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Humayun R H Kabir - One of the best experts on this subject based on the ideXlab platform.
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Frequency Response of a Three-Node Finite Element for Thick and Thin Plates:
Journal of Vibration and Control, 2020Co-Authors: Humayun R H Kabir, Abdullateef M. Al-khaleefiAbstract:A Shear-Locking free isoparametric three-node triangular finite element is presented to study the frequency response of moderately thick and thin plates. Reissner/Mindlin theory that incorporates Shear deformation effects is included into the element formulation. A Shear correction term is introduced in transverse Shear strain components to avoid the Shear-Locking phenomenon. The element is developed with a full integration scheme, hence, the element remains kinematically stable. Natural frequencies and mode shapes are obtained and compared with the available analytical and finite element solutions.
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Free vibration response of a three-node Shear flexible finite element for moderately deep shells
Finite Elements in Analysis and Design, 2003Co-Authors: Humayun R H KabirAbstract:A free vibration response of a Shear-Locking free isoparametric Shear flexible three-node triangular finite element suitable for moderately deep shell configurations is presented. The moderately deep shell configuration based on the Sanders' shell theory is incorporated into the element formulation. A Shear correction term is introduced in transverse Shear strain components to alleviate the Shear-Locking phenomenon. The element is developed with a full integration scheme. Natural frequencies and mode shapes are obtained and compared for doubly curved shells with the available analytical and finite element solutions.
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a Shear Locking free robust isoparametric three node triangular finite element for moderately thick and thin arbitrarily laminated plates
Computers & Structures, 1995Co-Authors: Humayun R H KabirAbstract:A Shear-Locking free robust isoparametric three-node triangular finite element is developed for advanced fiber-reinforced arbitrarily laminated moderately-thick and thin plates. The strain-displacement relations are based on Reissner and Mindlin plate theory that accounts for transverse Shear deformations into the plate formulation. A Shear correction term is introduced into the finite element formulation to circumvent the Shear Locking effect. Numerical results, for illustration purposes, are presented for a simply-supported plate with cross-ply laminations subjected to uniform transverse loads, constituting study of convergence and Shear Locking effects on transverse displacement and moment, and their variations for various parametric effects.
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a Shear Locking free robust isoparametric three node triangular element for general shells
Computers & Structures, 1994Co-Authors: Humayun R H KabirAbstract:Abstract A Shear-Locking free isoparametric three-node triangular finite element suitable for both moderately thick and very thin shells is developed. Reissner and Mindlin theory that incorporates transverse Shear deformation into the shell formulations is considered. The theory introduces five degrees of freedom, three translations and two rotations, at each node of the element. This isoparametric-based element is well known for its Shear-Locking effects in thin situations when a full or reduced integration scheme is used. These Shear-Locking effects are eliminated by imposing a constant transverse Shear strain criterion and introducing a Shear correction expression in the formulations. The element has shown a robustness in all types of triangular mesh configurations. The numerical results include convergence tests for transverse displacement and moment for shells of rectangular planform for moderately thick and very thin situations. These numerical results are compared with the recently available analytical solutions for moderately-thick and thin shells and Reissner and Mindlin theory-based finite element solutions.
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a Shear Locking free isoparametric three node triangular finite element for moderately thick and thin plates
International Journal for Numerical Methods in Engineering, 1992Co-Authors: Humayun R H KabirAbstract:A Shear Locking free isoparametric three-node triangular plate bending element, KEYA, is developed. Reissner/Mindlin theory that incorporates transverse Shear deformation is assumed in the plate formulation. Numerical results include patch tests, convergence of transverse displacement and stress resultants, and variations of them for various parametric effects on cantilever, simply supported and clamped plates.
R A F Valente - One of the best experts on this subject based on the ideXlab platform.
