-through induced local buckling event may cause early global collapse of the shell which was validated in [46] and shown with nonlinear dynamic simulations in [71]. Therefore, the minimum local buckling load is defined as design load within the framework of the SBPA.…”

Section: Stacking Sequencementioning

confidence: 94%

Decision tree-based machine learning to optimize the laminate stacking of composite cylinders for maximum buckling load and minimum imperfection sensitivity

Wagner

Köke

Dähne

et al. 2019

Composite Structures

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Köke, H.; Dähne, S.; Hühne, C.; Niemann, S.; Khakimova, R. Decision tree-based machine learning to optimize the laminate stacking of composite cylinders for maximum buckling load and minimum imperfection sensitivity, Composite Structures AbstractLaunch-vehicle primary structures like cylindrical shells are increasingly being built as monolithic composite and sandwich composite shells. These imperfection sensitive shells are subjected to axial compression due to the weight of the upper structural elements and tend to buckle under axial compression. In the case of composite shells the buckling load and imperfection sensitivity depend on the laminate stacking sequence.Within this paper multi-objective optimizations for the laminate stacking sequence of composite cylinder under axial compression are performed. The optimization is based on different geometric imperfection types and a brute force approach for three different ply angles. Decision tree-based machine learning is applied to derive general design recommendations which lead to maximum buckling load and a minimum imperfection sensitivity.The design recommendation are based on the relative membrane, bending, in-plane shear and twisting stiffnesses. Several optimal laminate stacking sequences are generated and compared with similar laminate configurations from literature. The results show that the design recommendations of this article lead to high-performance cylinders which outperform comparable composite shells considerably. The results of this article may be the basis for future lightweight design of sandwich and monolithic composite cylinders of modern launch-vehicle primary structures. t Wall thickness of cylindrical shells tply Ply thickness u Axial shortening  Ply angle  Ply angle  Ply angle  knockdown factor Wilkins [1975]

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“…The use of simplex elements in an isogeometric framework has been of interest in recent years. Similar work that has already been carried out include the implementation of Bézier triangles in the framework of IGA for applications in vibrations [16], thin plates and shells [20,42], damage mechanics [17] and phase separation [43]. The increase of continuity to C 1 Bézier triangles has been studied in [11,40].…”

Section: Introductionmentioning

confidence: 94%

CAD-compatible structural shape optimization with a movable Bézier tetrahedral mesh

López

Anitescu

Rabczuk

2020

Computer Methods in Applied Mechanics and Engineering

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Rotation-free Bernstein–Bézier elements for thin plates and shells — development and validation

Cited by 16 publications

References 31 publications

Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression

Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression

Decision tree-based machine learning to optimize the laminate stacking of composite cylinders for maximum buckling load and minimum imperfection sensitivity

CAD-compatible structural shape optimization with a movable Bézier tetrahedral mesh

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