Static and dynamic analyses of one- and two-dimensional microstructures based on higher-order elasticity theories

In this thesis, mechanical behavior characteristics of micro-sized structural members in form of beam and plate, which have become popular and have a wide application area in nanotechnology due to the rapid developments in technology in recent times, are investigated based on higher-order (non-classical) elasticity theories. Sinusoidal shear deformable beam theory is used besides Bernoulli-Euler and Timoshenko beam theories widely used for modelling of one-dimensional structures. Similarly, sinusoidal shear deformable plate theory is employed to model two-dimensional structures in addition to the widely known Kirchhoff and Mindlin plate theories. It is considered that these structures are embedded in an elastic medium and the interactions between these structures and elastic medium are taken into consideration by Winkler and Pasternak elastic foundation models. Governing differential equations and corresponding boundary conditions for bending, buckling and free vibration are derived with the aid of variational principle with modified strain gradient elasticity theory. A detailed parametric study is performed to indicate the effects of small size, elastic foundation and shear deformation on bending, buckling and free vibration behaviors of these structures. Also, bending and buckling behaviors of thick micro beams made of functionally graded materials are investigated. It is observed that size effect becomes more important when thickness (diameter) is close to additional material length scale parameter. By taking into account the elastic foundation effect, it is reached that there is a decrement in the displacements while there is an increment in buckling loads and natural frequency. Also, it is found that effects of shear deformation are more significant for lower values of length-to-thickness ratio. Moreover, it is determined that classical shear correction factors are inadequate for Timoshenko beam and Mindlin plate models based on higher-order elasticity theories and the new size-dependent shear correction factors are firstly proposed for these models.