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Hui-shen Shen - One of the best experts on this subject based on the ideXlab platform.
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postbuckling of free edge reissner mindlin Plates elastically supported on a two parameter foundation and subjected to biaxial compression and transverse loads
Engineering Structures, 2001Co-Authors: Hui-shen ShenAbstract:Abstract A postbuckling analysis is presented for a rectangular Reissner–Mindlin Plate with all four free edges subjected to biaxial compression combined with a transverse central patch load and resting on a two-parameter (Pasternak-type) elastic foundation. The lateral pressure is first converted into an initial deflection and the initial geometric imperfection of the Plate is also taken into account. The formulations are based on Reissner–Mindlin Plate Theory considering the first order shear deformation effect, including Plate-foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick Plates with all four free edges under combined loading conditions and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, Plate aspect ratio, loaded area parameter and initial lateral pressure are studied. Typical results are presented in dimensionless graphical form.
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nonlinear bending of simply supported rectangular reissner mindlin Plates under transverse and in plane loads and resting on elastic foundations
Engineering Structures, 2000Co-Authors: Hui-shen ShenAbstract:Abstract A nonlinear analysis is presented for a simply supported, rectangular moderately thick Plate subjected to transverse central patch load and in-plane compressive loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner–Mindlin Plate Theory considering the first order shear deformation effect, and including the Plate–foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the load–deflection curves and load–bending moment curves. Numerical examples are presented that relate to the performances of moderately thick Plates subjected to combined loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences played by a number of effects, among them foundation stiffness, loaded area, the Plate aspect ratio, transverse shear deformation and initial compressive load are studied. Typical results are presented in dimensionless graphical form.
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Nonlinear bending of simply supported rectangular Reissner–Mindlin Plates under transverse and in-plane loads and resting on elastic foundations
Engineering Structures, 2000Co-Authors: Hui-shen ShenAbstract:Abstract A nonlinear analysis is presented for a simply supported, rectangular moderately thick Plate subjected to transverse central patch load and in-plane compressive loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner–Mindlin Plate Theory considering the first order shear deformation effect, and including the Plate–foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the load–deflection curves and load–bending moment curves. Numerical examples are presented that relate to the performances of moderately thick Plates subjected to combined loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences played by a number of effects, among them foundation stiffness, loaded area, the Plate aspect ratio, transverse shear deformation and initial compressive load are studied. Typical results are presented in dimensionless graphical form.
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nonlinear bending of reissner mindlin Plates with free edges under transverse and in plane loads and resting on elastic foundations
International Journal of Mechanical Sciences, 1999Co-Authors: Hui-shen ShenAbstract:Abstract A nonlinear bending analysis is presented for a rectangular Reissner–Mindlin Plate with free edges subjected to combined transverse partially distributed load and compressive edge loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner–Mindlin Plate Theory considering the first-order shear deformation effect, and including the Plate-foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the load–deflection curves and load–bending moment curves. Numerical examples are presented that relate to the performances of moderately thick rectangular Plates with free edges subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, transverse shear deformation, loaded area, the Plate aspect ratio and initial compressive load are studied. Typical results are presented in dimensionless graphical form.
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Nonlinear bending of Reissner–Mindlin Plates with free edges under transverse and in-plane loads and resting on elastic foundations
International Journal of Mechanical Sciences, 1999Co-Authors: Hui-shen ShenAbstract:Abstract A nonlinear bending analysis is presented for a rectangular Reissner–Mindlin Plate with free edges subjected to combined transverse partially distributed load and compressive edge loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner–Mindlin Plate Theory considering the first-order shear deformation effect, and including the Plate-foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the load–deflection curves and load–bending moment curves. Numerical examples are presented that relate to the performances of moderately thick rectangular Plates with free edges subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, transverse shear deformation, loaded area, the Plate aspect ratio and initial compressive load are studied. Typical results are presented in dimensionless graphical form.
Giuseppe Tomassetti - One of the best experts on this subject based on the ideXlab platform.
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a justification of the reissner mindlin Plate Theory through variational convergence
Analysis and Applications, 2007Co-Authors: Roberto Paroni, Paolo Podioguidugli, Giuseppe TomassettiAbstract:We provide a justification of the Reissner–Mindlin Plate Theory, using linear threedimensional elasticity as framework and Γ-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Γ-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.
