A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

Ansari, R.; Shakouri, Amir; Bazdid-Vahdati, M.; Norouzzadeh, A.; Rouhi, H.

doi:10.1115/1.4034678

Cited by 27 publications

(15 citation statements)

References 60 publications

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“…For web-core beams this was done in (Karttunen et al, 2019) and for full 3-D web-core panels this will be carried out in future studies. Finally, this study introduced a theoretical micropolar plate model which can be used as the basis for micropolar finite element developments similar to those presented by Ansari et al (2017bAnsari et al ( , 2018. Furthermore, the micromorphic continuum theory may provide a suitable framework for modeling local buckling and vibrations of lattice core sandwich panels through its additional degrees of freedom (Eringen, 2012;Isbuga and Regueiro, 2011;Ansari et al, 2016Ansari et al, , 2017a.…”

Section: Discussionmentioning

confidence: 98%

“…The works of Eringen (2012), Altenbach and Eremeyev (2009) and Altenbach et al (2010) discuss the key theoretical aspects of micropolar plate theories and the literature reviews therein encompass a lengthy period of research on such plates. Of the more recent papers on micropolar plates we mention those of Kvasov and Steinberg (2013); Sargsyan and Sargsyan (2014); Abadikhah and Folkow (2015); Ansari et al (2017b) and Zozulya (2018). However, the aforementioned models are not applicable in the present context as their constitutive equations do not address any particular microstructure such as a webcore.…”

Section: Unit Cellmentioning

confidence: 99%

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Two-scale micropolar plate model for web-core sandwich panels

Karttunen

Reddy

Romanoff

2019

International Journal of Solids and Structures

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A 2-D micropolar equivalent single-layer (ESL), first-order shear deformation (FSDT) plate model for 3-D web-core sandwich panels is developed. First, a 3-D web-core unit cell is modeled by classical shell finite elements. A discrete-to-continuum transformation is applied to the microscale unit cell and its strain and kinetic energy densities are expressed in terms of the macroscale 2-D plate kinematics. The hyperelastic constitutive relations and the equations of motion (via Hamilton's principle) for the plate are derived by assuming energy equivalence between the 3-D unit cell and the 2-D plate. The Navier solution is developed for the 2-D micropolar ESL-FSDT plate model to study the bending, buckling, and free vibration of simply-supported web-core sandwich panels. In a line load bending problem, a 2-D classical ESL-FSDT plate model yields displacement errors of 34-175% for face sheet thicknesses of 2-10 mm compared to a 3-D FE solution, whereas the 2-D micropolar model gives only small errors of 2.7-3.4% as it can emulate the 3-D deformations better through non-classical antisymmetric shear behavior and local bending and twisting.

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Section: Discussionmentioning

confidence: 98%

Section: Unit Cellmentioning

confidence: 99%

Two-scale micropolar plate model for web-core sandwich panels

Karttunen

Reddy

Romanoff

2019

International Journal of Solids and Structures

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“…More on this relation can be found. Detailed study comparing the classical and micropolar theory can be found in the work of Ansari et al [28].…”

Section: Resultsmentioning

confidence: 99%

MHD Mixed Convection Micropolar Fluid Flow through a Rectangular Duct

Ayano

Sikwila

Shateyi

2018

Mathematical Problems in Engineering

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Mixed convection flow through a rectangular duct with at least one of the sides of the walls of the rectangle being isothermal under the influence of transversely applied magnetic field has been analyzed numerically in this study. The governing differential equations of the problem have been transformed into a system of nondimensional differential equations and then solved numerically. The dimensionless velocity, microrotation components, and temperature profiles are displayed graphically showing the effects of various values of the parameters present in the problem. The results showed that the flow field is notably influenced by the considered parameters. It is found that increasing the aspect ratio increases flow reversal, commencement of the flow reversal is observed after some critical value, and the applied magnetic field increases the flow reversal in addition to flow retardation. The microrotation components flow in opposite direction; also it is found that one component of the microrotation will show no rotational effect around the center of the duct.

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“…Kvasov and Steinberg (2013) presented finite element model for the bending analysis of micropolar elastic plates. Godio et al (2015) proposed a displacement-based finite element model for micropolar plates, Ansari et al (2017) proposed a nonlinear finite element model for micropolar plates where the nonlinear micropolar strains were considered. Ansari et al (2018) used 3-D micropolar elements to study the vibrations of micro-beams and micro-plates.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite element analysis of lattice core sandwich plates

Nampally¹,

Karttunen²,

Reddy³

2020

International Journal of Non-Linear Mechanics

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A displacement-based, geometrically nonlinear finite element model is developed for lattice core sandwich panels modeled as 2-D equivalent single-layer (ESL), first-order shear deformation theory (FSDT) micropolar plates. The nonlinearity is due to the moderate macrorotations of the plate which are modeled by including the von Kármán strains in the micropolar strain measures. Weak form Galerkin method with linear Lagrange interpolations is used to develop the displacementbased finite element model. Selective reduced integration is used to eliminate shear locking and membrane locking. The novel finite element model is used to study the nonlinear bending and linear free vibrations of web-core and pyramid core sandwich panels. Clamped and free edge boundary conditions are considered for the first time for the 2-D micropolar ESL-FSDT plate theory. The present 2-D finite element results are in good agreement with the corresponding detailed 3-D FE results for the lattice core sandwich panels. The 2-D element provides computationally costeffective solutions; in a nonlinear bending example, the number of elements required for the 2-D micropolar plate is of the order 10 3 , whereas for the corresponding 3-D model the order is 10 5 .

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A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

Cited by 27 publications

References 60 publications

Two-scale micropolar plate model for web-core sandwich panels

Two-scale micropolar plate model for web-core sandwich panels

MHD Mixed Convection Micropolar Fluid Flow through a Rectangular Duct

Nonlinear finite element analysis of lattice core sandwich plates

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