A partial hybrid stress solid-shell element for the analysis of laminated composites

Rah, K.; Paepegem, Wim Van; Habraken, Anne Marie; Degrieck, Joris

doi:10.1016/j.cma.2011.08.020

Cited by 19 publications

(8 citation statements)

References 74 publications

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“…Here letters , , and refer to resultants of membrane stresses, bending stresses, and transverse shear stresses. Based on (10) and (11), the stress resultants can be defined by…”

Section: Hierarchical Shape Functionsmentioning

confidence: 99%

“…Acknowledging the need of three-dimensional shell elements, several formulations have been presented based on a degenerated shell concept [7,8]. Since 1990s, some solid-shell approaches, which have some benefits as compared to the degenerated shell element because of the simplicity of their kinematics, have been introduced by some researchers [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

Ahn

Yang

Woo

2015

Mathematical Problems in Engineering

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We introduce higher-order cylindrical shell element based on ESL (equivalent single-layer) theory for the analysis of laminated composite shells. The proposed elements are formulated by the dimensional reduction technique from three-dimensional solid to two-dimensional cylindrical surface with plane stress assumption. It allows the first-order shear deformation and considers anisotropic materials due to fiber orientation. The element displacement approximation is established by the integrals of Legendre polynomials with hierarchical concept to ensure theC0-continuity at the interface between adjacent elements as well asC1-continuity at the interface between adjacent layers. For geometry mapping, cylindrical coordinate is adopted to implement the exact mapping of curved shell configuration with a constant curvature with respect to any direction in the plane. The verification and characteristics of the proposed element are investigated through the analyses of three cylindrical shell problems with different shapes, loadings, and boundary conditions.

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“…Here letters , , and refer to resultants of membrane stresses, bending stresses, and transverse shear stresses. Based on (10) and (11), the stress resultants can be defined by…”

Section: Hierarchical Shape Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

Ahn

Yang

Woo

2015

Mathematical Problems in Engineering

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“…(20)(21)28), the element stiffness matrix Ke for element QCSS8 with domain Ωe used in the modeling of laminated composites takes the following form.…”

Section: Eflcient Analysis Of the Laminated Composites By Element Qcss8mentioning

confidence: 99%

“…Since 1964, the hybrid [24] and the mixed element formulation [25,26] have been used for the solid-shell element. For instance, Rah et al [21] proposed the partial hybrid stress solid-shell element based on the modified Hu-Washizu variational principle, where displacements, strains and stresses can be approximated independently from each other, therefore providing the highest possible flexibility in selecting the trial functions for primary variables. And eight partial stress modes are used to capture interlaminar stresses accurately in the laminated composite plate.…”

Section: Introductionmentioning

confidence: 99%

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Displacement and stress analysis of laminated composite plates using an eight-node quasi-conforming solid-shell element

Wang

Shi

Wang

2017

Curved and Layered Structures

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This paper presents the efficient modeling and analysis of laminated composite plates using an eightnode quasi-conforming solid-shell element, named as QCSS8. The present element QCSS8 is not only lockingfree, but highly computational efficiency as it possesses the explicit element stiffness matrix. All the six components of stresses can be evaluated directly by QCSS8 in terms of the 3-D constitutive equations and the appropriately assumed element strain field. Several typical numerical examples of laminated plates are solved to validate QCSS8, and the resulting values are compared with analytical solutions and the numerical results of solid/solidshell elements of commercial codes computed by the present authors in which fine meshes were used. The numerical results show that QCSS8 can give accurate displacements and stresses of laminated composite plates even with coarse meshes. Furthermore, QCSS8 yields also accurate transverse normal strain which is very important for the evaluation of interlaminar stresses in laminated plates. Since each lamina of laminated composite plates can be modeled naturally by one or a few layers of solidshell elements and a large aspect ratio of element edge to thickness is allowed in solid-shell elements, the present solid-shell element QCSS8 is extremely appropriate for the modeling of laminated composite plates.

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Eight‐node nonconforming hexahedral element based on reverse adjustment to patch test for solids, beams, plates, and shells

Liu

et al. 2019

Numerical Meth Engineering

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An eight-node 24-DOF nonconforming brick element is developed. It contains nine internal modes, including quadratic and cubic forms, wherein each local coordinate component is at most quadratic. The reverse adjustment to patch test is applied to quadratic modes to eliminate shear locking. To rectify the ill-condition of the element stiffness matrix caused by irregular element shape such as large aspect ratio, a modified regularization method is introduced. It is based on Riley's series expansion of the solution to the ill-conditioned linear system and is coupled in the condensation procedure of the internal degrees of freedom. With the regularization parameter = 10 −3 , the first three terms are enough, which are achieved by two additional refinements in addition to the initial value. To validate the accuracy and robustness, a variety of linear benchmark tests is conducted on solid, beam, plate, and shell structures. The results are in good agreement with the reference solutions, provided the mesh is not too coarse or distorted. The overall performance implies that the new element is competitive with almost all the elements cited, including solid, solid-shell, and shell elements, and is a potential one-size-fits-all solution to linear structure problems. KEYWORDSill-conditioned linear system, nonconforming element, regularization, reverse adjustment Int J Numer Methods Eng. 2019;119:361-382.wileyonlinelibrary.com/journal/nme

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A partial hybrid stress solid-shell element for the analysis of laminated composites

Cited by 19 publications

References 74 publications

ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

Displacement and stress analysis of laminated composite plates using an eight-node quasi-conforming solid-shell element

Eight‐node nonconforming hexahedral element based on reverse adjustment to patch test for solids, beams, plates, and shells

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