Static and Dynamic Models of Bending for Elastic Sandwich Plates
This work is an attempt to solve the problem how to describe static and dynamic bending deformations of elastic sandwich plates in the frame of two–dimensional theories. We focus here on the case of so-called hard-skin plates, i.e. the sandwich plates the faces of which are very hard. We consider only the hard-skin plates of symmetric structure on thickness. In this case the any static and dynamic problem can be represented as a superposition of two problems: one considers the deformations “in plane of the plate” (tension deformations) and the other considers deformations “out of plane of the plate” (bending deformations). It is proposed to solve the problem of static and dynamic bending for hard-skin plates on the basis of governing two- dimensional models derived from linear three-dimensional elasticity with the help of variational asymptotic method . We show in which cases the bending problem must be solved on the basis the equations considering transverse shear effects both in statics and dynamics.
KeywordsSandwich elastic plate Asymptotic theory Transverse shear effect
The reported study was funded by Russian Foundation for Basic Research, according to the research projects No. 18-58-00008.
- 1.Berdichevski, V.L.: Variational Principles of Continuum Mechanics. Springer, Berlin (2009)Google Scholar
- 2.Berdichevski, V.L.: An asymptotic theory of sandwich plates. Int. J. Eng. Sci. 48, 383–404 (2010)Google Scholar
- 4.Heng, H., Belouettar, S., Potier-Ferry, M., Daya, E.M.: Review and assessment of various theories for modeling sandwich composites. Composite Structure, vol. 84, pp. 282–292. Elsevier (2008)Google Scholar