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a new approach to reduce membrane and transverse Shear Locking for one point quadrature shell elements linear formulation
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Rui P R Cardoso, Jeong Whan Yoon, R A F ValenteAbstract:In the last decade, one-point quadrature shell elements attracted many academic and industrial researchers because of their computational performance, especially if applied for explicit finite element simulations. Nowadays, one-point quadrature finite element technology is not only applied for explicit codes, but also for implicit finite element simulations, essentially because of their efficiency in speed and memory usage as well as accuracy. In this work, one-point quadrature shell elements are combined with the enhanced assumed strain (EAS) method to develop a finite element formulation for shell analysis that is, simultaneously, computationally efficient and more accurate. The EAS method is formulated to alleviate Locking pathologies existing in the stabilization matrices of one-point quadrature shell elements. An enhanced membrane field is first constructed based on the quadrilateral area coordinate method, to improve element's accuracy under in-plane loads. The finite element matrices were projected following the work of Wilson et al. (Numerical and Computer Methods in Structural Mechanics, Fenven ST et al. (eds). Academic Press: New York, 1973; 43–57) for the incompatible modes approach, but the present implementation led to more accurate results for distorted meshes because of the area coordinate method for quadrilateral interpolation. The EAS method is also used to include two more displacement vectors in the subspace basis of the mixed interpolation of tensorial components (MITC) formulation, thus increasing the dimension of the null space for the transverse Shear strains. These two enhancing vectors are shown to be fundamental for the Morley skew plate example in particular, and in improving the element's transverse Shear Locking behaviour in general. Copyright © 2005 John Wiley & Sons, Ltd.
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development of Shear Locking free shell elements using an enhanced assumed strain formulation
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Renato Natal Jorge, R A F Valente, P AreiasAbstract:The degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse Shear Locking effects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse Shear terms of the strain field. In the first part of the work the analysis of the null transverse Shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking effects are then justified by the inability of the null transverse Shear strain subspace, implicitly defined by a given finite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse Shear strain subspace is provided by the EAS method, enforcing Kirchhoff hypothesis for low thickness values and leading to a framework for the development of Shear-Locking-free shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation. Copyright © 2001 John Wiley & Sons, Ltd.
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Development of Shear Locking‐free shell elements using an enhanced assumed strain formulation
International Journal for Numerical Methods in Engineering, 2001Co-Authors: Renato Natal Jorge, R A F Valente, P AreiasAbstract:The degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse Shear Locking effects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse Shear terms of the strain field. In the first part of the work the analysis of the null transverse Shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking effects are then justified by the inability of the null transverse Shear strain subspace, implicitly defined by a given finite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse Shear strain subspace is provided by the EAS method, enforcing Kirchhoff hypothesis for low thickness values and leading to a framework for the development of Shear-Locking-free shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation. Copyright © 2001 John Wiley & Sons, Ltd.
P Areias - One of the best experts on this subject based on the ideXlab platform.
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development of Shear Locking free shell elements using an enhanced assumed strain formulation
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Renato Natal Jorge, R A F Valente, P AreiasAbstract:The degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse Shear Locking effects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse Shear terms of the strain field. In the first part of the work the analysis of the null transverse Shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking effects are then justified by the inability of the null transverse Shear strain subspace, implicitly defined by a given finite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse Shear strain subspace is provided by the EAS method, enforcing Kirchhoff hypothesis for low thickness values and leading to a framework for the development of Shear-Locking-free shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation. Copyright © 2001 John Wiley & Sons, Ltd.
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Development of Shear Locking‐free shell elements using an enhanced assumed strain formulation
International Journal for Numerical Methods in Engineering, 2001Co-Authors: Renato Natal Jorge, R A F Valente, P AreiasAbstract:The degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse Shear Locking effects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse Shear terms of the strain field. In the first part of the work the analysis of the null transverse Shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking effects are then justified by the inability of the null transverse Shear strain subspace, implicitly defined by a given finite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse Shear strain subspace is provided by the EAS method, enforcing Kirchhoff hypothesis for low thickness values and leading to a framework for the development of Shear-Locking-free shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation. Copyright © 2001 John Wiley & Sons, Ltd.
