A hierarchic 3D finite element for laminated composites

Kuhlmann, G.; Rolfes, Raimund

doi:10.1002/nme.1060

Cited by 19 publications

(14 citation statements)

References 37 publications

(36 reference statements)

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“…As investigated by Kuhlmann and Rolfes [3] the stacked brick element yields a satisfactory result for transverse normal stresses 33 σ . Transverse shear stresses 13 τ and 23 τ however contradict the exact solution since the step like displacement distribution over the thickness of composite structures can not be reproduced.…”

Section: Discussionmentioning

confidence: 87%

“…The failure behavior of Ultra Thick Laminates (UTL) is investigated using 3D stacked brick elements implemented in MSC Marc/ Mentat [2]. Due to the linear shape function of the element, transverse shear stresses can not be calculated accurately on a ply level, as shown by Kuhlmann and Rolfes [3]. A reasonable prediction of these stresses is however achieved by discretising the components over thickness.…”

Section: Figure 1 Main Landing Gear With Metallic Side Stay Fitting (mentioning

confidence: 99%

“…υ is primarily based on sources found in the literature, [3], [9]. Similar properties as for G1157 with RTM6 are assumed; see [12] and Table 2.…”

Section: Materials and Processmentioning

confidence: 99%

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Testing and analysis of ultra thick composites

Zimmermann¹,

Zenkert

Siemetzki³

2010

Composites Part B: Engineering

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Testing and analysis of ultra thick composites. ABSTRACT: For the development of a composite main landing gear fitting in carbon fiber reinforced plastics the behavior and performance of Ultra Thick Laminate components is investigated. Material thicknesses exceeds 60mm. For the purpose of validation a test program is arranged using T-cross sections subjected to multiple load cases. The components are manufactured entirely with non crimped fabrics (NCF) using an adapted open mould manufacturing process. In addition to these T-Sections large full scale subcomponents of the entire fitting are manufactured and tested. As main topic of this paper standard FE methods are investigated and validated for thick structures using the generated test results. Due to the presence of transverse shear and normal stresses a 3D modeling approach is chosen. Transverse shear and normal stresses are indentified as main failure cause and failure is mainly initiated in the curved regions. Solid composite brick elements offer an efficient way to model thick structures. These are incapable of calculating accurate shear stresses on a ply level; usable results are however achieved by discretisation of the component with multiple elements over thickness. In addition stress gradients in the failure region are small; stress variations on a ply level are minimal. Out of plane material properties are not available and initial assumptions are made. Material correction factors (degradation) are introduced and discussed. Composites

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Section: Discussionmentioning

confidence: 87%

Section: Figure 1 Main Landing Gear With Metallic Side Stay Fitting (mentioning

confidence: 99%

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Testing and analysis of ultra thick composites

Zimmermann¹,

Zenkert

Siemetzki³

2010

Composites Part B: Engineering

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“…For example, the transverse shear stresses typically violate the C 0 z -requirements of interfacial traction continuity. More accurate transverse stresses can be recovered a posteriori by integrating the in-plane stresses in Cauchy's 3D indefinite equilibrium equations [21], and various techniques exist to achieve this within the displacement-based FEM [22][23][24][25]. The disadvantage of this technique is that the post-processed transverse stresses no longer satisfy the underlying equilibrium equations, and are therefore variationally inconsistent.…”

Section: Displacement-based Theoriesmentioning

confidence: 99%

“…In general, this transformation follows the rule ê x e y = n x −n y n y n x ê n e s (A. 25) whereê is a unit vector.…”

Section: Appendix a Derivation Of Hr Governing Equationsmentioning

confidence: 99%

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part I: Model formulation

Groh

2016

Composite Structures

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Current consensus suggests a trade-off for predicting accurate 3D stress fields in multilayered plates. Relatively expensive layerwise models facilitate accurate stress predictions from underlying models assumptions, whereas more efficient equivalent single-layer theories often rely on variationally inconsistent transverse stresses from recovery steps. In contrast, we show that variationally consistent 3D stress fields are predicted from an equivalent single-layer model using a contracted form of the Hellinger-Reissner functional. Notably, this procedure facilitates computationally efficient analysis of 3D heterogeneous plates, i.e. laminates comprising layers with material properties that differ by multiple orders of magnitude and that can also vary continuously in-plane. The model includes effects of higher-order transverse shearing and zig-zag deformations by expressing the in-plane stress field as a Taylor series expansion of global and local higher-order stress resultants. Equilibrated transverse stress assumptions are derived from Cauchy's 3D equilibrium equations, which identically satisfy the interfacial and surface traction equilibrium conditions when applied within a variational statement that enforces the 3D equilibrium equations as constraints, hence the Hellinger-Reissner mixed-variational statement. By using inherently equilibrated stress fields as model assumptions, it is shown that only the classical membrane and bending equilibrium equations have to be enforced explicitly. As a result, a contracted Hellinger-Reissner functional emerges that requires fewer displacement Lagrange multipliers than when independent stress fields are assumed. The governing equations are derived in a generalised framework such that the order of the model, and hence its accuracy, increases automatically when implemented in a computer code. By refining the order of the stress assumptions, the model is adaptable to plate-like structures ranging from thin engineering laminates to highly heterogeneous, thick laminates comprising straight-fibre or tow-steered variable-stiffness laminates, foam, honeycomb or other compliant layers.

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Layerwise zig‐zag model with selective refinement across the thickness

Icardi

Ferrero

2010

Numerical Meth Engineering

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SUMMARYIn this paper a multilayered model with a hierarchic representation of displacements is developed. The representation, which is based on Jacobi polynomials, can be different for any computational layer, from point to point across the thickness and for any functional d.o.f., aimed at adapting the model to the local variations of solutions. This refinement is obtained by keeping the number of d.o.f. unchanged. The displacements are described through a zig-zag representation in any computational layer, in order to fulfil the stress contact conditions at the inner interfaces. A displacement-based version of the model with the six displacement components at the upper and lower faces as functional d.o.f. and a mixed version with the six interlayer stress components are developed. The numerical results mainly concern simply supported thick sandwich beams under sinusoidal loading, but results are also presented for thin cantilevered sandwich beams and laminated plates. The model accurately predicts displacements and stress fields using a single computational layer, even when material properties abruptly change. The computational effort for the adaptive representation is advantageous by the viewpoint with respect to a fixed representation or with the use of post-processing methods.

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A hierarchic 3D finite element for laminated composites

Cited by 19 publications

References 37 publications

Testing and analysis of ultra thick composites

Testing and analysis of ultra thick composites

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part I: Model formulation

Layerwise zig‐zag model with selective refinement across the thickness

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