On the anticlastic curvature in free edges and the corner transverse shear in soft simply-supported edges in anisotropic rectangular thick plates

Tales de Vargas Lisbôa¹; Rogério José Marczak¹

¹ Universidade Federal do Rio Grande do Sul

doi:10.20906/CPS/CILAMCE2017-0010

Resumo

The paper's objective is to revisit two phenomena of plate bending: the anticlastic curvature and the corner transverse shear and its relation to the reaction forces that can be observed in plates evaluated by the Kirchhoff Plate Theory. The anticlastic curvature is a phenomenon which occurs only in plates with two opposite free edges. The name is taken due to the opposite direction between the principal normal of the deformed plate, resulting in bending moments acting in opposite directions. It is shown that this response is dependent on the stiffness' ratio of the anisotropic material, affecting the size in which the anticlastic curvature can be observed. Another effect that can be noted in the plates evaluated by the classical plate theory is the reaction forces in non-smooth boundary regions, in simply- supported edges. Such phenomenon is generated by the twisting moment "jump", due to the abrupt geometric change. Given the kinematic hypothesis which bonds the transverse shear and the plate's rotation, the simply-supported boundary condition in Classical Plate Theory is translated to the soft simply-supported in Mindlin plate theory. These reaction forces are observable in Mindlin's theory as the transverse shear in a region close to the corner. By tending the thickness to zero, the region of transverse shear responsible to generate the reaction changes in format and gets close to a punctual force. The phenomena are presented and discussed.

Palavras-chave: Anticlastic curvature; Corner transverse Shear; Anisotropic thick plates; thick plates in bending