High-frequency asymptotics for microstructured thin elastic plates and platonics

T. Antonakakis; R. V. Craster

doi:10.1098/rspa.2011.0652

High-frequency asymptotics for microstructured thin elastic plates and platonics

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2011.0652 ◽

2012 ◽

Vol 468 (2141) ◽

pp. 1408-1427 ◽

Cited By ~ 38

Author(s):

T. Antonakakis ◽

R. V. Craster

Keyword(s):

High Frequency ◽

Continuum Model ◽

Two Dimensional ◽

Elastic Plates ◽

Dimensional Model ◽

Defect Modes ◽

High Frequencies ◽

Two Dimensional Model ◽

Thin Elastic Plates ◽

Zero Frequency

We consider microstructured thin elastic plates that have an underlying periodic structure, and develop an asymptotic continuum model that captures the essential microstructural behaviour entirely in a macroscale setting. The asymptotics are based upon a two-scale approach and are valid even at high frequencies when the wavelength and microscale length are of the same order. The general theory is illustrated via one- and two-dimensional model problems that have zero-frequency stop bands that preclude conventional averaging and homogenization theories. Localized defect modes created by material variations are also modelled using the theory and compared with numerical simulations.

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Homogenization of a second order plate model

Mathematics and Mechanics of Solids ◽

10.1177/1081286517719939 ◽

2017 ◽

Vol 23 (9) ◽

pp. 1323-1332 ◽

Cited By ~ 3

Author(s):

E Pruchnicki

Keyword(s):

Fourier Series ◽

Series Expansion ◽

Displacement Field ◽

Order Approximation ◽

Second Order ◽

Fourier Series Expansion ◽

Two Dimensional ◽

Elastic Plates ◽

Dimensional Model ◽

Two Dimensional Model

This work is concerned with the asymptotic analysis of linearly elastic plates with periodically rapidly varying heterogeneities. For the sake of simplicity we assume that the structure of heterogeneity is homogeneous in the direction perpendicular to the mid-surface of the plate. We want to derive a homogenized two-dimensional model which is independent of the magnitude of the applied load. Consequently we have to proceed in the following manner. Firstly, we consider a two-dimensional model of the plate obtained by expanding the displacement field by Fourier-Series expansion in thickness direction of the plate with respect to a basis of scaled Legendre polynomials. We consider a second order approximation of the displacement field which gives a good compromise between the accuracy of the approximate solution and the complexity of the approximate problem. This approximation result from an approximation of the Fourier series expansion of the displacement field up to order h6 ( h denotes the thickness of the plate). By considering standard argument for this type of problem, we can rigorously formulate a two-dimensional homogenized boundary value problem for the plate.

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Analysis of orthotropic tensegrity plate strips using a continuum two-dimensional model

MATEC Web of Conferences ◽

10.1051/matecconf/201926210010 ◽

2019 ◽

Vol 262 ◽

pp. 10010 ◽

Cited By ~ 1

Author(s):

Paulina Obara

Keyword(s):

Continuum Model ◽

Orthotropic Plate ◽

Thick Plate ◽

Geometrical Parameters ◽

Two Dimensional ◽

Dimensional Model ◽

Moderately Thick Plate ◽

Two Dimensional Model ◽

Plate Strip ◽

Internal Forces

A continuum two-dimensional model of orthotropic moderately thick plate strip is proposed in this paper. The model considers the different reference planes (lower, middle and upper) thus the different planes of support may be taken into account. The linear six-parameter and five-parameter shell theories are applied to the analysis. In case of a considered plate strip a number of parameters are reduced to four and to three respectively. The closed form of displacements and internal forces for any orthotropic plate strips are determined. As an example a continuum model of orthotropic tensegrity plate strip is considered. The influence of the self-stress state and some geometrical parameters on displacements are analyzed. The proposed approach can be used for all orthotropic systems.

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Commitment to pro- versus counter-attitudinal behavior and the dynamics of social representations

Swiss Journal of Psychology ◽

10.1024//1421-0185.61.1.34 ◽

2002 ◽

Vol 61 (1) ◽

pp. 34-44 ◽

Cited By ~ 8

Author(s):

Eric Tafani ◽

Lionel Souchet

Keyword(s):

Higher Education ◽

Social Representations ◽

Cognitive Restructuring ◽

Social Representation ◽

Two Dimensional ◽

Dimensional Model ◽

Social Actions ◽

The Social ◽

Two Dimensional Model ◽

Students Attitudes

This research uses the counter-attitudinal essay paradigm ( Janis & King, 1954 ) to test the effects of social actions on social representations. Thus, students wrote either a pro- or a counter-attitudinal essay on Higher Education. Three forms of counter-attitudinal essays were manipulated countering respectively a) students’ attitudes towards higher education; b) peripheral beliefs or c) central beliefs associated with this representation object. After writing the essay, students expressed their attitudes towards higher education and evaluated different beliefs associated with it. The structural status of these beliefs was also assessed by a “calling into question” test ( Flament, 1994a ). Results show that behavior challenging either an attitude or peripheral beliefs induces a rationalization process, giving rise to minor modifications of the representational field. These modifications are only on the social evaluative dimension of the social representation. On the other hand, when the behavior challenges central beliefs, the same rationalization process induces a cognitive restructuring of the representational field, i.e., a structural change in the representation. These results and their implications for the experimental study of representational dynamics are discussed with regard to the two-dimensional model of social representations ( Moliner, 1994 ) and rationalization theory ( Beauvois & Joule, 1996 ).

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