New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

Dhananjaya, HR; Pandey, Prafull; Nagabhushanam, J.

doi:10.12989/sem.2009.33.4.485

Cited by 12 publications

(6 citation statements)

References 24 publications

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“…The design of 8-node plane elements that can both improve the accuracy and overcome the above shortcomings has been a research hotspot. Dhananjaya et al [36] presented a new 8-node Serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using the integrated force method. This new element performs excellently in both thin and moderately thick plate bending situations.…”

Section: Introductionmentioning

confidence: 99%

An 8-Node Plane Hybrid Element for Structural Mechanics Problems Based on the Hellinger-Reissner Variational Principle

Li,

Wang,

Shen

et al. 2024

CMES

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The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanical design of various structural parts. However, the elements produced by conventional FEM are easily inaccurate and unstable when applied. Therefore, developing new elements within the framework of the generalized variational principle is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PH-Q8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle. According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes to avoid the zero energy modes. Meanwhile, the stress functions within each element satisfy both the equilibrium and the compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate the effectiveness and robustness of the proposed finite element. Numerical results show that various common locking behaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmark problems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonable mesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means to improve numerical accuracy.

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Section: Introductionmentioning

confidence: 99%

An 8-Node Plane Hybrid Element for Structural Mechanics Problems Based on the Hellinger-Reissner Variational Principle

Li,

Wang,

Shen

et al. 2024

CMES

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“…The formulation of IFM was extended for continuous systems in ulterior studies [6,7]. New elements for finite element analysis via IFM have been proposed [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Comparison between the stiffness method and the hybrid method applied to a circular ring

Insausti

Adarraga

Urruzola

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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This study deals with the comparison of stresses and displacements of a circular ring obtained by two numerical formulations, namely the stiffness method and the hybrid method, applied to isoparametric quadrilateral elements. After explaining the formulation of the hybrid method in finite elements, an orthogonalization method proposed previously for hybrid elements is applied. Then, the computational cost per element of the stiffness method and of the hybrid method with and without orthogonalization has been evaluated for the first time. A circular ring loaded by two opposing forces is analyzed in order to compare the solution obtained by the hybrid method and the stiffness method with experimental and analytical results. The agreement between analytical and experimental results with those numerical is better in the case of the hybrid method than in the case of the stiffness method. It is observed that the element ratio needed to obtain a given relative error is one magnitude order greater in the stiffness method than in the case of the hybrid method.

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“…Zhang and Kuang (2007) developed a new 8-node Reissner-Mindlin plate element with a special interpolation within the element, this special interpolation is an extension of the element boundary interpolation that employs Timoshenko beam function for the boundary segment interpolation; Dhananjaya et al (2009) adopted the integrated force method to construct an 8-node serendipity quadrilateral thin-thick plate bending element (MQP8); Li et al (2015) presented an 8-node quadrilateral assumed stress hybrid Mindlin plate element with 39 unknown parameters. These efforts more or less improved the element resistance to shear locking problem…”

Section: Introductionmentioning

confidence: 99%

“…So, many attempts have also been devoted to construct high-order models free of shear locking. Ahmad et al (1970) applied the Mindlin-Reissner plate theory in the degenerated shell approach and developed an eight-node isoparametric element; Crisfield (1984) developed a quadratic element using shear constraints; Spilker and Munir (1980) and Spilker (1982) proposed eight-node hybrid-stress elements for analysis of thin and moderately thick plates; Hughes and Cohen (1978) presented a so-called "heterosis" element which used an eight-node interpolation for rotations and nine-node interpolations for deflections; Kant et al (1982) proposed an element based on a higher-order displacement mode and a three-dimensional state of stress and strain; Hinton and Huang (1986) developed a family of elements, including 8-, 9-, 12-and 16node elements, with substitute strain fields; Donea and Lamain (1987) provided a modified representation of transverse shear component in eight-and nine-node quadrilateral plate elements; Polit et al (1994) proposed an eight-node quadrilateral element, in which each monomial term of the interpolation functions for the normal rotations is matched by the derivatives of its corresponding deflection; Zhang and Kuang (2007) developed a new eightnode Reissner-Mindlin plate element with a special interpolation within the element, and Eight-node elements this special interpolation is an extension of the element boundary interpolation that uses Timoshenko beam function for the boundary segment interpolation; Dhananjaya et al (2009) adopted the integrated force method to construct an eight-node serendipity quadrilateral thin-thick plate-bending element (MQP8); Li et al (2015) presented an eight-node quadrilateral assumed stress hybrid Mindlin plate element with 39 unknown parameters. These efforts more or less improved the element resistance to shear locking problem.…”

Section: Introductionmentioning

confidence: 99%

Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates

Bao

Cen

2017

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Purpose-A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin-Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method. Design/methodology/approach-This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko's beam functions. Then, three locking-free 8-node, 24-DOF quadrilateral plate bending elements, HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary, and HDF-P8-FREE for edge effects along free boundary, are formulated. Findings-The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing 8-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and Free boundaries. The proposed 8-node models possess the potential in the engineering application and could be easily integrated into the commercial software. Originality/value-This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh-distortion resistant Mindlin-Reissner plate bending elements.

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New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

Cited by 12 publications

References 24 publications

An 8-Node Plane Hybrid Element for Structural Mechanics Problems Based on the Hellinger-Reissner Variational Principle

An 8-Node Plane Hybrid Element for Structural Mechanics Problems Based on the Hellinger-Reissner Variational Principle

Comparison between the stiffness method and the hybrid method applied to a circular ring

Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates

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