Equivalent Single Layer, Zig-Zag, and Layer Wise theories for variable angle tow composites based on the Generalized Unified Formulation

Demasi, Luciano; Biagini, Giacomo; Vannucci, Federico; Santarpia, Enrico; Cavallaro, Rauno

doi:10.1016/j.compstruct.2017.06.033

Cited by 45 publications

(25 citation statements)

References 37 publications

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“…Also, it does not depend on the mechanical properties of layers and is often presented as an effective enrichment of the displacement field, regardless of the type of stacking sequence. Numerous studies in literature [14,29] show that superior representation of displacements and stresses, combined with less computational cost, can be achieved by including MZZF for constant-and variable-stiffness laminates and sandwich structures. However, for symmetric (with more than three layers) and unsymmetric sandwich lay-ups, or for laminates with externally weak layers, MZZF fails to predict the stress response accurately [19].…”

Section: B Zig-zag Kinematicsmentioning

confidence: 99%

“…The derivatives of material stiffness coefficients can be computed exactly as given in Ref. [29] or by employing finite differences.…”

Section: E Posteriori Calculation Of the Transverse Stressesmentioning

confidence: 99%

“…The accuracy of the transverse stresses evaluated via Hooke's law is not acceptable when ESL models are employed. Moreover, transverse stresses calculated by integration of the equilibrium equations were shown to provide, in general, the best overall results, as [29]. For this reason, the in-plane stresses are herein calculated by using Hooke's law, whereas the transverse stresses are obtained via integration of the equilibrium equations.…”

Section: A Constant-stiffness Composite Laminatesmentioning

confidence: 99%

“…Demasi et al [29] formulated ESL models refined with MZZF and LW models based on the Generalized Unified Formulation (GUF) [30][31][32], and benchmarked the performance of the different approaches. However, the study mainly focused on highlighting the computational efficiency gains over 3D FE models.…”

Section: Introductionmentioning

confidence: 99%

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Efficient 3D Stress Capture of Variable-Stiffness and Sandwich Beam Structures

et al. 2019

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Accurate modeling of composite structures is important for their safe application under different loading conditions. To provide accurate predictions of three-dimensional (3D) stress fields in an efficient computational framework, we employ a modeling approach that builds upon the recently developed hierarchical Serendipity Lagrange finite elements. The approach provides Layer-Wise (LW) and Equivalent Single-Layer (ESL) models for analyzing constantand variable-stiffness laminated beam structures. To enhance the capability of the ESL model, two ZigZag (ZZ) functions, namely Murakami's ZZ function (MZZF) and the Refined ZZ theory function (RZT), are implemented. For constant-stiffness laminated and sandwich beams, the RZT ZZ function predicts the structural response more accurately than the MZZF. However, for variable-stiffness laminated structures, the applicability of RZT remains unknown and its accuracy is therefore tested within the present formulation. Results obtained are validated against 3D closed-form and 3D Finite Element (FE) solutions available from the literature. For similar levels of accuracy, significant gains in computational efficiency are achieved over 3D FE and LW models by using the ESL approach with RZT ZZ functions.

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Section: B Zig-zag Kinematicsmentioning

confidence: 99%

“…The derivatives of material stiffness coefficients can be computed exactly as given in Ref. [29] or by employing finite differences.…”

Section: E Posteriori Calculation Of the Transverse Stressesmentioning

confidence: 99%

Section: A Constant-stiffness Composite Laminatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient 3D Stress Capture of Variable-Stiffness and Sandwich Beam Structures

et al. 2019

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“…In this regard, several attempts have been made to develop computationally more efficient numerical models. Demasi et al [32] formulated equivalent single-layer, zigzag and layer-wise models based on the Generalised Unified Formulation (GUF) [33] and benchmarked the performance of the different approaches. However, the study mainly focused on highlighting the computational efficiency gains over 3D FE models.…”

Section: Introductionmentioning

confidence: 99%

On the accuracy of localised 3D stress fields in tow-steered laminated composite structures

Patni

Minera

Groh

et al. 2019

Composite Structures

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Variable Angle Tow (VAT) composites offer increased freedom for tailoring material properties compared to traditional straight-fibre composites. This increased freedom leads to greater design flexibility for enhanced structural performance but comes at the cost of more complex, spatially-varying displacement, strain and stress fields. To maximise the utility of VAT composites, a computationally efficient, yet accurate, numerical framework is needed. To this end, we employ a modelling approach that builds upon the recently developed, hierarchical Serendipity Lagrange finite elements. Three-dimensional (3D) stress distribution is obtained using the present modelling technique and verified against 3D finite element solutions, as well as other formulations available in the literature. A key advantage of the present approach is the ability to predict accurate 3D stress fields efficiently, i.e. with reduced computational effort, including around local features such as geometric, kinematic or constitutive boundaries. Moreover, the present work concerns the peculiarities of commonly used mathematical expressions for describing spatially varying fibre orientations across VAT laminates. The presence of an absolute value in the function used to describe fibre orientation can lead to discontinuities in fibre angle slope and curvature. In turn, these discontinuities lead to mathematical singularities in the constitutive relations along the laminate. If this singularity is not appropriately modelled as a boundary of the continuum, but rather as an interior point of the continuum, stresses may be predicted inaccurately. Compared to other models in the literature, our method is capable of unveiling detailed 3D stresses readily and accurately also in the vicinity of this singularity.

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Introduction

Mikhasev¹,

Altenbach²

2019

Advanced Structured Materials

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Equivalent Single Layer, Zig-Zag, and Layer Wise theories for variable angle tow composites based on the Generalized Unified Formulation

Cited by 45 publications

References 37 publications

Efficient 3D Stress Capture of Variable-Stiffness and Sandwich Beam Structures

Efficient 3D Stress Capture of Variable-Stiffness and Sandwich Beam Structures

On the accuracy of localised 3D stress fields in tow-steered laminated composite structures

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