C0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

Gherlone, Marco; Tessler, Alexander; Sciuva, Marco Di

doi:10.1016/j.compstruct.2011.05.015

Cited by 110 publications

(67 citation statements)

References 30 publications

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“…(35) are obtained in closed form by exact integration. This characteristic of the EEBZ2 element is in contrast the zigzag beam elements presented in [20][21][22][23] which require reduced integration of some stiffness matrix terms to avoid shear locking.…”

Section: -1) Introductionmentioning

confidence: 99%

“…Some researchers consider that the 1 C continuity requirement for the deflection field of the EBT is a drawback versus the simpler 0 C requirement of the TBT [18,20]. The main reason for this consideration is the theoretical difficulty for the 1 C approximation to satisfy the equilibrium of forces at clamped supports.…”

Section: -) Introductionmentioning

confidence: 99%

“…Different works [18][19][20] have shown that beam models requiring 1 C continuity for the deflection field, such as that presented in Eq. (1), have theoretical difficulties to represent correctly the shear strain and the shear stress distributions in a clamped support where the following kinematic conditions are required…”

Section: Remarkmentioning

confidence: 99%

“…Then the shear stress distribution is defined by simple piecewise-constant functions that approximate the true distribution in an average sense. A more accurate thickness distribution of the shear stress can be obtained via a post-processing of the axial stress field by integrating the equilibrium equations [20].…”

Section: -) Introductionmentioning

confidence: 99%

“…Based in the RZT different two and three-noded 0 C beam elements have been developed [20][21][22][23] for the analysis of multilayered composites and sandwich beams.…”

Section: -) Introductionmentioning

confidence: 99%

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Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

Capua

Oñate

2015

Composite Structures

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We present a new 2-noded beam element based on the refined zigzag theory and the classical EulerBernoulli beam theory for the static analysis of composite laminate and sandwich beams. The proposed element is able to take into account distortion effects due to shear elastic strains and can predict delamination. The element has four degrees of freedom per node. A 1 C cubic Hermite interpolation is used for the vertical deflection while a 0 C linear interpolation is employed for the other kinematics variables. The stiffness matrix and the load vector are calculated in explicit form using exact integration. The element is free from shear locking as confirmed with numerical tests on a wide range of the slenderness ratios. Numerical results show the ability of the EEBZ2 element to reproduce accurately the vertical deflection along the beam length and complex zigzag distributions of the axial displacement and the stresses across the thickness. Delamination effects are modeled by incorporating of an additional zigzag function corresponding to the kinematics of a zero thickness layer where delamination occurs. An example showing the capability of the new EEBZ2 element for accurately reproducing delamination effects is presented.

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Section: -1) Introductionmentioning

confidence: 99%

Section: -) Introductionmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: -) Introductionmentioning

confidence: 99%

“…Based in the RZT different two and three-noded 0 C beam elements have been developed [20][21][22][23] for the analysis of multilayered composites and sandwich beams.…”

Section: -) Introductionmentioning

confidence: 99%

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Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

Capua

Oñate

2015

Composite Structures

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A four‐noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory

Eijo

Oñate

Oller

2013

Numerical Meth Engineering

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A new bilinear four-noded quadrilateral element (called quadrilateral linear refined zigzag) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20-noded hexahedral elements.Peer ReviewedPostprint (published version

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An improved isoparametric quadratic element based on refined zigzag theory to compute interlaminar stresses of multilayered anisotropic plates

Biswas

Ray

2019

Numerical Meth Engineering

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Summary An improved eight‐noded isoparametric quadratic plate bending element based on refined higher‐order zigzag theory (RHZT) has been developed in the present study to determine the interlaminar stresses of multilayered composite laminates. The C0 continuous element has been formulated by considering warping function in the displacement field based on the RHZT. Shear locking phenomenon is avoided by considering substitute shear strain field. The continuity of transverse shear stresses cannot be ensured by the proposed zigzag formulation directly, and hence, the continuity conditions of transverse shear stresses have been established by using the three‐dimensional (3D) stress equilibrium equations in the present study. The transverse shear stresses are computed in a simplified manner using the differential equations of stress equilibrium. A finite element code is developed by using MATLAB software package. The performance of the present finite element model is validated by comparing the results with 3D elasticity solutions. The superiority of the proposed element in view of computational efficiency, simplicity, and accuracy has been examined by comparing the present solutions with those available in published literature using other elements.

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C0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

Cited by 110 publications

References 30 publications

Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

A four‐noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory

An improved isoparametric quadratic element based on refined zigzag theory to compute interlaminar stresses of multilayered anisotropic plates

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