Mechanical analysis of nanoscale thin plates and conveying belt structures

Plate-like structures are widely used both in scientific research and industrial applications. Understanding the mechanical properties of such structures is important for design, installation and operation of many devices and equipment. Although they are classified as a traditional topic in the realm of engineering mechanics, plates have some new applications and thus, problems do arise: e.g. large deformation problems of nanoscale plates and twist problems of long conveying belts. This thesis represents an effort to improve the understanding of such problems and provide possible solutions to overcome such problems. It employs a mathematical approach to investigate the static and dynamic behaviours of nanoscale beams, plates and films, and adapts a finite element method (FEM) to study the dynamic responses of complex large-scale conveying belts. To study the bending behaviours of multi-layered nanoscale plates or plate-like structures, an improved core-shell model with multiple layers is established, which takes into account the surface/interface tension and elasticity, size-dependent properties and geometrical nonlinearity. Modified governing equations are obtained and solved. Approximate solutions in closed form are also obtained. Based on these solutions numerical studies are conducted to further investigate the influences of surface/interface effect. The mathematical models are refined to consider the free and forced vibrations of multi-layered nanoscale plates with the focus on size-dependent properties and geometrical nonlinearity. The Motion equations and Duffing equations are derived and solved numerically. Based on the closed form solutions for different boundary conditions such as circular plates and rectangular plates with all edges simply supported or clamped, the nature of vibration of nanoscale plates is explored. To further understand the dynamic behaviours, different load and boundary situations are also studied. An FEM model is established to explore the twist phenomenon of pipe belt conveyors (PBC). This FEM model is validated by comparing the results of contact forces with those from a previous experiment. It adopts three realistic steps to assemble the PBC system and can give a credible prediction of the stress and strain in belts. The results demonstrate that this FEM model is able to reproduce the belt twist phenomenon and the twist is sensitive to many factors such as the effective centre of mass and shear centre of the closed belt. These findings offer a good guideline for the design, installation and operation of PBCs in industry.