Third-order nonlocal elasticity in buckling and vibration of functionally graded nanoplates on Winkler-Pasternak media

The focus of the present work is to present an analytical approach for buckling and free vibrations analysis of thick functionally graded nanoplates embedded in a Winkler-Pasternak medium. The equations of motion are derived according to both the third-order shear deformation theory, proposed by Reddy, and the nonlocal elasticity Eringen's model. For the first time, the equations are solved analytically for plates with two simply supported opposite edges, the solutions also turning helpful as shape functions in the analysis of structures with more complex geometries and boundary conditions. Sensitivity analyses are finally performed to highlight the role of nonlocal parameters, aspect and side-to-thickness ratios, boundary conditions, and functionally graded material properties in the overall response of plates and cylindrical shells. It is felt that the proposed strategy could be usefully adopted as benchmark solutions in numerical routines as well as for predicting some unexpected behaviors, for instance, in terms of buckling load, in thick nanoplates on elastic foundations.

Design space for bifurcation buckling of laser-welded web-core sandwich plates as predicted by classical and micropolar plate theories

The strength of laser-welded web-core sandwich plates is often limited by buckling. In design of complex thin-walled structures the combination of possible structural and material combinations is basically infinite. The feasibility of these combinations can be assessed by using analytical, numerical and experimental methods. At the early design stages such as concept design stage, the role of analytical methods is significant due to their capability for parametric description and extremely low computational efforts once the solutions have been established for prevailing differential equations. Over the recent years significant advances have been made on analytical strength prediction of web-core sandwich panels. Therefore, aim of the present paper is to show impact of this development to the design space of web-core sandwich panels in buckling. The paper reviews first, briefly the differential equations of a 2-D micropolar plate theory for web-core sandwich panels and the Navier buckling solution for biaxial compression recently derived by Karttunen et al. (Int J Solids Struct 170(1):82–94, 2019) by exploiting energy methods. By comparing the micropolar and widely-used classical first-order shear deformation plate theory (FSDT) solutions, it is shown that the different equivalent single layer (ESL) formulations and plate aspect ratios have a significant impact on the practical outcomes of the feasible design space and this way motivating further developments for micropolar formulations from practical structural engineering viewpoint.