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A JUSTIFICATION OF THE REISSNER–MINDLIN Plate Theory THROUGH VARIATIONAL CONVERGENCE
Analysis and Applications, 2007Co-Authors: Roberto Paroni, Paolo Podio-guidugli, Giuseppe TomassettiAbstract:We provide a justification of the Reissner–Mindlin Plate Theory, using linear three-dimensional elasticity as framework and Γ-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Γ-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.
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the reissner mindlin Plate Theory via γ convergence
Comptes Rendus Mathematique, 2006Co-Authors: Roberto Paroni, Paolo Podioguidugli, Giuseppe TomassettiAbstract:Abstract We obtain the energy functional of Reissner–Mindlin Plates as the Γ -limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument. To cite this article: R. Paroni et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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The Reissner–Mindlin Plate Theory via Γ-convergence
Comptes Rendus Mathematique, 2006Co-Authors: Roberto Paroni, Paolo Podio-guidugli, Giuseppe TomassettiAbstract:Abstract We obtain the energy functional of Reissner–Mindlin Plates as the Γ -limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument. To cite this article: R. Paroni et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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mathematical problems in mechanics the reissner mindlin Plate Theory via γ convergence
2006Co-Authors: Roberto Paroni, Paolo Podioguidugli, Giuseppe TomassettiAbstract:We obtain the energy functional of Reissner–Mindlin Plates as the Γ -limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument. To cite this article: R. Paroni et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
Irwan Katili - One of the best experts on this subject based on the ideXlab platform.
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A unified polygonal locking-free thin/thick smoothed Plate element
Composite Structures, 2019Co-Authors: Irwan Katili, Jauhari Maknun, Andi Makarim Katili, Stéphane Bordas, Sundararajan NatarajanAbstract:Abstract A novel cell-based smoothed finite element method is proposed for thin and thick Plates based on Reissner-Mindlin Plate Theory and assumed shear strain fields. The domain is discretized with arbitrary polygons and on each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The Plate is made of functionally graded material with effective properties computed using the rule of mixtures. The influence of various parameters, viz., the Plate aspect ratio and the material gradient index on the static bending response and the first fundamental frequency is numerically studied. It is seen that the proposed element: (a) has proper rank; (b) does not require derivatives of shape functions and hence no isoparametric mapping required; (c) independent of shape and size of elements and (d) is free from shear locking.
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An evaluation on the performance of two simple triangular bending Plate elements
MATEC Web of Conferences, 2018Co-Authors: Dian Rahmawati, Jauhari Maknun, Irwan KatiliAbstract:This paper will study and compare two different three-node triangular bending Plate elements with three degree of freedom per node, i.e. MITC3 and DKMT. Both elements, which were developed based on Reissner-Mindlin Plate Theory and independent shear strain field, have simple formulation and have already been used widely. In this paper, numerical tests for circular Plate case are conducted to verify the performance and show the convergence of these two triangular elements.
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Isogeometric Galerkin in rectangular Plate bending problem based on UI approach
European Journal of Mechanics - A Solids, 2018Co-Authors: Irwan Katili, Ricky AristioAbstract:Abstract This paper presents the development of Isogeometric Analysis for Plate bending problems based on unified and integrated (UI) approach, which is a modification of Reissner-Mindlin Plate Theory for solving thick to thin Plate problems. In Reissner-Mindlin, the total displacement and two rotations are independent of each other, while in this UI approach the total displacement is split into bending displacement and shear displacement which causes the rotations, curvatures and shear deformations can be defined as first, second and third derivatives of bending displacement, respectively. The virtual work of Galerkin Method is used to define bending stiffness and shear stiffness of the element. Several convergence tests were conducted to observe the performance of unified and integrated approach in rectangular Plate of different types of boundaries conditions. The result of thick and thin Plate showed good results despite of low number of element with fourth degree of polynomial or increasing degree of polynomial with only one element.