Sven Klinkel - One of the best experts on this subject based on the ideXlab platform.
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adjusted approximation spaces for the treatment of transverse Shear Locking in isogeometric reissner mindlin shell analysis
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Georgia Kikis, Wolfgang Dornisch, Sven KlinkelAbstract:Abstract Transverse Shear Locking is an issue that occurs in Reissner–Mindlin plate and shell elements. It leads to an artificial stiffening of the system and to oscillations in the stress resultants for thin structures. The thinner the structure is, the more pronounced are the effects. Since transverse Shear Locking is caused by a mismatch in the approximation spaces of the displacements and the rotations, a field-consistent approach is proposed for an isogeometric degenerated Reissner–Mindlin shell formulation. The efficiency and accuracy of the method is investigated for benchmark plate and shell problems. A comparison to element formulations with Locking alleviation methods from the literature is provided.
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Adjusted approximation spaces for the treatment of transverse Shear Locking in isogeometric Reissner–Mindlin shell analysis
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Georgia Kikis, Wolfgang Dornisch, Sven KlinkelAbstract:Abstract Transverse Shear Locking is an issue that occurs in Reissner–Mindlin plate and shell elements. It leads to an artificial stiffening of the system and to oscillations in the stress resultants for thin structures. The thinner the structure is, the more pronounced are the effects. Since transverse Shear Locking is caused by a mismatch in the approximation spaces of the displacements and the rotations, a field-consistent approach is proposed for an isogeometric degenerated Reissner–Mindlin shell formulation. The efficiency and accuracy of the method is investigated for benchmark plate and shell problems. A comparison to element formulations with Locking alleviation methods from the literature is provided.
Remko Akkerman - One of the best experts on this subject based on the ideXlab platform.
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simple tests as critical indicator of intra ply Shear Locking
Key Engineering Materials, 2013Co-Authors: D J Wolthuizen, R Ten H W Thije, Remko AkkermanAbstract:Standard finite elements can exhibit the numerical artifact of intra-plyShear Locking during forming simulations. The displacement fields of elementsare piecewise continuous and cannot correctly capturediscontinuities in the Shear field. This Shear Locking is illustrated insimulations of bias-extension experiments with an unaligned mesh. Two simpletests were developed as a critical indicator of intra-ply Shear Locking intriangular elements. A single-element-test shows the origin of the Locking anda pull-out test indicates Locking caused by small misalignments of theelements.
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solutions to intra ply Shear Locking in finite element analyses of fibre reinforced materials
Composites Part A-applied Science and Manufacturing, 2008Co-Authors: R Ten H W Thije, Remko AkkermanAbstract:Intra-ply Shear Locking results in unrealistic fibre stresses and spurious wrinkling in composite forming simulations. Three remedies were investigated: aligning the mesh, applying reduced integration and using multi-field elements. Several triangular and quadrilateral elements were tested on their capability to avoid Locking in a two-dimensional bias extension simulation. The resulting Locking-free elements were tested in a realistic three-dimensional drape simulation of a biaxial fabric as well. The new triangular multi-field element seems to be the best Locking-free element for unaligned meshes. It has a semi-quadratic in-plane and a linear out-of-plane displacement field. This combination improves the accuracy of the element and avoids contact problems in 3D simulations.
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intra ply Shear Locking
ESAFORM 2007: 10th ESAFORM Conference on Material Forming, 2007Co-Authors: R Ten H W Thije, Remko AkkermanAbstract:Intra-ply Shear Locking results in unrealistic fibre stresses and spurious wrinkling in composite forming simulations. Three remedies are investigated: aligning the mesh, applying reduced integration and using multi-field elements. The bias extension simulation is used to test several triangular and quadrilateral elements on their capability to avoid Locking. Their performance under large deformations is tested as well. The new multi-field element seems to be the best Locking free element in random meshes.
