Error estimation between simple, closed-form analytical formulae and full-scale FEM for interlaminar stress prediction in curved laminates

Most, Jermaine; Petry, D.

doi:10.1016/j.compstruct.2015.03.075

Cited by 17 publications

(9 citation statements)

References 18 publications

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“…In areas of high curvature, as for example in T-shaped stringers of aircraft wings, interlaminar stresses are pronounced and can lead to premature delamination failure [1,2]. To mitigate this debonding failure, it is crucial to robustly predict the stress fields in these curved laminated structures [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Most et al [3] emphasized the importance of accurate stress prediction for delamination failure in thick curved composites. The researchers compared different models in the literature and concluded that finite element (FE) models are able to predict stress fields accurately, but with enormous computational costs, whereas models based on first-order shear theory are easy and fast to use, but are not capable of predicting stresses with high accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Higher-order beam model for stress predictions in curved beams made from anisotropic materials

Thurnherr

Groh

Ermanni

2016

International Journal of Solids and Structures

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A higher-order beam model for analyzing the flexural response of curved multilayered beams with constant curvature and arbitrary constant thickness is developed. The new model is derived from the Hellinger-Reissner mixed variational statement and predicts inherently equilibrated 3D stresses from an equivalent single-layer model. As a starting assumption, the hoop stress is formulated as a series of higher-order stress resultants multiplied by Legendre polynomials. The governing equations are derived in a generalized manner such that the modeling order can be adjusted and is not defined a priori. Hence, the highest order Legendre polynomial determines the modeling order. The through-thickness shear and normal stresses are derived by integrating the generalized hoop stress in Cauchy's polar equilibrium equations. As a result, all stress fields are based on the same set of variables, thereby considerably reducing the computational effort. The three stress fields, and two displacements in the radial and hoop directions are used in the Hellinger-Reissner functional to derive a new set of stress-displacement relations. The enforcement of the classical membrane and bending equilibrium equations of curved beams in the Hellinger-Reissner functional guarantees that all interlaminar and surface traction equilibrium conditions are satisfied exactly. A validation study of a composite laminate using a high-fidelity 3D finite element model shows that the stresses are captured very accurately by the present model, but with much less computational effort than the finite element model. As a result, the developed model can provide rapid and accurate insights into the expected damage onset behavior of curved laminates.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Higher-order beam model for stress predictions in curved beams made from anisotropic materials

Thurnherr

Groh

Ermanni

2016

International Journal of Solids and Structures

View full text Add to dashboard Cite

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“…Most et al [3] highlighted the importance of accurately quantifying the stress distribution when analysing debonding failure in thick curved laminates, and various methods have been suggested in the literature to cal-culate stresses in curved laminates. Three-dimensional (3D) finite element models are of course the most natural option, but their computational cost is prohibitive for iterative design studies as many elements are required through the thickness of each layer to obtain accurate stress results [3].…”

Section: Introductionmentioning

confidence: 99%

“…In curved laminates, such as T-shaped stringers on aircraft wings, interlaminar stresses arise even for thin wall-thicknesses when the curved geometry is straightened and these interlaminar stresses are known drivers of delamination onset [1,2]. To account for delamination failure as early as possible in the design process, analytical tools that accurately predict the stress fields in a computationally efficient manner are key [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Three-dimensional (3D) finite element models are of course the most natural option, but their computational cost is prohibitive for iterative design studies as many elements are required through the thickness of each layer to obtain accurate stress results [3]. Computationally more efficient models include closed-form solutions based on first-order shear deformation theory [10,11], but these models do not account for higher-order terms and are therefore less accurate for thicker laminates or when layerwise anisotropy of the laminate increases [12].…”

Section: Introductionmentioning

confidence: 99%

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Investigation of failure initiation in curved composite laminates using a higher-order beam model

Thurnherr

Groh

Ermanni

2017

Composite Structures

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractCurved laminates are prone to delamination failure from applied bending moments that straighten out the laminate and induce tensile stresses in the unreinforced radial direction. These non-classical through-thickness stresses are important even for thinner configurations and need to be accounted for in the design of lightweight composite structures, preferably in a computationally efficient manner. Here, we investigate failure-inducing critical stresses for a number of curved laminates using a higher-order beam model derived from the Hellinger-Reissner mixed variational principle, which guarantees that the hoop, interlaminar shear and radial stresses are equilibrated. By solving the governing equations of the theory in the strong form using the pseudo-spectral differential quadrature method, the model is capable of predicting accurate 3D stress fields in curved laminates, even in the vicinity of loacalised features such as supported edges. The model is used alongside commonly used failure criteria to reproduce experimental failure initiation results found in the literature, and the comparison suggests that failure mode, location and load are all predicted accurately. Finally, failure maps that highlight the critical stress component for failure initiation are constructed. As the thickness of the curved laminate increases, the critical stress component transitions from intralaminar hoop stress to interlaminar shear or radial stress depending on the specific laminate configuration. These findings and failure maps collectively provide insights into the mechanics of failure initiation that should also prove useful for design purposes.

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Thermal shock analysis of functionally graded sandwich curved beams using a new layerwise theory

Pandey

Pradyumna

2021

Z Angew Math Mech

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This work for the first time presents a simple, accurate and straightforward finite element formulation that requires a C0 continuity of transverse displacement for the transient stress analysis of curved beams under thermal shock using a new layerwise theory. The FGM sandwich curved beam is considered to be made of three layers in which the top, middle and the bottom layer is considered to be made of pure ceramic, functionally graded material (FGM) core and pure metal constituents, respectively. The proposed new layerwise theory assumes a higher‐order displacement field for FGM core and first‐order displacement field for both top and bottom layers. The material properties are assumed to be temperature‐dependent. The governing differential equation for the present investigation is formulated using Hamilton's principle. A wide range of comparison studies are presented to establish the accuracy of the present layerwise finite element formulation. A parametric study is conducted to show the simplicity and wider applicability of the proposed formulation. It is shown here that by selecting an appropriate value of volume fraction index, core to facesheet thickness ratio, magnitude of thermal shock, curvature and thickness ratio, the transient thermal stresses induced in FGM sandwich curved beams can be reduced substantially.

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Error estimation between simple, closed-form analytical formulae and full-scale FEM for interlaminar stress prediction in curved laminates

Cited by 17 publications

References 18 publications

Higher-order beam model for stress predictions in curved beams made from anisotropic materials

Higher-order beam model for stress predictions in curved beams made from anisotropic materials

Investigation of failure initiation in curved composite laminates using a higher-order beam model

Thermal shock analysis of functionally graded sandwich curved beams using a new layerwise theory

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