The (3,2)-Mixed Refined Zigzag Theory for generally laminated beams: Theoretical development and C0 finite element formulation

Iurlaro, Luigi; Gherlone, Marco; Sciuva, Marco Di

doi:10.1016/j.ijsolstr.2015.07.028

Cited by 40 publications

(19 citation statements)

References 39 publications

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“…Substituting the expressions for U, W, and T from Equations (32,36) and (37) into Equation (31) and integrating by parts, and collecting the coefficients of u 0 , w 0 , c , t and b , the following equations of motion for the sandwich beam with soft core are obtained…”

Section: Governing Equations and Associated Boundary Conditionsmentioning

confidence: 99%

“…Therefore, this numerical example well validates the high accuracy of the present model in static analysis of symmetric sandwich beams. For the second numerical example, an asymmetric sandwich beam, which was previously studied in the literature, 32 is considered. The beam is simply supported at both ends and subjected to a transverse sinusoidal distributed load q(x) = q 0 sin( x/L) applied on the top surface.…”

Section: Bending Analysis Of Sandwich Beamsmentioning

confidence: 99%

“…Gherlone presented a comparison between two existing zigzag theories (Murakami' zigzag theory and RZT) for laminated composite and sandwich beams. More recently, Iurlaro et al presented a mixed RZT (

{italicRZT}_{((), 3, 2)}^{((), m)}

) for laminated sandwich beams based on Reissner's mixed variational theorem (RMVT), and the accuracy of

{italicRZT}_{((), 3, 2)}^{((), m)}

for the prediction of the displacement and stress distributions was well demonstrated. The unknown variables of zigzag theories are independent of the number of layers, and with the introduction of zigzag functions, zigzag theories can provide better predictions for local responses in laminated sandwich beams compared with global ESL theories.…”

Section: Introductionmentioning

confidence: 99%

“…Equations(43)(44)(45)(46)(47) into Equations(32,36) and(37), and using the Hamilton principle from Equation(31), the dynamic governing equation of the sandwich beam element takes the following form M eüe + K e u e = q e ,…”

mentioning

confidence: 99%

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A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

Ren

Zhao

2019

Numerical Meth Engineering

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Summary This article presents a novel formulation for sandwich beams with soft core based on a layerwise description of continuous transverse shear stress field. The transverse shear stress field is assumed to follow a quadratic distribution in thick face layers and a uniform distribution in soft core. Based on stress‐strain relations, transverse shear strain is obtained, and in‐plane displacement field is determined by taking the integral of the transverse shear stain. By enforcing interlaminar displacement continuity, an explicit displacement field expression containing only displacement variables is formulated. In this formulation, interlaminar continuity conditions of displacement and transverse shear stress are satisfied simultaneously, and transverse shear and crosssectional warping effects in thick face layers are accurately taken account. To show characteristics and advantages of the present model, some classical theoretical models are further developed under different kinematic assumptions. The governing equations are derived using Hamilton principle, and finite element solutions for static and dynamic analysis of sandwich beams are presented. Comparisons with exact solution and other well‐known solutions, well demonstrate high accuracy of the present model for sandwich beams with different features. Besides, numerical discussions further reflect accuracy advantages of the present model in static and dynamic analysis of sandwich beams.

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Section: Governing Equations and Associated Boundary Conditionsmentioning

confidence: 99%

Section: Bending Analysis Of Sandwich Beamsmentioning

confidence: 99%

{italicRZT}_{((), 3, 2)}^{((), m)}

) for laminated sandwich beams based on Reissner's mixed variational theorem (RMVT), and the accuracy of

{italicRZT}_{((), 3, 2)}^{((), m)}

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

Ren

Zhao

2019

Numerical Meth Engineering

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“…These lower order two-and threenoded elements were then extended to an entire class of higher-order elements by Di Sciuva et al [37]. The same interpolation scheme was also used in a version of RZT (m) with cubic in-plane displacement field and quadratic transverse displacement [38].…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient beam elements for accurate stresses in sandwich laminates and laminated composites with delaminations

Groh

Tessler

2017

Computer Methods in Applied Mechanics and Engineering

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Effective Modeling of Interlaminar Damage in Multilayered Composite Structures Using Zigzag Kinematic Approximations

Massabò¹

2020

Handbook of Damage Mechanics

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The chapter gives an overview of the main approaches formulated to model interlaminar damage and imperfections in layered structures using zigzag kinematic approximations and concentrates on the models which have been extended to analyze delamination damage progression. The zigzag theories are structural theories which assume different kinematic fields in the layers, to account for zigzag effects associated to their elastic mismatch, and use a fixed number of variables that is independent of the number of layers. Interfacial imperfections, interlayer damage, and delaminations are included using the compliant layer concept, imperfect interfaces, or by adding additional variables.

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The (3,2)-Mixed Refined Zigzag Theory for generally laminated beams: Theoretical development and C0 finite element formulation

Cited by 40 publications

References 39 publications

A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

Computationally efficient beam elements for accurate stresses in sandwich laminates and laminated composites with delaminations

Effective Modeling of Interlaminar Damage in Multilayered Composite Structures Using Zigzag Kinematic Approximations

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