Two-Dimensional Model of Second-Order Accuracy for an Anisotropic Plate

2019 ◽  
Vol 52 (1) ◽  
pp. 112-121
Author(s):  
P. E. Tovstik
2017 ◽  
Vol 23 (9) ◽  
pp. 1323-1332 ◽  
Author(s):  
E Pruchnicki

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.


2002 ◽  
Vol 61 (1) ◽  
pp. 34-44 ◽  
Author(s):  
Eric Tafani ◽  
Lionel Souchet

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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