Study of Edge-Zone Equation of Mindlin-Reissner Plate Theory

Nosier, A.; Yavari, Arash; Sarkani, Shahram

doi:10.1061/(asce)0733-9399(2000)126:6(647)

Cited by 9 publications

(4 citation statements)

References 15 publications

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“…In this way, the ReissnerMindlin equations decouple into a boundary-layer equation for rot( ) and an interior equation for the transversal displacement w (cf. Reference [7] for details and further references). In a simple model problem with known analytical solution for the boundary layer equation (obtained as in Reference [7] by series expansion) we monitor here edge e ects on a free curved boundary.…”

Section: The Adaptive Finite-element Schemementioning

confidence: 97%

“…Reference [7] for details and further references). In a simple model problem with known analytical solution for the boundary layer equation (obtained as in Reference [7] by series expansion) we monitor here edge e ects on a free curved boundary. We consider a quarter of a circular plate with radius r =1 m and plate thickness t =0:001 m, the material parameters are constant as above.…”

Section: The Adaptive Finite-element Schemementioning

confidence: 97%

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An adaptive non‐conforming finite‐element method for Reissner–Mindlin plates

Carstensen

Weinberg

2003

Numerical Meth Engineering

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SUMMARYAdaptive algorithms are important tools for e cient ÿnite-element mesh design. In this paper, an error controlled adaptive mesh-reÿning algorithm is proposed for a non-conforming low-order ÿnite-element method for the Reissner-Mindlin plate model. The algorithm is controlled by a reliable and e cient residual-based a posteriori error estimate, which is robust with respect to the plate's thickness. Numerical evidence for this and the e ciency of the new algorithm is provided in the sense that non-optimal convergence rates are optimally improved in our numerical experiments.

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Section: The Adaptive Finite-element Schemementioning

confidence: 97%

Section: The Adaptive Finite-element Schemementioning

confidence: 97%

An adaptive non‐conforming finite‐element method for Reissner–Mindlin plates

Carstensen

Weinberg

2003

Numerical Meth Engineering

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“…In earlier time, scholars have analyzed this problem by using the analytical or semi-analytical methods. For instance, Arnold and Falk (1996) mathematically demonstrated its existence by utilizing the asymptotic expansion method; Kant and Gadgil (2002) analyzed orthotropic and isotropic square plates by using the segmentation method, finding that the Mindlin-Reissner plate theory and other high-order plate theories can correctly describe the edge effect phenomenon, while the classical Kirchhoff thin plate theory failed; Hinton et al (1995) analyzed the edge effects of variablethickness plates by using the finite strip method; Nosier et al (2000Nosier et al ( , 2001aNosier et al ( , 2001b systematically derived the analytical solutions related to the edge effects of square and circle composite laminated plates. Nonetheless, above analytical or semi-analytical methods can only handle the plates with regular geometrical configurations.…”

Section: Introductionmentioning

confidence: 99%

New hybrid-Trefftz Mindlin–Reissner plate elements for efficiently modeling the edge zones near free/SS1 edges

Shang

Cen

Ouyan

2018

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Purpose The purpose of this paper is to propose a new finite element method (FEM) solving strategy for efficient analysis of the challenging edge effect problem in plate structures. Its main ideas are to develop special-purpose plate element models to effectively simulate the behaviors in the plate’s edge zones near free/SS1 edges. Design/methodology/approach These new elements are developed based on the hybrid-Trefftz element method. During their construction procedures, the analytical solutions of the edge effect problem, which are in exponential forms, are used to enhance the interior displacement fields. Besides, the Lagrangian multipliers are introduced into the modified hybrid-Trefftz functional for considering the stress resultant constraints at free/SS1 edges. Thus, these elements theoretically possess the abilities to correctly capture the very steep gradients of the resultant distributions in the boundary layers. Findings These new specialized hybrid-Trefftz plate elements can very efficiently solve the edge effect problem with high accuracy, even when distorted meshes are used. Moreover, because these elements’ construction procedures contain only boundary integrals, the computation expense for accurately integrating the exponential trial functions can be considerably saved. Originality/value This work presents an alternative novel idea for using the FEM to more effectively handle the local stress problems by incorporating the use of the analytical trial functions.

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“…method , and so on . But most of these semi‐analytical methods can only handle the plates with rectangular shape.…”

Section: Introductionmentioning

confidence: 99%

Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

Shang

Cen

et al. 2017

Numerical Meth Engineering

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Summary For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effective hybrid displacement function (HDF) finite element method was successfully developed for solving such difficulty . Although good performances can be obtained in most cases, the distribution continuity of some resulting resultants is destroyed when coarse meshes are employed. Moreover, an additional local coordinate system must be used for avoiding a singular problem in matrix inversion, which makes the derivations more complicated. Based on a modified complementary energy functional containing Lagrangian multipliers, an improved HDF (IHDF) element scheme is proposed in this work. And two new special IHDF elements, named by IHDF‐P4‐Free and IHDF‐P4‐SS1, are constructed for modeling plate behaviors near free and soft simply supported boundaries, respectively. The present modeling scheme not only greatly improves the precision of the numerical results but also avoids usage of the additional local Coordinate system. The numerical tests demonstrate that the new IHDF element scheme is an effective way for solving the challenging edge effect problem in Mindlin–Reissner plates. Copyright © 2016 John Wiley & Sons, Ltd.

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Study of Edge-Zone Equation of Mindlin-Reissner Plate Theory

Cited by 9 publications

References 15 publications

An adaptive non‐conforming finite‐element method for Reissner–Mindlin plates

An adaptive non‐conforming finite‐element method for Reissner–Mindlin plates

New hybrid-Trefftz Mindlin–Reissner plate elements for efficiently modeling the edge zones near free/SS1 edges

Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

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