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On a simple triangular reissner/mindlin Plate element based on incompatible modes and discrete constraints
International Journal for Numerical Methods in Engineering, 1992Co-Authors: Jean-louis Batoz, Irwan KatiliAbstract:In this paper the formulation of a new triangular element based on the Reissner/Mindlin Plate Theory is presented. The element has three nodes and three d.o.f. per node only. It is based on constant bending modes plus incompatible energy orthogonal higher order bending modes. The transverse shear effects are represented using the moment equilibrium and the constitutive equations. Discrete (collocation) shear constraints are considered on each side to relate the kinematical and the independent shear strains. The element has a proper rank, is completely locking free, passes all constant patch-tests exactly. The detailed numerical evaluation shows that the element, called DST-BK, is a robust and high-performance element for thick and thin Plates.
Roberto Paroni - One of the best experts on this subject based on the ideXlab platform.
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a justification of the reissner mindlin Plate Theory through variational convergence
Analysis and Applications, 2007Co-Authors: Roberto Paroni, Paolo Podioguidugli, Giuseppe TomassettiAbstract:We provide a justification of the Reissner–Mindlin Plate Theory, using linear threedimensional elasticity as framework and Γ-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Γ-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.
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A JUSTIFICATION OF THE REISSNER–MINDLIN Plate Theory THROUGH VARIATIONAL CONVERGENCE
Analysis and Applications, 2007Co-Authors: Roberto Paroni, Paolo Podio-guidugli, Giuseppe TomassettiAbstract:We provide a justification of the Reissner–Mindlin Plate Theory, using linear three-dimensional elasticity as framework and Γ-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Γ-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.
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the reissner mindlin Plate Theory via γ convergence
Comptes Rendus Mathematique, 2006Co-Authors: Roberto Paroni, Paolo Podioguidugli, Giuseppe TomassettiAbstract:Abstract We obtain the energy functional of Reissner–Mindlin Plates as the Γ -limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument. To cite this article: R. Paroni et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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The Reissner–Mindlin Plate Theory via Γ-convergence
Comptes Rendus Mathematique, 2006Co-Authors: Roberto Paroni, Paolo Podio-guidugli, Giuseppe TomassettiAbstract:Abstract We obtain the energy functional of Reissner–Mindlin Plates as the Γ -limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument. To cite this article: R. Paroni et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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mathematical problems in mechanics the reissner mindlin Plate Theory via γ convergence
2006Co-Authors: Roberto Paroni, Paolo Podioguidugli, Giuseppe TomassettiAbstract:We obtain the energy functional of Reissner–Mindlin Plates as the Γ -limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument. To cite this article: R. Paroni et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
Peter J Attar - One of the best experts on this subject based on the ideXlab platform.
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some results for approximate strain and rotation tensor formulations in geometrically non linear reissner mindlin Plate Theory
International Journal of Non-linear Mechanics, 2008Co-Authors: Peter J AttarAbstract:Abstract Finite element deflection and stress results are presented for four flat Plate configurations and are computed using kinematically approximate (rotation tensor, strain tensor or both) non-linear Reissner–Mindlin Plate models. The finite element model is based on a mixed variational principle and has both displacement and force field variables. High order interpolation of the field variables is possible through p-type discretization. Results for some of the higher order approximate models are given for what appears to be the first time. It is found that for the class of example problems examined, exact strain tensor but approximate rotation tensor theories can significantly improve the solution over approximate strain tensor models such as the von Karman and moderate rotation models when moderate deflections/rotations are present. However, for each of the problems examined (with the exception of a postbuckling problem) the von Karman and moderate rotation model results compared favorably with the higher order models for deflection magnitudes which could be reasonably expected in typical aeroelastic configurations.
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Some results for approximate strain and rotation tensor formulations in geometrically non-linear Reissner–Mindlin Plate Theory
International Journal of Non-linear Mechanics, 2008Co-Authors: Peter J AttarAbstract:Abstract Finite element deflection and stress results are presented for four flat Plate configurations and are computed using kinematically approximate (rotation tensor, strain tensor or both) non-linear Reissner–Mindlin Plate models. The finite element model is based on a mixed variational principle and has both displacement and force field variables. High order interpolation of the field variables is possible through p-type discretization. Results for some of the higher order approximate models are given for what appears to be the first time. It is found that for the class of example problems examined, exact strain tensor but approximate rotation tensor theories can significantly improve the solution over approximate strain tensor models such as the von Karman and moderate rotation models when moderate deflections/rotations are present. However, for each of the problems examined (with the exception of a postbuckling problem) the von Karman and moderate rotation model results compared favorably with the higher order models for deflection magnitudes which could be reasonably expected in typical aeroelastic configurations.