# A microstructure-dependent Kirchhoff plate model based on a reformulated strain gradient elasticity theory

Published on Jan 18, 2021in Mechanics of Advanced Materials and Structures4.03

· DOI :10.1080/15376494.2020.1870054

Published on Jan 18, 2021in Mechanics of Advanced Materials and Structures4.03

· DOI :10.1080/15376494.2020.1870054

References39

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The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations

ABSTRACTThe modified couple stress theory (MCST) is utilized to investigate the bending of viscoelastic nanobeams laying on visco-Pasternak elastic foundations based on a new shear and normal deformations beam theory. This model consists of the material length scale coefficient that captures the size impact on small-scale beams. The simply supported beam is made of viscoelastic material, subjected to time harmonic transverse load. The nanobeam is presumed to be laying on double layers of foundat...

A new non-classical Bernoulli–Euler beam model is developed using a reformulated strain gradient elasticity theory that incorporates both couple stress and strain gradient effects. This reformulate...

AbstractMarine structures are advanced material and structural assemblies that span over different length scales. The classical structural design approach is to separate these length scales. The us...

Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates

Abstract In this study, bending, free vibration, and buckling response of functionally graded porous micro-plates are investigated using the classical and first-order shear deformation plate theories. The Navier solution technique is utilized to obtain analytical solutions to simply supported rectangular plates. A power-law distribution is used to model the variation of two material constituents through the plate thickness. Three different porosity distributions are considered and assumed to tak...

A non-classical model for an orthotropic Kirchhoff plate embedded in a viscoelastic medium is developed by using an extended version of the modified couple stress theory and a three-parameter foundation model. The equations of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton’s principle. The new plate model contains three material length scale parameters to capture the microstructure effect, one damping coefficient to account for ...

Abstract Simplified isotropic models of strain gradient elasticity are presented, based on the mutual relationship between the inherent (dual) gradient directions (i.e. the gradient direction of any strain gradient source and the lever arm direction of the promoted double stress). A class of gradient-symmetric materials featured by gradient directions obeying a reciprocity relation and by 4 independent h.o. (higher order) coefficients is envisioned, along with the sub-classes of hemi-collinear m...

A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects

A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale param...

A non-classical Kirchhoff plate model incorporating microstructure, surface energy and foundation effects

A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale param...

Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory

Abstract A size-dependent functionally graded piezoelectric microplate model is developed in this paper. It is based on the modified couple-stress and sinusoidal plate theories. The main advantages of the modified couple-stress theory over the classical couple-stress theory are the introduction of the symmetric couple-stress tensor and the involvement of only one material length-scale parameter. The material properties of functionally graded piezoelectric plate are assumed to vary through the th...

A non-classical model for circular Kirchhoff plates incorporating microstructure and surface energy effects

A new non-classical model for circular Kirchhoff plates subjected to axisymmetric loading is developed using a modified couple stress theory, a surface elasticity theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. The new plate model contains a material length scale parameter to capture the microstructure effect and three surface elasticity constants to describe the surface energy effect. The current non...

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Abstract null null A new non-classical Bernoulli-Euler (B-E) beam model is developed using a simplified micromorphic elasticity theory. This micromorphic theory, which contains 7 independent material constants, is first proposed by simplifying the classical Eringen-Mindlin micromorphic theory for isotropic linear elastic materials, which includes 18 elastic constants. The new B-L beam model is then formulated by applying the simplified micromorphic theory and employing a variational approach bas...

Magnetically induced electric potential in first-order composite beams incorporating couple stress and its flexoelectric effects

A new model of a first-order composite beam with flexoelectric and piezomagnetic layers is developed. The new model is under a transverse magnetic field and can capture the couple stress and its flexoelectric effects. The governing equations are obtained through a variational approach. To illustrate the new model, the static bending problem is analytically solved based on a Navier’s technique. The numerical results reveal that the extension, deflection, and shear deformation of the current or co...

Isogeometric analysis of size-dependent Bernoulli–Euler beam based on a reformulated strain gradient elasticity theory

Abstract null null In this paper, we present an efficient and accurate numerical approach for static bending and free vibration analyses of microstructure-dependent Bernoulli-Euler beams. The current approach includes strain gradient, couple stress (rotation gradient) and velocity gradient effects simultaneously through a reformulated strain gradient elasticity, which applies only one material parameter for each gradient effect. Based on the Hamilton’s principle and an Isogeometric Analysis (IGA...