A novel microstructure-dependent shear deformable beam model

• A novel shear deformation microbeam model is developed.
• Modified strain gradient and hyperbolic beam theories are utilized.
• Static bending and buckling behaviors of microbeams are investigated.
• Effects of size and shear deformation are discussed in detail.
• Elastic medium is modeled by Winkler foundation model.

A new size-dependent beam model is introduced on the basis of hyperbolic shear deformation beam and modified strain gradient theory. The governing differential equations and corresponding boundary conditions are obtained with the aid of minimum total potential energy principle. The static bending and buckling behaviors of simply supported microbeams embedded in an elastic medium are investigated. The interactions between the microbeam and elastic medium are simulated by Winkler foundation model. Navier solution procedure is employed to obtain analytical solutions for deflections under sinusoidal load and critical buckling loads. The effects of material length scale parameter, length-to-thickness ratio, shear correction factors and Winkler modulus on the bending and buckling responses of microbeams are discussed in detail. The results are comparatively presented with the results of other beam theories. It is observed that the new results predicted by the present model and the results evaluated by sinusoidal shear deformation beam model are in good agreement.