Florian Hache
Florida Atlantic University, USA
Title: Development of continualized models for the analytical study of nanoplates in buckling and vibration: principles and perspectives
Biography
Biography: Florian Hache
Abstract
The aim of this presentation is to develop, through continualized processes, analytical models, more consistent than the well-known existing Eringen’s models for the study of the mechanical behavior in vibration and buckling of simply supported nano beams and nano-plates subjected to compressive forces. The nonlocal Eringen’s models are based on a phenomenological approach. Recent studies have shown that the inherent scale effects are captured by a small length scale coefficient, paradoxically varying with the geometry or the load. Using as a reference model the exact lattice model, the Eringen’s model is not consistent. It is suggested to develop new models based on continualization of the difference equations of the original lattice problem (labeled as continualized nonlocal models). A review of different continualization schemes is provided. Each of them is also supported by variational arguments giving an access to the boundary conditions. The buckling load and the natural frequencies obtained from each of the models were compared. Moreover, in contrast to the Eringen’s models, the continualized approach provides a small length-scale coefficient intrinsically constant, calibrated with respect to the element size of the microstructured structure. Consequently, the continualized approach supplants the traditionally used phenomenological Eringen’s approach. This presentation is the continuity of several papers published these last years and dealing with these issues.